People usually want to see the numbers for a single season, which is a relatively small sample size for a regression without a suitable prior. In most of its use cases, NPI RAPM has noticeable weaknesses. This leaves us with two versions of RAPM: non-prior informed RAPM (NPI RAPM) which uses nothing but the lineup metrics, or prior informed RAPM (PI RAPM) which improves the accuracy of the model in small samples by incorporating box score numbers. Instead of regressing to zero, you can regress to this prior value. Improvements upon RAPM like RPM and RAPTOR incorporate Bayesian priors with box score and tracking stats to give a better prior estimate of player value for the model. Or even points scored by a specific player – just the overall plus-minus in that duration of time. No assists, rebounds, steals, blocks, etc. Notice that at this point, the only stat that has been used is the stint plus-minus for each combination of players on the floor. This equation is the method used to calculate regularized adjusted plus-minus (RAPM). We can then solve for x which is a vector of coefficients corresponding to each players representing their on-court value.Īn optimal lambda value can be found which yields an approximate solution to the original Ax=b problem. Suppose that we have a matrix called A representing the players on the floor (one column for each player, a value of 1 if they’re on the floor for that stint and a value of 0 otherwise) and a vector b representing the plus-minus per 100 possessions for each stint. That’s the idea of Adjusted Plus-Minus (APM) – solving the system of linear equations representing the players on a court and the associating plus-minus for their duration on the floor. So, we need to adjust for the other players on the floor. Did he get that much better? Of course not – the Brooklyn Nets are just far more equipped to play at a high level without Harden on the floor than the Rockets were. James Harden posted an on-off plus-minus of +9.1 in 2020, which pales in comparison with his +0.2 mark in 2021 (albeit on a small sample size). Furthermore, while a quick look at on-off plus-minus may let you know that a player is carrying their team, it tells you more about how strong a team’s bench is than anything else. In other words, base plus-minus does not adjust for the strength of your teammates. If an inferior player’s minutes heavily aligned with Curry’s, their plus-minus would look far better than it should just because they get to play with Curry. While easy to understand, the traditional plus-minus metric is very flawed. Steph had a +8.6 on-off plus-minus, meaning that the Warriors outscore their opponents by 8.6 more points when Steph is on the floor than when he is not. You can also compare this to his net plus-minus compared to when he’s off the floor. This number means that with Curry on the court, the Warriors outscored their opponents by four points per every 100 possessions. For example, Steph Curry had a +4.0 plus-minus per 100 possessions in the 2021 season. What if we could really assess player impact without needing to rely on these numbers?Ī traditional way to represent player impact without box score stats is to just use base plus-minus. We can always look at basic statistics like points and rebounds, but what about everything that doesn’t show up in the box score? Skills like setting effective screens, contesting shots, boxing out, and off-ball gravity can all have a huge impact on any given basketball play while not showing up in the box score. Winslow Townson – Associated Press Backgroundīasketball analysts have searched for years for a viable all-in-one metric for quantifying the on-court impact of basketball players.
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