This theory is often a mask for preferring “talented” players over good, winning players – but the theory applied seriously is a good one. Football is a complex game. And it is fully possible for a quarterback to be carried by their team. Also, because a quarterback touches the ball every play, they can impact the game positively.

Peyton Manning is the quintessential truck. His ability to audible into new plays was unmatched when he was playing. And he had an unprecedented amount of control over his offenses.

This year, Matthew Stafford is the quintessential trailer.

Stafford is having a great season if you go by box score stats – but based on the metrics that we look at to project QB performance, he’s been just above average. And that is with an incredible amount of support. His offensive weapons are the best in the league, outside of Dallas. With Puka Nacua as his number one target and Davonte Adams – who was the league’s best receiver just three years ago – as his number two, Stafford has the best help a QB can ask for.

Despite that, he trails Drake Maye in all three P(100), yards per attempt and success rate.

Maye and the Patriots meanwhile have the 14th best weapons, with an aging Stefon Diggs as the number one and a tight end–Hunter Henry–as their number two option.

Conference mates Sam Darnorld and Brock Purdy compare favorably to Stafford as well.

Darnold has the edge in yards per attempt and P(100), with a slightly worse receiving corps. While Purdy’s receivers don’t come close – and Purdy beats Darnold on every margin. It wouldn’t be right to consider Purdy for MVP given that he missed half the season, but on the numbers we care about, there’s a lot more reason to think he’ll excel in the playoffs than Stafford.

And while we’re evaluating quarterback play in the context of their surroundings, Jordan Love and Josh Allen deserve some love. The Green Bay and Buffalo receiving groups come in at the bottom of the league, with Washington and the Jets, but those QBs have been excelling all year under center.

All that said, it doesn’t feel right to give the MVP to a trailer. Give it to a truck.

Who is going to win the next game? The championship?

We can then use these ideas to inform other questions. For instance, here at Wolohan Analytics, we use P(100) to evaluate quarterbacks. It’s a metric that measures how likely a quarterback is to play well enough to win the Super Bowl.

We use it to evaluate quarterbacks because we care more about winning the Super Bowl than we do putting up big yardage totals or highlight reel plays.

It’s not necessarily about the metric, though. It’s about the order of thinking.

1. First we think about what the phenomenon is;

2. then we think about how to measure it;

3. then we look at those measurements;

4. and then we make an assessment.

There’s another version of analytic-like thinking, that looks something like this:

1. Notice something;

2. Go look for a bunch of measurements that confirm that thing.

This – no matter which measurements you use – is worse than just going on gut feel.

Confirmation Bias, P-Hacking, and Analytics

We have a problem in 21st century sports: we have access to a tremendous amount of data. This let’s lots of well-intentioned people come up with Candy Analytics, analytics that sound nice, but don’t do anything to better inform us about the nature of the sport underway.

However, we also have another problem. And this is one that is especially bad during the NBA season. You can find stats to support almost any idea.

And if you start with the idea – and then go looking for stats as if they’re evidence – you will find those stats. But unfortunately, those stats that you find—especially if you’re a member of the media—are not evidence. They’re chance in action.

In the sciences, there’s a phenomenon called P-Hacking. Where people run many statistical tests on their data, in an attempt to find something to report as important.

The problem is not that you can’t run multiple tests on the same dataset. There are many valid reasons you might want to. The problem is, that every time you look for something – you risk finding something that isn’t there, purely by chance. And this needs to be accounted for.

Every time you open up ESPN, or Basketball Reference, or Pro Football Reference, or FanDuel, or what have you – you risk finding a trend that isn’t there.

And so if you are just browsing around, looking at numbers and stats, you are bound to find something that is both wrong and supports your conclusion.

Of course, that doesn’t mean your conclusion necessarily was wrong. Just because a piece of evidence gets thrown out, doesn’t mean the defendant is innocent.

But what it means is, we need to be skeptical about statistics we find, that just happen to conform to our views of something.

How do we do it right?

So you want to do it right? You have to work backwards. What is the problem at hand and what evidence do you want to be able to bring to the table. Are there established ways to look at this problem?

For example, you want to look at NFL team strength. Well, there are two really powerful ways to do that:

• Elo ratings

• Weighted EPA

You can pick one or both.

Or you could decide on some other formula, so long as you can defend your choice.

Maybe, total yards of offense and points surrendered. Sensible enough.

But then you have to live with your decision.

If you picked EPA, the Rams are the #1 team by EPA this year. Don’t like the Rams? That’s OK. But they’re your #1 team. You don’t get to decide you like the Broncos better because they’ve won more games.

If you picked passing yards and points surrendered, and you like the Bills (#3 by EPA), too bad. They have the 17th worst defense and 13th worst pass offense.

Accept when the numbers don’t come out the way you want.

Measure twice. Cut once.

Except measuring is thinking about what measurement to use. And cutting is measuring.

But what’s worse: they left out one of the best teams in the country.

By their own admission, the Playoff Committee left out Notre Dame and BYU, who they had as the 11th and 12th best teams in the country, in favor of the 20th and 24th ranked Tulane and JMU.

What is startling about this, is that the committee seems to be living in their own world.

The Associated Press had Notre Dame ranked 9th, ahead of final two at large teams – Miami and Alabama – and Vegas had Notre Dame as -2 to -4.5 point favorites over those teams. In fact, Vegas had Notre Dame as the third best team in the field: good enough for the second at large spot, after Ohio State.

The rules for the playoff are as follows: the five highest-ranking conference champions (Indiana, Georgia, Texas Tech, Tulane, and James Madison) get automatically admitted, along with seven at-large teams.

The goal, purportedly, is to make the regular season matter. But there’s a problem. People differ greatly on how they view what the regular season mattering means.

The traditional view: just win the games in front of you.

The traditional view is that a team has no control over its own destiny and that it can only play the teams on its schedule. From there, if it wins those games, they should be rewarded.

If you beat another team, that should count as a tiebreaker, if the records are even.

If we use this model: Alabama should be out. After all, there are simply too many undefeated, 1, and 2 loss teams to let in.

This naive approach has its problems, but it is fair. If you win, you can get in.

There are two obvious retorts.

1. Not every team plays similarly hard schedules. Power Four teams, especially, play harder schedules than Group of Five teams.

2. Not all losses are created equal.

The desire to include a Group of Five team is an odd one. College Football is hoping for an underdog story that never comes – or even seems likely. But this could still be easily addressed. Just penalize Group of Five teams whenever there is a tie, unless their losses come from Power Four schools.

James Madison’s one loss came to a respectable Louisville team that also beat Miami. It seems fair enough to treat them as a standard one loss team.

Tulane, however, has a loss to Group of Five UTSA. In that case, it seems fair enough to give preference to the teams that lost the same number of games, but against tougher competition.

If we applied that simple rule, we’d have 8-teams in, and we’d need to select four more teams from the following list: Notre Dame, Miami, Vandy, OU, Utah, and BYU.

Alabama and Tulane lose out.

The Season as a Giant Playoff

Another common, traditional view is to think of the season as a giant playoff. In this way, we’re still punishing teams for wins and losses, but we’re also thinking about it as a sort of feeder-system into the playoff.

The teams are not floating, free form. They’re aligned to conferences – like the National Football League has divisions or the World Cup has pools – and those conferences get slots in the playoff.

In effect, you’re in a giant tournament the whole season.

College Football wants to do something like this. That’s where their idea of the top-five highest ranking conference champions comes from.

The flaw comes from how each of the conferences determines its champion.

Conferences are deep. And just like we have a problem with determining who should be in the College Football Playoff, conferences have the same problem determining who should play in their championship game.

The ACC matched Virginia against Duke – but had several other two-loss options including: Miami, Pittsburgh, SMU, and Georgia Tech. All four of those teams were rated higher than Duke by Vegas, but because of the ACC’s selection criteria, Duke got the nod and upset Virginia in the championship.

Unfortunately, because of their poor performance outside the conference – they were ineligible for post-season play. Invalidating the idea that the season is a giant tournament.

You have some conferences – like the Power Four ACC – who simply do not subscribe to this model.

The other indication that College Football doesn’t take this idea seriously is that it doesn’t have automatic bids. If the champions matter, Duke should be in. After all, it won a Power Four conference.

Vegas would favor them over Tulane on a neutral site. Even somehow that is less offensive.

The Bayesian View

Another way to view seasons – especially popular among stats nerds and gamblers – is to view every game as a chance to update your rating about a team. Statisticians take a strict view about this. Every team gets a rating and then gets rewarded or penalized for their wins and losses. But it has also bled a bit into popular analysis.

This makes analysis of losses and head-to-head tricky, because the strict-statistical view is opposite the conventional wisdom here.

In the conventional view, if Miami and Notre Dame finish 10-2, and Miami beats Notre Dame during the season, Miami should get the nod over Notre Dame. Miami beat Notre Dame head to head, so we should reward them for winning that game.

Statistically, however, because Miami’s loss comes to a team worse than themselves, we would actually want to punish Miami more for losing to that team. In the statistical view, Notre Dame didn’t lose to “Miami”, they lost to a team with a Miami-like strength. Miami, on the other hand, lost to a team with worse than Miami-strength. So Notre Dame gets the nod in this case.

A naive way we can think about this is loss inheritance. Every time you lose to a team, instead of getting 1 loss, you inherit its losses. So Notre Dame lost to 1-loss Texas A&M and a 2-loss Miami, so it inherits 3 losses. Miami lost to 4-loss Louisville and 4-loss SMU, so it inherits 8 losses. 3 is fewer losses than 8, so Notre Dame is the better team.

We can use the same analysis to compare Vanderbilt (+2 from Alabama and +3 from Texas) and Alabama (+7 from Florida State and +1 from Georgia). Vanderbilt and Alabama both have 2 losses. Vanderbilt would be rated higher than Alabama in this case.

The flaw here is obvious: this is a second order analysis a bit detached from the actual results of the season. The statistician’s retort is that season performance itself is actual a second-order phenomenon, detached from the strength of any given team – but that argument is going to fall on deaf ears with most of the football-watching public.

What can work?

So, what can be done to fix this?

I think you have to take a bit from each group.

From the traditional view:

• At large teams are admitted to the College Football Playoff based on record

From the giant playoff view:

• Five conference champions get in automatically, selected by conference in order of number of teams in the top 25

From the statistical view:

• When there are apparent ties, an objective statistical rating system is used (Elo, Sagarin, or even a simple loss-inheritance model.)

Using this approach, what would our 12-teams be in 2025-26?

With this approach:

• Duke, BYU, and Notre Dame are in

• Alabama, Oklahoma, and JMU are out

Duke takes JMU’s place, sneaking in as a conference champ.

BYU gets in because they’re an 11-win team. And Miami and Notre Dame beat Oklahoma and Alabama on statistical tiebreakers (assuming Sagarin rating system, which was used previously by the Bowl Championship Series.)

Simply put, quarterbacks who have high P(100) are doing enough. There might be problems, but it is probably in other areas of the team.

Jalen Hurts has a P(100) of 0.48 – good for a top 10 rating. That’s good enough that the Eagles should be focusing on other areas of their team. Like their suddenly ancient running back, Saquon Barkley, who is averaging only 60% of his yards per carry from last year.

But for the sake of rigor, and to clear Jalen Hurts’ name, let’s take a look at how he compares to his peers across the metrics we care about when it comes to quarterbacks – P(100), Yards per Attempt, and Success Rate – and how he stacks up against quarterbacks with similar weapons.

P(100): Doing Less with Less

Jalen Hurts’ P(100) of 0.48 is good. It means that the Eagles have a 48% chance of Hurts playing well enough through the playoffs that they could reasonable expect to win the Super Bowl if all things go their way. This is good enough for top-10 in the league, but it puts him with other hit and miss QBs: Sam Darnold, Dak Prescott, Jordan Love, and Matthew Stafford.

Each of these QBs has their moments of greatness. And so does hurts. Each of these QBs also has their shortcomings. And so does hurts.

Hurts has a worse success rate and lower yards per attempt than those quarterbacks with a similar P(100) – but he is also working with worse weapons. In particular, Darnold, Stafford, and Prescott all have much better weapons.

That his success rate this season is 8 points below his peers is concerning on a drive-by-drive basis, but over the course of a game, the P(100) should dominate that statistic. It really just means the Eagles need to be ahead of the sticks and playing with momentum if they want to win.

Y/A: These are not the comps you’re looking for

Yards per attempt is a metric that we use to qualify quarterback play because throwing the ball down the field does a lot of good things. From a game theory perspective, it causes the defense to need to play more defensively, and defend more territory, opening the run game.

This has never been Jalen Hurts’ strength. Hurts yards per attempt puts him with journeyman quarterbacks like Jacoby Brissett and Mac Jones, as well as Patrick Mahomes, who is having an especially poor year.

Interestingly, Hurts is palying better than all these quarterbacks by a significant margin – but he still lags behind on success rate. He may even be worse at pushing the ball down the field than his yards/attempt number suggests.

And surprisingly, this is not because he has worse weapons. While his peers by P(100) averaged much better weapons, he has about hte same quality weapons as his peers by yards per attempt.

Success Rate: Outperforming his rating

Success rate is an indicator for how well a quarterback can meet the moment. How often do they take a bad situation and make it better. How well can they keep drives alive.

And when it comes to Hurts’, as we’ve seen, he’s not that good at it. His peers in this cateogry, likewise, are not going to be considered top of the league by anyone. Baker Mayfield is probably the best of a cohort that includes Caleb Williams, Bo Nix, and Aaron Rodgers.

But when we compare Hurts to this cohort, he does much, much better. He is 20 percentage points more likely to average a QB rating of 100 over four games, he averages more than a half a yard more per attempt.

Admittedly, his weapons are better in some cases – but not all, and not by much. Except for Rogers, it is not obvious that the Eagles skill position players are better than the skill position players for the Bears, Buccaneers, or Broncos.

Weapons score: Exactly what we expected?

And lastly, we can take a look at Hurts by his–the Eagles’–weapon score. A 68 weapon score is good for top third of the league. Nothing spectacular, but nothing terrible.

And Hurts compares favorably to two of the other three quarterbacks in this grouping. Like we’ve seen, his yards per attempt and success rate are lacking – but his P(100) is strong. His play is much more consistent that his peers.

What are we to take from all of this?

Well, previously, the Eagles had a much stronger running game. And that had a lot to do with their success.

The Eagle’s receiving corps likely feels they had a big role to play in the success. After all, they were incredible in 2022 and 2023. But in 2024 and now in the 2025 campaign, they’re just a bit better than average. This is what aging looks like. Ask the Chiefs.

AJ Brown is averaging the fewest yards per target of his career. And unlike years past, where Brown was the clear number one, this year, DeVonta Smith is as good if not better.

The Eagles roster is not the same as it was. It’s worse. Their quarterback is playing consistently. But consistent might not be enough this year.

But also, it might be just fine. Getting into the playoffs with a steady hand under center gives you more than a puncher’s chance in the NFL.

What has been validated, though, is that with this version of Wemby, the Spurs are a really good team. And we can be confident about that even 13 games into the season.

But… small sample size?

The chorus of sample size is an argument that is often by levied by people who are either (a) cherry picking data or (b) don’t have a good empirical sense for what they’re talking about: they just don’t want you to be confident based on a handful of observations.

The truth of the matter is, small samples are powerful. Even a sample of 1 can help us ground a distribution.

If we’re watching a pitcher warm up, and we see him throw a 98 MPH fastball. We might not know much about his pitch velocity, but we’d be crazy to think he couldn’t hit 90 consistently in a game. We can use our general understanding of biology to get there – even if we know nothing about baseball.

The faster a pitcher throws a single pitch, the more confident we can be he throws fast. In the same vein, the better a team plays over a small sample of games, the more confident we can be that a team is actually good.

In the NBA, if a team averages a point differential of 15 points over just three games, we can be confident (+90%) that that team is going to be make the playoffs. As the average point difference for a team goes down, the number of games we need to be confident they’re going to make the playoff goes up.

For example, the Thunder (+15.5), Nuggets (+11.9), and Rockets (+11.5) are all in after the opening month of games. We’ve seen what we need to see. These teams are good.

The rest of the teams – we won’t be able to tell until the season is over. Seriously. In most NBA seasons, the number of games played is simply not enough to delineate between medium-good teams. Great teams jump off the page. But medium-good teams? It’s hard to say.

The error rate of point differential after 82 games is +/- 1.9 points That means a team with a 5.0 point differential could be a 6.9 point differential team underperforming, a 3.1 point differential team over performing, or anywhere in between.

How good do teams need to be?

Lucky for all the teams we don’t yet know about – you don’t need to be a great team to win the NBA title. What you need to be is a good enough team with The Man on your team.

In recent history, only three teams have been good enough for us to confidently say – early in the season – that the teams are of playoff quality. This is one of the reasons we can’t really take total team quality into account when projecting performance within the playoffs: the error around team quality is bigger than the gaps.

Consider the NBA champions from 2017-2025. Only the ‘17 Warriors, ‘24 Celtics, and ‘25 Thunder passed the bar undisputedly good teams.

The others could just have plausibly been bad teams masquerading as good teams.

The worst team of the bunch, the ‘23 Nuggets, had a perfect storm of events: they had the reigning back-to-back MVP, a weak conference, and a complete collapse on the opposite side of the bracket. They faced the 7th seed Heat in the finals, who had a negative point differential on the season.

Crazy things happen. Call it small sample sizes.

What do we know about the best teams?

This year is looking special. At least at the top. The Thunder, Nuggets, and Rockets could all plausibly set the NBA single-season win record and it wouldn’t be that surprising. At least not based on how well they’ve been playing this far through the season.

The Rockets especially, who have a very team-centric style of play, are good candidates to charge through the season with a strong performance.

The reigning champion Thunder are harder to comment on, because being the champion places a bit less emphasis on the regular season. And the Nuggets are very reliant on a single player – so one injury could easily dash their record.

The table below shows estimated win rates for each of the top 7 teams, by point differential, as well as the lower and upper estimates of performance. That’s a 10th or 90th percentile mark where we’d be a bit surprised if something exceeded that range. Not terribly surprised, but pretty surprised.

One thing a close observer will notice is that teams like the Spurs, Pistons, Knicks and T-Wolves, are also all playing quite well. Compare the projections in this table to the table of NBA Champions above and you’ll find that many are currently playing at a level above what previous champions played at.

This is an odd year in that respect.

We should expect some of these teams – about half – to be playing worse by the end of the season. But if the Thunder, Nuggets, Spurs, and Knicks are all playing worse than they are now – that probably only takes two teams, the Spurs and Knicks, below a 6.0 point differential. Two thirds of the time in the last decade, a 6.0 point differential better than the reigning NBA champ.

We could plausibly have five teams playing above that level this year.

The last time we saw that was the 1998 season: when Michael Jordan won his final title, final MVP, and final scoring title over a crowded field that included a basketball team in Seattle.

That the last time we saw this many teams playing this well, the team with the league MVP won the title, should not come as a surprise. In fact, this should be out default assumption: the team with the reigning MVP, or that years MVP, will win the title.

The teams to watch out for from that angle? The current two best teams – Denver and Oklahoma City – and the lingering Lakers. The Luka and LeBron combination could be scary, if it finds a groove at the right time.

How does this apply to other sports?

The analysis here is empirical and numerical. That means real results from real basketball games are used to derive the distributions and outcomes – not statistical theories (although, the bootstrap, a technique used heavily here, can be considered a statistical theory in another sense).

Each sport is going to have different rates of information gain. Point differential in all sports, however, is a useful proxy for performance.

In baseball, there’s even a pretty well respected theory of run creation that can estimate true run differential and indicate the direction we’d expect run differential to correct to over time.

The base idea, though, that teams that are doing very, very well, are less likely to be a fluke than teams doing just kind of sort of well, is something you can carry across all sports.

The Avalanche are good in the NHL this year. The Capitals… open question.

Likewise, there’s reason to feel more confident about the Colts than the Eagles.

Whether you can feel confident about either of them… that’s an empirical question for another day.

But not everything is the quarterback. We also have another metric – weapon score – that measures how good the players around the quarterback are.

And this metric can tell us something about Mahomes’ drop off as well.

Weapon Score Refresher

Since we’re the only site that uses Weapon Score, it’s always a good time for a refresher on how we calculate the metric.

Weapon score is defined as the receiving yards of a team’s number one receiver, by yards, times the geometric mean of the receptions of a teams number two and three receivers, by receptions.

This entire number is then multiplied by a constant (1/10,000 for an entire season of games) for ease of comparison.

Mahomes’ Career Weapon Score

When Patrick Mahomes came into the league, it was well understood that the Chiefs roster was loaded. The team went 10-6 with journeyman Alex Smith, in Mahomes’ rookie year. The offense was powered by a young Tyreek Hill and a prime Travis Kelce – both of whom exceeded 1,000 yards receiving.

That year, the Chiefs had a weapon score of 134 – an exceptional weapon score, achieved by about 5% of teams. In a typical year, only 1-2 teams each year have a weapon score this high. In some years, no teams will.

For most of the Chiefs’ championship run – the duo of Hill and Kelce kept the chiefs in this range. The low watermark weapon score during the first leg of Mahomes’ career was 110. 110 is the 75th percentile of weapon scores. Only 5 or 6 teams each year will have a weapon score better than 110.

In the last two years, however, the Chiefs weapon score has dropped dramatically. From the 130s to 72, then 62. Meaning who many think is the best quarterback in the league now has some of the worst weapons. Both of these weapon scores, 72 and 62, put the Chiefs in the bottom half of the league.

The Kelce Effect

The biggest driver of this, arguably, is the Chiefs’ over-reliance on an aging tight end as the centerpiece of their offense. Kelce was excellent during his prime, certainly. But offenses are at their best when they are driven by receivers.

Receiver-led offenses are 10-points better, by weapon score, which is enough to jump three or four teams.

Since Patrick Mahomes entered the league, there have been 37 instances of a team ending a season with a tight end as their leading receiver: about 3 per year. Of those, Travis Kelce is by far the most frequent. He has led the Chiefs in yards in six seasons. That’s twice as often as other elite pass-catching tight ends like George Kittle and Mark Andrews.

This is good, historically at least, for Kelce, but ultimately bad for the Chiefs.

The good news is, that it points to a ray of hope for Chiefs fans. As Kelce ages out of the league this year or next, it is probable that Patrick Mahomes and the KC offense actually get better.

The best formations for weapon score?

Perhaps unsurprisingly, the best formations–when it comes to average team weapon score–are all wide receiver led.

Having two strong wide receivers and a pass-catching tight end is your best option. The 62 teams that ended their season with that top 3 averaged a Weapon Score of nearly 100, followed closely by three wide receivers – which averaged a 94 across 69 occurrences.

Two wideouts and a tight end as either your best receiver or your second best receiver is about the same as two wideouts and a running back as your third best pass catcher. But having the running back anywhere besides that last spot is, on average, bad for your offense.

Most teams intend to pass to their receivers – good. About 90% of the teams end with two receivers contributing to their weapon score. Of those that don’t, the average weapon score is 85 – which is tolerable.

But the poor 1-in-50 teams that have only one good receiver AND manage to be led by either a running back or tight end? They average a weapon score of 54. Good for the basement of the league.

Here at Wolohan Analytics, we use a choice metric to evaluate quarterback play. The metric is called P(100), and it’s simple. It’s the probability that a quarterback will post a passer rating of 100 or more in 4 straight games: approximately what a team needs to be a serious contender for the Super Bowl.

As we’re coming up on the halfway point of the season, it seemed like a good time to check in. Baker Mayfield has quietly been ascending the rankings. Lamar Jackson has maintained a steady grip on the top spot. Jalen Hurts continues to play just well enough to give the Eagles a great chance. And Drake Maye has leaped from the depths of the rookie play into realm of contenders.

But the most interesting thing, bar none, is Patrick Mahomes’ continued decline.

When Mahomes broke into the league, he posted numbers we had never seen before. And it reflected on the field. Five Super Bowl appearances and three Super Bowl victories in five years. A truly incredible run.

But what started to become apparent in 2023-24 has become obvious now two seasons later: Patrick Mahomes is in a slump.

In a lot of ways, it’s hard to even talk about Mahomes’ slump, because he’s been so incredible. Now in his eighth season, Mahomes’ posted his career-worst P(100) in week 3 after a lackluster performance against the Giants: 26%. Since then, he’s climbed up a handful of points to 33%.

Peyton Manning, for comparison, had a similar nadir. But the cause of his ratings decline was lack of play due to neck surgery.

What is notable about both Brady and Manning though, is that they both started poor, and ascended to their heights. Mahomes started high and is coming crashing down to earth. Everything he has done the last eight seasons has made his rating worse.

We can expect him to rebound at some point – likely when the roster turns over in a few years after the departure of an aging Travis Kelce – but until then, it’s not clear that Mahomes’ drop is going to stop anytime soon.

Tom Brady played as poorly as Mahomes is now for a season and a half, starting in the 2014-15 season. So Mahomes’ poor performances could extend for a while – or get worse.

P(100) by career game played, for Mahomes vs. Brady and Manning

Black horizontal line is 50% – the P(100) benchmark for elite QB play.

One of the things about Mahomes’ starting at his peak, is that we don’t really have a sense for his floor. In a lot of ways, he’s in free fall. How low he can go is anyone’s guess.

This becomes all the more obvious as we compare Mahomes against his contemporaries.

Jackson, Allen, and Hurts are all getting better.

In an odd way, Mahomes is most similar to Brock Purdy: a young quarterback who had a strong start to his career, and is now in what can only be described as a decline–except their extended declines still put them in the top handful of quarterbacks in the league.

That, and Mahomes’ decline has now extended for eight seasons.

P(100) by career game played, for Mahomes, Jackson, Allen, Hurts, and Purdy

Black horizontal line is 50% – the P(100) benchmark for elite QB play.

Jackson, Allen, and Hurts all resemble the shape of a career we would expect for a good quarterback. It starts low, ascends, dips, ascends again. Neither Allen or Hurts have the heights that we have seen from Brady and Manning – but to be fair, neither of them is really in that conversation.

Hurts is a good enough piece on a strong team. Allen is occasionally great but inconsistent – which becomes a big penalty at quarterback.

Jackson, actually compares favorably to both Brady and Manning for the first 110 games of his career. This stretch of games from 80 to 130 or so is when both Brady and Manning found their first peak. And Jackson is hitting his stride around the same time.

He currently posts a league-leading P(100) of 81%. A score 15 percentage points higher than the second place quarterback: Jared Goff (66%). That 81% P(100) matches Manning’s peak – late in his career in Denver – and exceeds any peak Brady had.

P(100) by career game played, for Jackson, Manning, and Brady through their first 130 games.

Black horizontal line is 50% – the P(100) benchmark for elite QB play.

The question with Jackson, of course, is whether there is a Jekyll and Hyde property to his play. Is Jackson a different player in the regular season and the playoffs?

His early playoff experience would have us to believe yes – but more recently, his results are improved. Since 2024, in four playoff games, Jackson has surpassed the necessary 100 passer rating mark in 3-of-4 games.

And this year, when we look at supplemental stats like success rate and yards per attempt – which proxy how capable a quarterback is of pushing the ball down the field and managing in demanding situations – Jackson compares favorably to the top of the field. He is second in the league in yards per attempt and third in success rate.

The final way we might look at this is to say, no. Mahomes really was that great – he’s due for a rebound. So let’s match up his dive with other greats who had a dive and see what we can expect the bottom to catch.

If we look at Brady and Manning’s descents, we can see that both Brady and Manning had rebounded by now. In fact, both had rebounded four seasons ago.

To put that another way, Mahomes has been getting worse for 8 years, and neither Brady nor Manning had a slump that lasted longer than three.

It’s worth remembering that these dips from Brady and Manning are also between seasons 8 and 12. So you’re seeing accumulated injuries, coach turnover, and the general aging out of their primes. Both Brady and Manning had to learn new ways to play as they aged. Mahomes, turning 30 this year, is at the tail end of his prime and presumably has not had that dip yet.

In fact, if age alone was the predictor, we’d expect Mahomes to dip even farther these next two years as he adjusts to a new – less heroic – body.

Career-worst P(100) decline: Mahomes, Brady, and Manning

Black horizontal line is 50% – the P(100) benchmark for elite QB play.

How do you bet this?

Warning on gambling: Most bettors do really poorly and there is a reason that sports books make lots of money. Betting advice is for entertainment purposes only. For integrity purposes, we place a small wager on every bet we recommend.

This one is easy: pick some of your favorite AFC teams. Right now, the Chiefs have the second best odds to win the conference, but Mahomes is having an off year and they are third in the division standings. Take everyone you like in the AFC except the Chiefs and – because their odds are so over-inflated – you should still be getting good odds.

We took the Bills, Colts, Broncos, Patriots, and Ravens to win the conference at roughly these percentages: 31%, 22%, 22%, 15%, 10%. That distribution is going to favor the Broncos, Patriots, and Ravens. If you like the Bills or the Colts, there’s plenty of room to shift your mix that way.

We’re fading Aaron Rogers and Justin Herbert.

Wemby might be the best player in the league through five games. He’s averaging 30 points, 15 rebounds, 5 blocks, and is the undisputed leader of an undefeated team.

And while the season and Wemby’s career are both in their early stages, we already know a lot about the young French star. Namely: he’s never going to be the scoring threat that Michael Jordan was. If he’s going to be the best ever – and that’s the goal for Wembanyama at this point – he’s going to need to make the case like LeBron.

How prolific a scorer was Michael Jordan?

28 points per game prolific. From the year Jordan entered the league at 21, he averaged more than 28 points per game in every full season he played until he was 38 years old.

Durant fell short of that mark, though playing with Golden State and splitting shots with Steph Curry probably had something to do with that. And LeBron averages around 27 a year.

Jordan averaged 30. And won the scoring title in every full season he played during between 1987 and 1998.

That’s one of the reasons it’s so easy to call Michael the best ever. He dominated a decade the way no one else did. While other greats had to share their decade – Jordan didn’t. Bird and Johnson both defined and foiled one another. LeBron shared his come up with Kobe Bryant and Tim Duncan, and had his prime interrupted by Kevin Durant, Dirk Nowitzki, and Steph Curry.

When you’re just really good at a lot of things – you’re not the best scorer and you’re not winning the title every year – the case for the greatest becomes a lot muddier.

And right now, that seems like it will be the path Wembanyama has to tread.

Wembanyama’s free-throw percentage, a good proxy for true shooting ability and potential, lags behind both Jordan and Durant. Unless he starts to lead the league in field goal attempts, Wembanyama won’t be winning scoring titles.

And that means the case has to be made based on a holistic assessment of his play.

And that means he needs to win titles.

Is the Best Ever really fair for Wemby?

What’s all this Best Ever talk anyways? Is it fair to put these expectations on the kid at 22?

Actually, it’s more than fair. If Wembanyama turns out to be as good as Shaq, well, that’s kind of what we would expect an average Wembanyama career to be.

Four titles and three finals MVPs? He’d be great. One of the best centers of all time.

Maybe he could even leverage his size late into his career. Win a few titles early, and then a few on the back end of his career teaming up with an emerging star a la Kareem Abdul-Jabbar.

Either of those careers would place him as among the best to do it.

But that’s average.

What should we expect?

To get an approximate Wemby performance, we can take an average of other great players – with an emphasis on Wemby comps.

I chose these players:

• Michael Jordan – The best ever

• LeBron James – The other best ever

• Kevin Durant – The second-best scorer ever

• Shaq – The best scoring big

• Kareem Abdul-Jabbar – The second best scoring big

• Tim Duncan – the best “humble” big

If we average together their seasons during their ascendency phase, we get these approximate numbers of Wemby:

• 25 to 35 points per game

• 10 to 15 rebounds per game

• 2 to 4 blocks per game

And the expectations are about flat during this period. That is, Wemby should be as good at 22 as he is at 26. And he should be about MVP caliber for every year during that stretch.

That’s what we should expect from a GOAT-caliber player.

Right now, Wemby is on pace for 30, 14, and 5. So a bit on the upper end of where we would expect him to be for the next four years – but not outside anything we’ve ever seen.

If we check back in mid-season and Wemby is below these ranges – if he’s not averaging 25, 12, and 3 – we probably want to shift our expectations down. That is, we’ve got decent reason to think he’s not going to be the best ever, and that we should start to include some worse players in his pool of comps.

Note that those worse players would be hall-of-famers like Nicola Jokic, Dikembe Mutombo, Dirk Nowitzki and Dwight Howard. That’s the level that Wemby is playing at already. He needs to be worse for us to compare him to Hall of Famers, including the best player in the league for the last five years.

Wemby might have a half-decade worse than we expect and still be the most dominant player in the league.

How do you bet this?

Warning on gambling: Most bettors do really poorly and there is a reason that sports books make lots of money. Betting advice is for entertainment purposes only. For integrity purposes, we place a small wager on every bet we recommend.

Right now, the Spurs are 35:1 to win the finals. If the comps are any suggestion, Wemby will win 2 titles in the next 5 years.

I’d include them in a mix with Oklahoma City (+200), Denver (+700) and LA (+1700).

This gives you the top 4 players in the league – SGA, Jokic, Luka, and Wemby – at plus odds.

Why not take anyone from the East? – The top talent isn’t very good. Donavon Mitchell is not consistent enough to water down the odds.

With a 30:10:5:5 wager on OKC, Denever, LA, and San Antonio – you only need one of those teams to win once every four years to make money. And we expect the trophy to go to an MS10+ player at least 19-in-20 years or more.

Using the same approach we used in our recent post on information gain in college football, we find that the middle-seeded teams—Texas and Penn State—actually have the easiest path to the semifinal. Texas and Penn State can reach the semifinal without playing a single team “very strong” team, under our previous rating system. We give Texas and Penn State greater than 80% chances of winning against all four of: Arizona State, Boise State, Clemson, and SMU.

Oregon must play either Ohio State or Tennessee—both who are rated as very strong opponents. And Georgia may find themselves facing Notre Dame, who is also rated as a very strong opponent.

The presence of these strong opponents in their part of the bracket means that Oregon and Georgia’s likelihood of reaching the semifinal is nearly 20 percentage points worse than teams they beat in their conference finals!

Winning their conference championship games was actually detrimental to their odds of winning the national title.

Right now, Texas has the best odds of any team to win the national title at +360. Georgia shares this rating. And Oregon is only a bit behind at +380. But their odds are all so steep, there’s no value here.

Tennessee (+2600) and Penn State (+600) are undervalued significantly. And if you believe Notre Dame can be competitive with elite teams, they are undervalued as well at +1200.

If you’re going to bet on sports, please do so within your means. Information here is entirely for entertainment purposes. Almost all recreational sports bettors lose money.

College Football is a sport divided into haves and have nots. Every year, there are a handful of juggernaut teams, and a handful of also rans. This year, it looks like Oregon, Texas, Ohio State, and Georgia are the juggernauts—and everyone else is along for the ride.

But we don’t really know. Because apart from two games—Georgia versus Texas and Ohio State versus Oregon—most of the games these teams have played have not given us very much information about the teams.

When we think about team strength, it is helpful to use a metric like Elo rating, which abstracts everything about the team into a single number. These numbers are not perfectly accurate, but they have proven to be consistently effective across almost all paired competitions.

Elo ratings work by providing an estimate of teams strength, based on past performance, and then updating that estimate when teams play new games. The update amount is based on the probability of winning—which is, in turn, derived from the relative difference in estimated team strengths.

This updating method is also a convenient measure of information gain. A bigger update—up or down—means that we learned more information about the team.

When teams play teams of equal estimation—for example, when Georgia and Texas play—there is a high probability of a medium sized update.

When teams play teams of widely varying estimation—for example, when Ohio State plays Akron—there is a small chance of a big update, and a big chance of nearly no update.

To look at an example of the problems this causes, we can look at Ohio State’s schedule this year.

In all but two of Ohio State’s game, we expect to learn next-to-nothing about Ohio State. In more than 80% of the games, Ohio State has an 85% chance of winning.

The only two games we expect to learn something are their marquee matchups against Oregon and Penn State.

But because they play so few games relative to their very strong peers, we get next-to-no evidence to differentiate them from these peers.

In fact, in our example, Ohio State’s rating only moved 2 points over the entire season—even considering their “surprising” loss to Michigan. Surprising is in scare quotes there, because a loss to a Michigan-strength team was expected, given that Ohio State is a very strong team and they played the schedule composed the way it was. Ohio State’s expected record was 10-2 — and we expected them to beat either Oregon or Penn State, and lose one other game.

Let’s play this out with Indiana to see how this works for a borderline playoff team.

Indiana had a great season. They were expected to win 9 games and they won 11. The only game they lost was a game they had only a 15% chance of winning. They won their coin-toss game against Michigan and dominated a bunch of weak to very weak opponents.

But what did we really learn?

That IU is competitive against Michigan-level teams? Indiana is projected to play Texas or Georgia in the opening round, against whom they’ll be given about a 15% chance of winning. That may be generous.

If the goal of the season is to differentiate which teams are worthy of being in a 12- , soon to be 14-, team playoff—did we really accomplish that if we cannot differentiate Indiana from Michigan?

Last week, we proposed a flexible-scheduling approach, where teams could be flexibly scheduled against opponents where we could learn relatively more information than under the current system. What might that look like?

Big Ten teams play 9 conference games each year. So let’s assume the first four of those are fixed-schedule games, the last four are flexible scheduling games, and the final game is a fixed-rivalry game (e.g., OSU-Michigan, IU-Perdue, Minnesota-Wisconsin, etc.)

Under our recommended approach, IU would swap its games against weaker teams Washington and Michigan State for strong teams: Illinois and Iowa. IU would have a lower chance of winning these games—they would be near coin-flips—but we would learn much more about IU as a result. This would guarantee that if IU goes 11-1, it is not because they only played one meaningful game all season.

Under this scenario, the frequency that we learn something about teams is significantly increased. As is the amount we learn about teams that we expected to win.

But can you really do flexible scheduling? Won’t that create a logistics nightmare and make it hard for fans to buy tickets? No. Fans already do this for playoff games. Any playoff is effectively a flexibly scheduled event, and playoff games have excellent attendance.

Further, these games are de-risked by season ticket packages and student tickets. And the television dollars that will be brought in for these more competitive matchups will be bigger than for less competitive matchups.

The conferences might use a combination of the following criteria to set flexible scheduling:

• Wins

• Computerized Rankings, e.g., Elo- or BCS-style rankings

• Media / Coaches Poll Rankings

• Television Interest

What keeps a conference from giving their top teams the easiest path to the championship?

Nothing. But if we look at schools like Oregon, who played only one of the top three schools in their conference, there is a good argument that conferences are being lenient on their best teams now.

Similarly, Texas played Georgia (and lost big), while also dodging CFP-eligible teams like Alabama, South Carolina, Tennessee, and Ole Miss. Texas should have played better competition down the stretch so we know who they are.

Ultimately, the way we schedule games is leaving too much on the table. And if we want to take the playoff seriously, we need better information heading into the playoff. Right now, we simply don’t have meaningful evidence about the quality of the strongest teams.

History of the National Champion

From the beginning of college football until 1998, the national champion was crowned without a national championship game at all. This meant that the regular season—and standing in the eyes of the press—meant everything.

From 1998 until 2014, the national champion was determined by a single elimination game between the #1 and #2 teams in the country. This process, known as the Bowl Champion Series, was electric—if controversial. The regular season was still paramount, because there was no room for error, but the fans still got to enjoy a single elimination game for all of the marbles.

But the process was opaque and ultimately, too ripe for criticism. This led to college football adopting the playoff in 2014. From 2014 until 2023, college football was determined by a four-team playoff. Thirteen selectors used criteria of their own devising to rank a four-team field. And, arguably, they made no meaningful mistakes during that 9 year run.

Yet this too proved to be too suspect of a process. It was not right that mighty Florida schools like Florida State and Central Florida be left out of the playoff despite perfect records. So the playoff has been expanded yet again to twelve teams.

To what end?

What is college football hoping to achieve? Are they hoping to create more valuable television properties? They may be doing this. But they may also be undercutting the value of the regular season. It will be hard to tell as conference realignment has created some of the most interesting regular season matchups we have seen in some time—at least in the SEC. The other conferences are mostly not playing interesting football.

Despite the Big Ten’s perch atop the college football playoff rankings, the SEC has had a hold on eyeballs. Of the 25 most watched games this season, more than half have been SEC games. The top-rating Georgia-Texas game did almost 4-million viewers better than the top-rating Big Ten game: Oregon-Ohio State.

For it’s part, ESPN has committed more than $1B per year to the college football playoff—so they are hoping that the new properties outdraw the previous bowl game properties. As college football teams struggle to understand their economics in the post-NIL world, ESPN’s billion-dollar offer could be all the reason the sport needed to spring for the playoff.

But will it actually make a difference on the field?

First off, it is important to note that if the system runs long enough, poorly ranked teams will win. Multiple 4th seeded teams won during the nine-year four-team CFP, including Ohio State in the very first season of the college football playoff, and an Alabama team with two NFL quarterbacks on the roster.

Sometimes the regular season does an inadequate job of differentiating between the truly elite teams.

We talked about this problem with baseball. Because baseball teams play their 162 game season in a mostly arbitrary fashion, they throw away a lot of information. A better solution would be to break the season up into increasingly competitive play.

College football should have three objectives during it’s regular season: (1) separate the great teams from the rest, (2) generate revenue and attract eyeballs, (3) sustain fan-favorite rivalry games.

The easiest way to do this would be with some form of flexible scheduling where the leagues only partially assigned conference games, leaving from 1 to 3 games on each team’s schedule where only the home team was scheduled. Then, two or three weeks before the game, the league could announce the opponent to create the most competitive (informative) matchup.

This would have minimal disruption for in-stadium fans, and provide the best experience to television fans. Further, competitive matchups should attract eyeballs and generate the most revenue. An uncompetitive Ohio State - Indiana matchup garnered nearly 10M viewers last week because of the status of the teams. Had the Big Ten not had that game on their schedule, they should have made it.

A case and point is the other side of the Big Ten: Oregon. Oregon has played only one meaningful game this season: a narrow win against Ohio State. Ohio State has played against three teams currently in the top-10. Georgia played five teams ranked in the top twenty. We know much more about Georgia and Ohio State than we do about Oregon.

Lastly, we need to ask, will the 12-team playoff really help us find the best team? The distance between teams at the top of college football is often tight.

Last year, Michigan narrowly made the title game after beating Alabama in overtime. The previous year, Georgia needed a single point to escape Ohio State. In 2018, Alabama beat Georgia in overtime for the title. The two years before that, less than a touchdown separated Clemson and Alabama.

Some years, we’ll have incredible teams that blow everyone away and render the playoff meaningless. Other times, we’ll have a scrum at the top where the champion’s claim to be the best rests solely on having escaped the gauntlet of the playoff—regardless of the merit of their competitors.

In short, the 12-team playoff is not the most impactful thing that college football could do to help identify a national championship—but some years it will give us good football. And in the other years, at least it’s ESPN that’s paying for it and not us.

In the last post, we covered how professional bettors bet using the Kelly Strategy - and how oddsmakers—who are themselves professional bettors—use this, combined with knowledge about how other professional bettors bet, to create highly advantageous situations for themselves.

The key thing that makes this possible is that the difference between a professional bettor and a recreational player is massive. Not a few narrow percentage points. But rather, a massive philosophical difference in how to approach gambling.

Why do regular people bet?

Where professionals bet to win money, recreational players bet either to enhance their enjoyment of the game (entertainment bettors) or because they are gambling addicts (addict bettors). And make no mistake—unless you are placing bets using multiple algorithms to assess outcome likelihood, error, confidence of each, and bet-sizing—if you bet, you are either an entertainment bettor or a addict bettor.

Entertainment bettors bet to enhance their enjoyment of the game. They find sports more exciting to watch if they have “skin in the game”. For them, typically, watching sports is something they grew up with, but now that their youthful passion for sports fandom has worn off, they need something to sweeten the deal for themselves. Thus, they bet.

Addict bettors bet because they are gamblers. This group of people is not dissimilar from those who you can find decorating casino slot machine chairs throughout the country. When they say that Vegas wasn’t built on winners, these are the people that Vegas was built on; these people are going bankrupt because they cannot control their losses; these people are the reason that there is a national a gambling addiction hotline: 1-800-GAMBLER.

How do regular people bet?

Unlike professional bettors, whose behavior we can formalize—because it is rational and goal oriented—it is very difficult to formalize the irrational behavior of people who lose money on sports betting. And make no mistake, the public loses money on sports betting. Industry leader FanDuel makes nearly $1B / year on bets.

Entertainment Bettors

Entertainment Bettors bet for entertainment purposes. Therefore, we can imagine a theoretical inequality governing entertainment bettors decision making:

Where

• a is the amount bet

• p and q are the probabilities of winning and losing, respectively

• e_p and e_q are the excitement of winning and losing, respectively

• and u is the amount of money 1 unit of excitement is worth

Under this formulation, entertainment bettors are perfectly rational creatures. They’re paying for entertainment at a rate that makes sense for them.

However, there are two problems with this.

First off, we know that entertainment bettors do not know p and q. They might be able to make informed guesses about p and q, but if they were able to get accurate understandings of p and q, they would probably following professional betting patterns. In that case, the entertainment aspect would change—you are now watching to be entertained by winning money and being correct about your assessments—but the fundamental motivation stays the same.

Second, e_p and e_q are not constants. They are themselves variables that depend on a litany of factors, including the value of u and the value of a.

For example, we should expect that as a increases towards 100% of a persons net worth, the value of e_q goes to negative infinity rather quickly. In fact, by the time a has increased to a substantial portion of your bankroll, the pain of a loss — e_q —is much greater than the joy of a win. Some might call this loss aversion; most would call this sanity.

Tied up in that is one’s appetite for gambling, which is set by u. There’s a famous story about Michael Jordan gambling with an acquaintance, who asks him what the stakes are. To which Jordan replies, “whatever amount makes you uncomfortable.” Jordan’s insight here is that his desired u is much greater than his opponent’s. This gives him an advantage because as u increases, e_q increases faster than e_p. If he can sufficiently increase e_q, then Jordan can induce bad decision making in his opponent via loss aversion.

In practical terms, however, as we make more money, have higher net worths, or build up a tolerance to gambling over time, u will increase, relative to both e_q and e_p. That is that the quantities u/e_q and u/e_p will both increase. This means that the amount an entertainment bettor bets is expected to go up over time, despite them being negative expected value gamblers.

What is most important, however, is the first point: because entertainment bettors are wrong about p and q, they are highly profitable for oddsmakers. Because entertainment bettors do not factor in expected value of their bets—rather playing for excitement—they are not sensitive to the small changes in odds that make huge differences for professional players. Remember that a shift in a line from +105 to -110 can make a bet go from a no-play to a sizable bet for a professional. For the entertainment player, these differences don’t even register as differences at all.

Addict Bettors

Addict bettors are the lifeblood of oddsmakers business—regardless if bookmakers or bettors want to admit. Addict bettors are primarily fueled by hope. They see large payouts—especially from parleys or teasers—and look to cash in with big winnings. A few large scores propel them through tremendous, long-term losses.

And this is reflected directly in both the public reports these bookmakers must make to investors—where they talk up how they are going to capture more of the parley and in-game betting markets (which offer high payouts, but terrible odds)—and how the companies market themselves to users: again, an emphasis on same-game parleys, which offer relatively terrible (and hard to calculate odds).

What does this mean for oddsmakers?

As we have seen, oddsmakers are constrained only slightly by the public. The public is willing to bet large amounts of absurd propositions because it provides them entertainment and satisfies a fantasy of obtaining a high-payout event. These things are not tethered to reality.

As a result, professional gamblers can beat lines set by oddsmakers. But as we noted in the previous post, this is not the same as beating the oddsmakers themselves. In many ways, oddsmakers use the professional bettors to diversify their portfolio and align the size of their bets—which they do not have perfect, direct control over.

Provided you can open a book and offer lines, you should have access to what is effectively an infinite money machine. The trouble, of course, is your competitors. Line shopping—a behavior that only sharps do in practice—forces oddsmakers to offer better lines than they otherwise would, reducing their profits. That said, because line shopping is hard, the name of the game is customer acquisition.

A bookmaker wants to acquire as many customers as possible, because each customer is substantially positive EV for them—potentially up to $75/mo. based on recent research.

What does this mean for you?

Your first order rule should be not to bet. Just don’t do it.

We make recommended bets on this site, and our bets have paid out well above breakeven. Further, we put some nominal stake behind each recommended bet on FanDuel. But we do this primarily to “put our money where our mouth is”. It would be dishonest to recommend lines and not bet them.

Since this blog started, we’re getting a near 50% return on investment. If we have bet $100 to date, we would have $150 in our bankroll. That’s not exactly how it has worked, because the bets take place through time and we don’t stake each bet with even sizing (see the Kelly Strategy in the last post) — but it’s close enough.

And all that said, you shouldn’t bet. Betting now increases your likelihood of becoming an entertainment bettor or an addict bettor, and both of those are negative expected value shifts. Again, as an entertainment bettor, the more you bet, the more your u/e_q and u/e_p will both increase — causing you to bet (and lose) more money.

If you want to bet, come up with a system. You need a system for assessing what you think the odds are, comparing that with the odds that are actually offered by the book, and then sizing a bet based on that. Ideally, you can do this with a bankroll approach, where you set some palatable number as your bankroll and only bet fractions of that.

If you used a crude approach, and bet 6% of your bankroll for your favorite game each week of the NFL season and 3% of your bankroll for two other games, you should be able to make it through at least 20 seasons of football without needing to re-up your bankroll. If you want to bet and have some skin in the game—this is a measured and safe way to do it.

Should betting be legal?

Because sports betting’s legality is so recent, an obvious question that many are asking is: did we make the right decision?

The responses to this generally take two paths:

1. Sports betting is bad because the oddsmakers are predatory and people make bad decisions with their money when given the opportunity

2. Sports betting is just another thing and we shouldn’t make it illegal just because some people choose to spend lots of money on it

Similar—better—arguments can be made for a whole host of vices: alcohol and marijuana are two that come to mind because they have both been illegal in the near-past. These are also things that have massive negative effects on society, and yet, we choose to make them legal.

Why? Because the vast majority of consumers indulge in these things responsibly, and outlawing the practice creates a black market with its own (negative) knock on effects. Instead of funneling money to American corporations that can be taxed, black market revenue by and large goes to organized crime. It is no coincidence that the Mafia has strong associations with both prohibition and gambling.

So yes, sports betting should be legal. There is no reason that a sports fan should need to interact with violent criminal organizations to enhance their enjoyment of a sporting event—even if doing so costs them $1,000 per year. $1,000 per year might be a large number, but it might also be a reasonable number, given the amount of enjoyment that many derive from sports fandom.

Further conversation is warranted on the matter of how sports betting might be restricted. For example, we already have restrictions limiting betting to those over the age of majority. Could further restrictions apply to limit the most addictive behaviors? Certainly.

As a bettor myself, I would be reluctant to see the user experience for betting get significantly worse. As it is, complying with location restrictions and session time limits is burdensome enough. And as one adds restrictions, one needs to be careful not to tip the scales to make it a better experience to bet through a black-market bookies and illegal sports-betting sites. Today, about $60B in bets each year goes to illegal, online oddsmakers. Those oddsmakers do not conform to the restrictions put in place to provide a better experience—so we have to be careful about how much we disadvantage the lawful players in the market.

This post is something different. This post is about the fundamental theory of betting and line-making. In it, we don’t talk about how to measure anything. Rather, we talk about how lines work. How oddsmakers set lines and how professional betters—which oddsmakers are—determine whether or not to bet the lines that are offered.

This post is very algebra heavy. You won’t have to solve any equations. But you will be challenged to think in terms of abstract values. We’ll even use some calculus terms like limit.

But the reward for using this framing is large.

If you can stick with this post and work through the algebra. You’ll understand at a fundamental level how oddsmakers are thinking about setting lines, how sharps—professional bettors—think about betting, and where to look for opportunities to make money betting.

If that’s something you want to do.

What’s a line?

The line for a bet is part way between truth of how likely an event is to occur and the widespread opinion about how likely that event is to occur.

Market theory says that enough informed participants in a market, the market should converge to the truth. However, sports betting neither has informed participants nor liquid markets.

Participants are emotionally invested in their teams, misinformation about sports teams relative strength is rampant in the media, and engagement typically happens at the qualitative level—only a few people dig into quantitative value.

Further, betting markets are not liquid. Big dollar, profitable sports bettors are blocked from placing wagers—or highly throttled in the degree to which they can wager. This means that the market—to the extent its a market at all—does not fully account for all of the information.

Oddsmakers don’t need to care about this.

Oddsmakers job is to set a line that will attract good action.

Setting the stage, and initial observations.

To understand how lines operate, we need to think of a few different variables:

• t - the true outcome

• q - the amount of public money in play

• r - the amount of sharp money in play

• a_q , a_r - The ratio of public (and sharp) money on the A side

• v - the Vegas line

From here we can start drawing relationships between the variables.

• As v gets farther from t, r increases faster than q.

• As v gets farther from t, a_r increases faster than a_q.

This is to stay, because the sharps are by definition sharp, they will notice a line that is very wrong and bet it heavily.

As corollaries

• The limit of s, as v goes to t, is 0.

• The limit of a_r as v goes to t, is .5

Which is to say, that as the oddsmaker gets the line more and more correct, the sharps will both dial back their betting and bet more evenly.

In contrast, we have two corollaries about public money.

• The limit of q, as v goes to t, is greater than 0.

• The limit of a_q, as v goes to t, is greater than .5.

This is to say, public money will be in play even if Vegas sets the line perfectly.

But if oddsmakers do something extreme…

• As the distance between v and t grows, q will increase and a_q will approach 0 or 1.

When the line is very wrong, people will notice and take advantage.

Given that v≅t, the oddsmaker maximizes its profit when q and r are the largest.

Because of the VIG, oddsmakers have an inherent edge, so they will make the most money when q and r are large.

But because we also know that as v approaches t, r goes to 0. And oddsmakers wants r to not be zero. So v will not—in most cases—equal t.

The Vegas line will not in most cases represent the true likelihood of a team winning a game.

In fact, oddsmakers are incentivized to set v maximally far from t, such that it maximizes q+r, and keeps the quantity a_r x r + a_q x q - (1-a_r) x r - (1-a_q) x q below, say, 10%.

That is not always possible.

For example, consider last Super Bowl, where the money and the public heavily favored Kansas City. The Chiefs received 75% of the bets and 70% of the money—even though the relative strength of talent was on the 49ers.

In this situation, Vegas could hardly move the line to be more Chiefs friendly—this would expose them too heavily to sharp money. Rather, they tried to keep the line as close to “true” as possible and remove the sharp money from the field—leaving only the public money which is massively positive return for oddsmakers.

Kelly Strategy

But how does oddsmakers know what the pros are going to do?

Professional betters follow the Kelly Strategy, or similar rules, with their bets. The Kelly Strategy supposes that we can find an optimal size for our bets by comparing two quantities: the probability of winning and the ratio of return.

The higher the probability of winning a bet, and the higher the ratio of return, the more money we should wager on that bet.

Mathematically, a “Kelly Bet” is formalized as follows:

Where the terms are defined as follows:

• k is the correct “Kelly bet”, or the fraction of your bankroll you should wager

• p is the probability of winning the bet

• b is the return on the bet

How are these numbers influenced by our oddsmakers numbers above?

We know that as the distance between t and v increases, that professional bettors put more money in play. This occurs because oddsmakers are either increasing p while holding b constant, or increasing b while holding p constant. The former condition occurs for spread bets, while the latter occurs for money line bets.

Consider a hockey game between the Buffalo Sabers and the Detroit Red Wings. We know that the true likelihood of Buffalo winning the game is 60% and that they should be favored by 1.5 goals.

If oddsmakers move their line from Buffalo being favored by 1.5 goals to only being favored by 0.5 goals, the Kelly Strategy tells us to bet this game more than previously because p is now higher than it was before. In this example, Buffalo had a 50% chance of winning by 1.5 goals and a 60% chance of winning by 0.5 goals. So p has gone up 10%.

Assuming a standard -110 VIG, this changes our Kelly Bet size dramatically. We go from a no-bet (-0.06) to a massive pro-Buffalo bet: 15% of our bankroll, or about 7 units!

If instead, oddsmakers move the line from the standard -110 VIG to +115, they have now changed b. As b increases from 0.91 to 1.15, our bet size increases from no-bet (still -0.06) to a meaningful bet of 3 units (0.065).

In fact, oddsmakers moving the money line from -110 to +105 is enough to tip a 50/50 proposition from a no-bet into a 1 unit bet. This type of change goes unnoticed by even regular public bettors—but it changes the math for the professionals and the expected return from a line for oddsmakers.

So, the oddsmakers find themselves in a position where they can control what the professional bettors are going to do. And they can exploit what the public is going to do through the VIG or minor line tweaks. Therefore, oddsmakers can move individual lines to make sure that each game satisfies their own Kelly principles.

After all, oddsmakers cannot control the outcomes of games any more than sports fans. In every game, there is randomness. What oddsmakers must do, then, to avoid going broke, is make sure that each line is Kelly satisfying. That the amount of money they are exposed for on a given line is is appropriate to the likelihood that they win.

This is what creates the Pros versus Joes dichotomy in sports betting. Oddsmakers use the Pros to cover the risk of the Joes.

Again, let’s take a look at the last Super Bowl. San Francisco should have been about a 3.5 point favorite, for implied odds of about 65%. This means that at even money—assuming for simplicity that books lose about as much on a KC win as they win on a KC loss—our Kelly Bet size should be about 15 units, or 30% of our total bankroll. Being a bit more conservative and assuming KC wins 40% of the time, our Kelly Bet size is still 10 units—20% of our bankroll.

So if we make the assumption that $200 million of the $300 million in Super Bowl bets FanDuel took last year was on the point spread, FanDuel would need to have around $400 million in cash to support the size of their position comfortably.

So what is a line, and what does that mean for you?

To oddsmakers, lines are the vehicles by which they adjust their financial stake in the outcome of sporting events.

This means that at times it is not only possible, but strategically imperative for an oddsmaker to have a line that is wrong — because having a line that is correct could be catastrophic to one’s business.

As an individual, you can take advantage of that by looking for lines that are wrong.

There’s some zagging (the aforementioned Chiefs). But there’s also some truth in advertising: the Washington Commanders really are playing as well as it looks like they are.

Let’s dive in and take a look at the top of the table.

Top NFL Teams

Halfway through the NFL season we have a lot of data under foot. And we are mostly going to be talking about the teams we thought we would be talking about. If at the start of the season you had said the Bills, Lions, Ravens, Chiefs, Packers, and 49ers were among the best eight teams, someone might rightfully have asked if you were talking about 2024 or 2023. After all, all six of those teams played in the Divisional round games. And four made it to the conference championships: the Ravens, Chiefs, 49ers, and Lions.

That said, how consistent the top teams are disguises how much change there really has been at the top.

The 49ers are no longer dominant. The Chiefs are winning, but weakened. Meanwhile the Lions and Ravens look to be in stronger positions than ever. And the Commanders—wait, what?—are charging hard towards the top of the league.

Jayden Daniels

Washington was not the team we expected to be talking about and Jayden Daniels was not the breakout star that I expected. But then again, there are not good, data-driven ways of assessing the college-to-pros likelihood of QB success.

It is also the case that a good quarterback can change a lot—and Washington was already knocking on the door of relevance last season.

Daniels has not had unbelievably impressive games; however, he passed for 270 yards and racked up a 110 passer rating against regional rival Baltimore. His lanky build and running ability no doubt also draw comparisons to the Ravens’ two-time MVP Lamar Jackson.

What Daniels has accomplished is keeping the ball safe (only two interceptions), and having courage to throw the ball downfield: 8.4 yards per attempt. He scores only 11% on our P(100) rating. But we punish young players for the lack of evidence. Assuming he can stay healthy—which may be a strong assumption given his playing style and an existing rib injury—we’ll see his P(100) creep into alignment with his PSY rating. And we’ll see his PSY creep up as a result of his increasing P(100).

Right now, Daniels’ PSY of 50 is a solid, middle of the league rating. Not outstanding by any means. But 50 places him with veterans like Sam Darnold and Kyler Murray. And well above fellow rookies: Caleb Williams (18), Drake Maye (15), and Bo Nix (3).

Another Jackson MVP Season

True! — nervous — very, very dreadfully nervous I had been and am; but why will you say that I am mad?

— The Tell-Tale Heart, Edgar Allen Poe

Lamar Jackson has played in three full NFL seasons. He has won the MVP in two of them. That is a fact that Jackson doubters have to accept.

What is easier for them to accept is that in the playoffs Jackson is 2-4 with a combined passer rating of 75.

Jackson might be the league’s best “just a game” quarterback. When a game is just a game, Jackson delivers unmatched athleticism and a powerful arm. When he can be half of a two-headed rushing attack, he’s especially dangerous.

When the games and competition tightens, and Jackson is forced into a one-dimensional passing role—as inevitably happens with all quarterbacks—Jackson has historically been limited.

This year, Jackson is in top form. So if he is going to buck the trend, this should be the year. Jackson is top 3 in P(100), Yards/Att, and Success Rate - all the criteria that make up our PSY ratings. And he has recorded passer ratings above 100 in his last six games.

With who the Ravens play the rest of the year, it will likely be the playoffs that reveal the real Jackson.

🚨Fade Alert: Patrick Mahomes?!🚨

Of course, there’s another oddity about the top teams this year. The Chiefs are winning (unsurprising) and wildly over-valued (very surprising). Mahomes and the Chiefs do not have an inspired passing attack this year. The Chiefs frog-voiced phenom is having what could be the worst season of his career.

P(100) says Mahomes has a 46% chance of being good enough to lead the Chiefs to a Super Bowl; 5+ percentage points worse Jackson, Goff, and Purdy. An our PSY metric gives him a B-/C+ grade, while the three aforementioned rivals all receive As.

Yet Vegas gives the undefeated Chiefs the best odds to win the Super Bowl at +450.

Because Vegas’ odds do not need to be strictly probabilistic, that doesn’t necessarily mean there is arbitrage in the market—but when a middle of the road team like the Chiefs is valued so highly, there usually is.

Wait, but aren’t the Chiefs the sole undefeated team in the league?

Yes. And if the year was 1970, we would think that wins and losses were a meaningful way to assess a team’s strength. But we know better in 2024.

The Chiefs don’t even have the best point differential in their division (the Broncos do). By weighted expected points added, the Chiefs should be about touchdown underdogs when they travel to Buffalo in a few weeks. And plainly, they just don’t pass the eye test.

The unblemished record and name recognition boost their standing—but it shouldn’t fool us.

If you want to fade the Chiefs—and we do—here’s how to do it. Take the AFC half of the field and bet the Ravens, Bills, and Texans. Make both the Ravens and Bills 40% of your bet, and splash the Texans with 20%. Assuming this pays out around 1/3 of the time, you’re in the black.

What does that mean? It means you can believe there’s a 50% chance that the NFC will win the Super Bowl, and a 16% chance the Chiefs or another AFC team win, and still be making money on this bet.

15-16% is consistent with the Chiefs being a top 6 or 7 team, but not a top 3 or 4 team. And there are too many good numbers suggesting that Kansas City is not a top 3 team right now.

This year, we’re most interested in two types of players: young quarterbacks and injured quarterbacks. And both of these players share a trait: we have less recent data on them than we’d like, so we don’t know exactly how they’ll perform.

To that end, we’re making some changes to the P(100) ratings so that the ratings better account for this uncertainty. And namely, so that they handle the limited information we have about players more cautiously.

CJ Stroud, for instance, has barely played a full season of football. How much do we really know about him? Aaron Rodgers has just been injured for an entire season. What do we know about his recovery? The updates to the P(100) algorithm address these questions.

Changes to the P(100) Ratings

Previously, P(100) sampled with replacement from a quarterbacks historic performances to assess the likelihood that a four-game sequence would average a Passer Rating of more than 100. We deemed this to be the threshold at which a player was playing “Super Bowl winning football”.

This had the problem of over-weighting hot-streaks of top performers. In some sense, this is no different than what the media does, celebrating the likes of Vince Young and Robert Griffin III before they would disappoint with lackluster careers. But that is not what we want to do.

Now, players that have played less than a full slate of games—30 games within the last three years—we randomly sample at a player specific rate from a generic pool of games, based on the number of games they have played.

We create three pools of generic games, as follows:

• Players playing between 1 and 10 games

• Players playing between 11 and 20 games

• Players playing between 21 and 30 games

The player specific rate of sampling from the generic pool is defined by:

Where G is the number of games a player has played.

So C.J. Stroud, for example, has played 18 eligible games. Therefore, his resamples are composed of 60% of his own games (18/30) and 40% of random games from quarterbacks playing between 11 and 20 games.

This has the effect of reducing Stroud’s rating, which makes sense. We don’t know how Stroud will perform this year. As the year progresses, we’ll get more data, and have higher confidence in his ability to play well for a four game stretch.

PSY Rankings: Probability, Success, Yards

Also, beginning this week, we’ll be publishing a new ordinal metric alongside P(100): PSY. PSY, which incorporates P(100), Success Rate, and Yards per Attempt, measures how good a quarterback is relative to their peers.

Unlike P(100), which has a specific real-world, on-field meaning—PSY is more abstract. It is a comparative measure: how good is a quarterback compares to their peers on three measures that we care about: P(100), Success Rate, and Yards per Attempt. Together these three measures provide a holistic picture of how good a quarterback is over the course of a few games and for a single, dramatic play.

We will still use P(100) as our primary rankings—but PSY adds another perspective.

PSY is designed on a 0 to 100 scale, with 100 indicating a quarterback who is the best in the league at all 3 categories, and 0 indicating a quarterback who is the worst in the league at all 3 categories.

For our initial PSY ratings, Patrick Mahomes leads the league (94) and Bo Nix comes in last (6).

Because we’re using 0 to 100 scores, these can easily—and somewhat faithfully—be interpreted as letter grades. In that case, across the league, only three players earned better than a C: Mahomes, Purdy, and Allen.

Early-Season QB Ratings

Which brings us, finally, to our early season QB ratings. Normally, we’d be reluctant to use any data after week one: a single football game is not a very conclusive sample. But that too is part of the magic of P(100). Because P(100) is a rolling metric that uses historical data from past seasons, we can weigh in—even after just one game.

Our QB ratings show that last years two Super Bowl contenders—the 49ers and the Chiefs—are in pole positions once again. Mahomes’ excellent Super Bowl run last year boosted his P(100) rating. And both Mahomes and Purdy have been falling from their heights at the start of last season, they still earn the top ratings—with some wiggle room. If the Chiefs and 49ers fail to make the Super Bowl this year, it is unlikely to be quarterback play that holds them back.

Was Paying Prescott Smart?

Dak Prescott got paid. Which makes sense considering his steady career play. However, one can’t help but look at his playoff performances and wonder if the Cowboys aren’t making a mistake. Prescott’s TD/INT ratio drops from >4:1 to just 2:1 in the playoffs; his passer rating drops 10 points; and he throws the ball less aggressively—averaging half a yard less per attempt than average.

Prescott will certainly not be a problem for the Cowboys in the regular season. And P(100) says he should be good enough just under 50% of the time. And he is if we just look at playoff outcomes. But if we dive into individual games, we find a handful of stinkers that got the Cowboys eliminated.

In particular, a 2022 game where the ‘Boys were eliminated after scoring only 12 points against the 49ers. This effort was led by Prescott’s 2 interceptions, 5.5 yards per attempt on 40 attempts, and passer rating of 63.

Performances like that make it hard to argue for Prescott as the highest paid quarterback in the league.

And our new QB grading system—PSY—agrees. While P(100) has him near the top of the league, PSY rates him near Kirk Cousins, Matthew Stafford, and an aging Aaron Rodgers; behind the likes of Baker Mayfield, Derek Carr, and Jared Goff.

Stroud, Murray, Rodgers

Three quarterbacks—C.J. Stroud, Aaron Rodgers, and Kyler Murray—sit around 20 games in our sample. Which means we’ll get a lot of information about them this year. And so far, we’re getting pretty good information. Murray and Stroud both had respectable opening weekends. Stroud, especially. But to me it was Murray, who many had written off, that stood out.

He needs to move the ball down the field more. But in his first three seasons when he was making Pro Bowls, his average was close to 7.5. Does that Kyler still exist?

Does the Aaron Rodgers of 2021 still exist? There were several throws on Monday night that said yes. And his success rating and yards per attempt ratings tell the story of a quarterback whose overall numbers will get better.

The Jets have one of the easiest schedules this year, so that may work in Rodgers’ favor. Murray and Stroud will both be taking on the schedules that rank in the most difficult 33% of schedules—but at least Houston has some easier games in division.

Tell me the Odds

We like three games this week—but got our money in when the lines were 1 point in the other direction. As long as the 49ers stay under a touchdown against the Vikings, that’s a great number. And the Panthers are exactly the type of team that a Jim Harbaugh Chargers team should beat up. Cardinals were originally a slight dog against the Rams. The Rams are too Cooper Cupp oriented for my taste, and I like Kyler Murray a bit more than the market does right now. Lastly, we’re getting almost a touchdown with the Saints—who could outright upset the Cowboys, and our metrics like Carr to keep the game competitive.

• 49ers (-6.5) @ Vikings

• Cardinals (-1.5) v. Rams

• Chargers (-5.5) @ Panthers

• Saints (+6.5) @ Cowboys

Baseball games are fun. They’re enjoyable to go to and enjoyable to watch on TV. The athletes are talented. Home runs, diving catches and strikeouts are exciting.

What baseball gets wrong is that it does a terrible job of deciding a winner. After 162 games and then multiple rounds of playoffs, the World Series champion, more likely than not, is not the best team. And that’s a shame.

Looking back on last season, does anyone feel good about the claim that the 90-win Texas Rangers were better than all three of the 100-win Orioles, Braves, or Dodgers?

The English Premiere League has a different problem: their league ends with a whimper. After a long season, jostling up and down the table, the teams in contention end their seasons against hapless foes, who are lucky to draw.

Last season, for example, Arsenal and Man City were neck and neck down the stretch. But instead of playing competitive matches, they both frequented bottom of the table teams, like Bournemouth and Nottingham Forest.

Both sports problems, however, are solvable, if only they’d take a page out of one another’s playbooks.

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Information in Baseball and Soccer Games

Baseball and Soccer are different sports. Obvious enough. The difference that is relevant here is the amount of information contained in any individual game.

In soccer—like basketball—games contain a lot of information. We can be confident that the winner of a soccer game was better than the loser of the soccer game. If you want to win the Premiere League, you can only afford to lose 3 to 5 of your 38 games. That’s a winning percentage of around 80%, after we start factoring in draws.

In baseball, the amount of information per game is low. An excellent season, might end with a team winning 65% of their games and 105 wins. That’s 15% worse than their EPL counterpart.

Current Method of Crowning Champions

Which brings us to the current method each sport has for crowning champions.

In Major League Baseball, each team plays a 162 game season—a combination of frequent division play, regular within-league play, and infrequent interleague play. Then, the top six teams—three division winners and three wild cards—play off in series of increasing length.

In the EPL, the structure is more simpler. Each teams plays every other twice, earning three points for a win and one for a draw. The team with the most points at the end of the season is the champion. Additionally, simultaneous to the season, is a season-long tournament: the FA Cup. Every team in the Premiere League (among others), gets to compete in this tournament.

To measure the properties of these formats, we ran 100,000 simulations of each format, using team strength estimates from FiveThirtyEight’s MLB Elo ratings and ClubElo’s English club-strength ratings. As it currently sits, baseball’s format crowns the best team as champion only 35% of the time, and the EPL’s format crowns the best team only 66% of the time.

Meanwhile, both formats do an okay job of crowning a competitive team. About 4-in-5 winners can be considered an “elite” team across formats. Here, we define elite as within 5% points of beating the best-team in the league heads up. or no worse than +120 on the Moneyline for a single game.

And both formats do an excellent job of crowning winners from the top 10 teams in the league. We’ve seen this happen recently in the EPL. in 2016, Leicester City shocked the world, winning the EPL just two years after being promoted from the Championship league.

Of those numbers, the one that concerns me the most—and one of the reasons why we don’t cover a lot of baseball—is baseball’s mere 35% crowning the best team as their champion. This means that more often than not, we expect baseball to name a World Series winner who is not the best team in the league.

It makes it hard to get invested in a sport when you know the outcome is not telling you what you want to know.

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Taking a page from each other’s playbooks.

To improve the situation, what if baseball was a bit more like soccer and soccer was a bit more like baseball?

The Baseball Proposal

For baseball, we’re proposing they adopt a 160-game regular season, split into three parts:

1. 88 games of Division Play

2. 36 games of Qualifying Play

3. 36 games of Championship Play

In the the first 88 games, each team would play:

• 12 games against division opponents

• 4 games against every team from another division

• 4 games against a mix of rivals and randomly drawn teams

Following the Division stage, the league would be split into thirds, by standing: a top third, a middle third, and a bottom third. Each team would then play 4 games against the other 9 teams in their third. This would constitute Qualifying Play.

After Qualifying Play, a promotion and relegation cycle would take place, based on team records during the Qualifying Play stage. The top third would drop its worst two teams into the middle third. The best teams from the middle and bottom third would advance to the top third. And the worst team from the middle third would drop to the bottom third.

Then, the teams would play 36-games of Championship Play, with each team playing 4 games against each of the 9 teams in their third. The team in the top third with the best record during Championship Play would win the league.

This has three effects:

1. The team that wins the league is more likely to be the best team.

2. The final games played are likely to be competitive and consequential.

3. The integrity and legacy of baseball’s divisional play is maintained.

For added flavor, like English soccer, Major League Baseball could add a tournament featuring all 30 teams in best-of-7 series, that go on throughout the season, and conclude immediately following, or shortly after, the regular season.

The Soccer Proposal

For English soccer, our proposal is simpler: add a six team playoff to the end of the season. Give the top two teams a bye round. And have a home-and-away knockout tournament, a la the Champions League.

This adds 10 new, exciting games to the schedule, and ensures that the season ends with a bang, not a whimper.

Proposals by the Numbers

But what do these proposals do by the numbers? Do they increase the likelihood of the best team winning? Indeed, both do, by substantial margins.

After 100,000 simulations, the proposed baseball format increases the likelihood of baseball’s winner being the best team by 15 percentage points—up to 50% from 35%. Meaning under the new format, the winner of the baseball title would actually have claim to being the best team. In the Premier League, the likelihood of the best team winning it all goes from a 2-in-3 chance to a 3-in-4 chance. A substantial, change—even if it’s not as critical as the leap in baseball.

The new format also improves the Premier League’s odds of crowning an elite team as their winner, which goes up by 10 percentage points. And under our proposed format, the MLB improves slightly in their ability to recognize a top-third of the league team: jumping up to 98% from 95%.

In practical terms, this would solve both of the problems we mentioned at the start:

• Baseball would crown a meaningful champion

• The Premier League would have exciting end of season matches

But is also raises an interesting question.

Why does switching formats work?

How is it that baseball’s format is better for soccer and soccer’s format is better for baseball? If the playoff works for soccer, shouldn’t it work for baseball too? Or vice versa: if crowning the season leader is a good fit for baseball, why shouldn’t it be a good fit for soccer?

Which gets at an underlying emphasis of this post: all sports are different. We need to keep that in mind when analyzing them. We cannot blindly take things from one sport and drop it into another, assuming it carries with it all of its meaning.

Most often, this comes when we borrow baseball concepts and bring them to other sports. Sometimes this works. Sometimes this is foolish. In this case, carrying baseball’s playoff system into soccer works well. But even then, baseball has more to gain by copying soccer’s league system.

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That said, defense is still half the game.

This season, we’re going to dive deep into defense at Wolohan Analytics, with a five-part series.

Here’s the plan

• September: Overview of Defensive Metrics

• October: Pass Rush

• November: Pass Coverage

• December: Rush Defense

• January: Overall Defense

So grab your chinstrap, and get ready to hit someone. This NFL season, we’re highlighting defense.

To come up with this list, we found the quarterbacks who have the widest range of outcomes by P(100)—a Wolohan Analytics original metric that estimates the likelihood of a quarterback playing at 100 Passer Rating level, for four or more games. This is approximately the level of performance needed for a quarterback to win the Super Bowl. For example, Patrick Mahomes had an average Passer Rating of 100.3 in his ‘23-’24 Super Bowl run.

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Can they come back?

The first two quarterbacks we’re watching this season are Joe Burrow and Aaron Rodgers. Both Burrow and Rodgers have had elite seasons. Rodgers won back-to-back MVPs in 2020 and 2021, and Burrow took an uninspired Cincinnati franchise to the brink of a Super Bowl title in 21. But both found themselves on the bench last year, due to injuries.

Can either reprise their great form?

Burrow entered the league after a long college career and is already 27, with only 2 full NFL seasons in the books. His performance isn’t a question when he’s on the field, but if his durability wasn’t a concern before—it must be one now.

While Mahomes may have the recent hardware, Rodgers still has a claim to being the best quarterback in the league. But at 40 years old, it’s hard to know what the 4-time MVP has left. 2024 will be Rodgers 19th season and his first with the perennial loser New York Jets.

Can they keep it up?

For three quarterbacks, the question isn’t can they be great. It’s how long can they keep being great? Brock Purdy, C.J. Stroud, and Jordan Love all fall into this category.

Purdy is coming off of 20+ great games—but he has never had the shine that the others have. Meanwhile, Stroud and Love have much thinner resumes—each only playing well for about half a season. But memories are short in the National Football League, and the hype around Love and Stroud is high.

Can any of these three keep up their masterful performances?

Purdy is the best bet to repeat his performance, as we already have more than a season of evidence that he can produce. Stroud was inconsistent throughout his rookie year, while Love was streaky. Because of that, if asked to pick a player second most likely to have a great year—Stroud or Love—I’d choose Love.

Can they stand out?

There are two quarterbacks who ostensibly have good spots and solid resumes, but are still underwhelming: Tua Tagovailoa and Justin Herbert.

Tagovailoa looks to be at the helm of one of the NFL’s hungriest offenses, down in Miami. And Herbert is paired with one of football’s all-time great coaches in Jim Harbuagh.

There’s little to say about these two, other than that, we’re expecting a lot from them this season. Can they deliver?

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Can they compete?

And lastly, our attention turns to the rookies. Best case scenario, they find themselves in the “Can they keep it up?” category next year—but being compared to C.J. Stroud, Brock Purdy, or Jordan Love means a playoffs run in your first season at the helm.

There’s no NFL data yet on Caleb Williams, Bo Nix, Jayden Daniels, or Drake Maye. So it’s anyone’s guess what we’ll get from these four. Williams is the favorite to make a splash, but plays on the offensively inept Chicago Bears. And the NFC North is tough, featuring both the Packers and Lions.

Bo Nix—who is paired with head coach Sean Payton—is my favorite to make a splash.

So, what about everyone else?

We only mentioned eleven quarterbacks that we’re watching. Why so few? Simple. The performance of the other quarterbacks in the league has been consistent—so we do not need to worry about their performance.

Patrick Mahomes and Jared Goff will put up strong, but not overwhelming regular season numbers.

Dak Prescott and Kirk Cousins will do the same, but lose all the big games.

Lamar Jackson will have a great season, but is ultimately a weak and exploitable opponent.

Jalen Hurts, Geno Smith are fine starters—but if they’re on your team, you should be wishing you had someone else.

We don’t have reason to suspect these players performances will vary much this year. So we’re slotting them back into their performance over the last two years. For some that’s not bad.

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Both were gold medalists this year.

But not all gold medals are created equal.

Because some sports are more upset prone than others, greatness can really only be measured within a sport.

So, while it may make sense to compare LeBron James and Michael Jordan, it makes no sense to compare Michael Jordan and Tom Brady. Even comparing Babe Ruth and Shohei Ohtani is on tenuous ground: the equipment, rules, and overall professionalism of the sports render “greatness” in the two games markedly different.

This all leads us to the question: Which sports are the easiest to be “great” in, and which are the hardest to be great in?

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Causes of Greatness

Greatness, as measured by success over time, is a result of an athlete’s average ability and variance, compared to the average ability and variance of their competitors.

For example, an athlete who is much, much better than their competitors (on average), may have a hard time demonstrating it if the sport is sufficiently random. Think about baseball or golf here. Season to season, or tournament to tournament changes in performance are so large, that no single baseball season or golf tournament tells us much about anything.

Indeed, the best golfers in the world right now all have two career major victories to their names: Scottie Scheffler (2024 Gold Medalist), Bryson DeChambeau, and Xander Schauffele. Brooks Koepka is the exception with five major titles.

Compare that to Carlos Alcaraz, the rising Spanish tennis star, who has won 4 grand-slam titles in two calendar years (2023-2024).

Tennis is a sport—like basketball—with relatively less randomness. In tennis, we expect that the top players will win a vast majority of the time. At least this is true for men’s tennis.

Heuristics for Difficulty of Greatness

What makes a sport like swimming or the 100m dash easy to be great in, but a sport like golf or archery hard to be great in? Here are some heuristics we can use.

1. Simplicity. Sports that are simple are easier to be great in. Sports that are complex are harder to be great in. Swimming and sprinting involve moving your body in a single motion again and again. The devil in the details—but neither requires you to master as many skills as golf, or soccer, or gymnastics. The more skills one has to master, the more room for error.

2. Standardization. Some sports are standardized and some are not. The 100m dash takes place on a similar track every time it is raced. The 200m freestyle takes place in a similar pool. But golf? Every course is different. The same with events like sailing or cycling or even long-distance running events. As the weather changes or the courses change, the complexity changes. Some athletes will do better in calm conditions and some will do (relatively) better in poor conditions. This is in part why football (an outdoor game) is more variable than basketball (an indoor game).

3. Size and Structure. Sports with small teams are going to be easier to excel at than sports with large teams, and some tournament structures will favor the stronger competitors over others. For example, the NFL’s single-elimination playoff and the NCAA March Madness tournament favor underdogs; the NBA’s best-of-seven format and the Champions’ League home-home format preference the favorites. Individual sports are the easiest to demonstrate greatness in, because one needs not rely on anyone but themselves. Team sports are the hardest, because one must depend heavily on their teammates. How many titles would Derek Jeter have had without Andy Pettitte or Mariano Rivera?

4. Strategy. Strategic sports are more difficult than those without a strategic component. The sports that boil down to go and do the best thing that you can—such as gymnastics—are much easier than those that involve a competitive tit-for-tat. The variety of options in a sport like table tennis make it more complex than something like weightlifting. There are more things you need to prepare for in boxing, badminton or volleyball than air pistol or equestrian.

5. Small Margin of Victory. Sports where the margin of victory is smaller than the variance in performance are going to be much harder to be great in than sports where the margin of victory is larger than the variance in performance. In American Football, for example, is often won by less than a touchdown. The Chiefs scores throughout the season ranged from 13 points to 31 points: an 18 point difference! That means it is hard to be great. Usain Bolt, on the other hand, had performance variance of about .1 seconds—only a hair larger than his closest Olympic 100m race, which was separated by .09 seconds! On his worst best day, Usain Bolt was beating his competitors.

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Assessing Difficulty of Being Great by Sport

We can use these heuristics to assess how hard it is to be great in each sport. And, if our heuristics are good, this should comport with the on-the-ground reality of the sports.

Let’s approach these sports in two ways: by category (popular sports, secondary sports, and olympic sports), and by how much they lend themselves to greatness (less, somewhat, more).

Greatness by Sport Category

Among the popular American Sports, football is the hardest to be great at and basketball is the easiest. This compatible with reality. The Lakers and Celtics both have twice as many championships, during the Super Bowl era, as the top NFL teams. The prevalence of dynasties in basketball—often multiple at the same time—is further evidence of this. LeBron James and Steph Curry; Kobe Bryant and Tim Duncan; Michael Jordan and Hakeem Olajuwon; Magic Johnson and Larry Bird—that basketball has dueling greats is assumed.

Soccer, Baseball, and Hockey fall in the middle. It is possible to have great runs—especially when a star studded cast assembles—but the fundamentals of the sports require those stars to be surrounded by other great talents. Ronaldo, for instance, has been much less potent on Portugal than on Manchester United or Barcelona.

The less popular American sports—golf, auto racing, combat sports, tennis—are all in the same ballpark as the non-football sports. Tennis, like basketball, lends itself to dynasties and champions. And we can see the lineage clearly from the Federer dynasty, to the Djokovic dynasty, to the blossoming Alcaraz dynasty.

Golf is much more like soccer. The best are better than the rest—but upsets happen regularly.

It’s worth taking a look at why the sports are rated as they are. For example, tennis and boxing/MMA get similar ratings, because both are defined by being individual sports with relatively large skill gaps between the best and the rest. Meanwhile, they differ in that tennis is highly variable—with multiple surface types and weather conditions—while, combat sports are more strategic. There is truth in the old saying “styles make fights”.

Lastly, the olympic sports all finish after the popular and secondary American sports. These sports—mostly simple, standardized, strategy-less, individual affairs that have relatively large margins of victory between the greats and the rest—are almost designed to encourage greatness. Of the four popular Olympic sports that we score, only beach volleyball is comparable to popular American sports.

Sports by Tier of Greatness

Looking at the sports in our list, we can quickly come up with three tiers of sports: sports in which greatness is rare, sports in which greatness is expected, and sports in which greatness is common.

Greatness is Rare Tier. In Football, Soccer, Baseball, and Golf, great teams are rare. At the accomplishments of the great will be modest relative to the accomplishments of the good. In these sports, we expect a relatively even playing field. Many teams and players will be in contention. And even when a team is elite, many of their victories will be close.

Greatness is Expected. In basketball, NASCAR, boxing, hockey, tennis, and beach volleyball, we expect to have a dominant force in the sport at any given time. For instance, it’s odd that there’s no clearly elite team in the NBA. It might be the first time in the history of the league there is a serious run of parity.

Greatness is Common. In gymnastics, running, or swimming, a great athlete will run head and shoulders above the competition—able to win without much challenge or suspense. For instance, Michael Phelps, Usain Bolt, Katie Ledecky, Simone Biles. None of those athletes was particularly challenged in their runs to gold.

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Ultimately, when thinking about sports, it is helpful to think about the things that make that sport different than other sports. How sports relate to the fundamental human movements and skills, can tell us a lot about how to analyze them.

For the most part, the sports we’re interested in will be complex team sports. Their complexity makes them the most interesting to watch and to root for—and the hardest to analyze.

Anthony Edwards has taken the league commentariat by surprise. Several blowout wins over the defending champion Denver Nuggets, and he is being proclaimed the next Michael Jordan.

Meanwhile, the Nuggets are out. What credit should we give or take away from Jokic?

And how are our Manalytics-based NBA finals predictions going?

Ant Man: Already a Superhero?

Minnesota has a really good team. And Anthony Edwards is the beneficiary of Minnesota’s completeness. He is not yet a complete player. His offense is inconsistent. And yet, dropping 40 points on the defending champs—who struggled through the regular season and had a limited roster—is something.

What should we make of this?

Not much, yet.

Edwards still needs to prove himself, and this next round against Doncic and Irving is just the matchup.

Unlike Denver—who struggled with shooting throughout the series—Dallas comes out of a series in which their shooting was the difference maker. And unlike Denver whose number 2 player—Jamal Murray—was inconsistent and easily denied, Kyrie Irving is unlikely to be.

Irving showed as much in Dallas’ Game 1.

We did not advise betting the Wolves, despite their place atop the Western Conference standings on and off throughout the year, because of Anthony Edwards not in spite of him. The 22 year old is too inconsistent.

If the Wolves do win, it will need to be his Edwards’ teammates who step up to win games. At this point in his career, Edwards is worth a game or too—but not a series.

Jokic and not much else.

Denver has never been held back by Jokic, who many believe is the best player in the world. And who, by virtue of his greatness, puts his team in title contention every year. However, basketball is a not baseball. Basketball is a team sport.

Jokic cannot win titles with such mediocre play around him.

The Ringer produces a ranking of the Top 100 NBA players (Jokic is #1.) Here is how the other quarterfinal teams compare to the Nuggets.

Denver has talent. 5 guys who are undeniable contributors around the league. But they lack options compared to Boston or Minnesota. And they lack the versatility of the Doncic/Irving combo in Dallas.

One of the great things about Doncic and Irving is that they can play independent of one another. Irving can score on his own. Doncic can score on his own. Facing two guys who can generate offense is a complex defensive challenge.

Jokic doesn’t get that luxury. And the league is just too good for one excellent player to overcome a team talent mismatch in a seven game series.

In our NBA eras discussion, noting that the LeBron era was over, we said that this era could be the era of Jokic.

However, for Jokic to have his own era, he’s going to need a better supporting cast. Jamal Murray and wishful thinking is not going to be enough for a sustained championship run.

NBA prediction review

How are our NBA predictions doing? We teased this already at the top, but they’re going well. Especially with our two remaining teams up a combined 3-0 after 3 games of the NBA Conference Finals. Another win by the Mavericks could put us in the money.

The Wolves have been the spoiler for us all along. But again, Anthony Edwards inconsistency is a promising sign. And we just haven’t seen anyone match up with Boston to any real effect all post-season.

Doncic is undeniably the best player left in the tournament. And you have to feel good about getting the best player and a one game edge.