P(100) Changes and Start of Year QB Rankings
Modifying our signature QB metric and introducing another to kick off the year. Plus some picks.
The first week of football has come and gone. And because of our top QB storylines this year, we’re making some changes to the P(100) ratings for this season.
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