Hi, had an idea for a basketball stat, want to know what you guys think of it. This could be potentially very embarrassing... as its very possible this is just geeky trash... but here goes Right now I find that traditional +/- we see in the yahoo box scores these days is more useful for measuring the strength of the groups a player plays in when he is on the floor, than it is for telling us how much of an impact a player has on the groups he plays in. My basic idea is to measure the impact of a player on the team by comparing the +/- of the specific 5 man groups he plays in with the +/- of the groups that contain all of the other 4 players EXCLUDING him. Concept is similar to VORP in baseball but here we are measuring value over replacement players within the player's own team using +/-. For discussion sake I'll call this stat "Player Impact" or PI. Simplified example of calculation: Player A is a rotation player averaging 15 minutes a game with a traditional +/- of +2. He avgs 10 mins a game with players A,B,C and D. This line up of "A,B,C,D,E" has an avg +/- of +4 in 10 mins of play every game. He avgs another 5 mins a game with players C,D,E and F. Line up "A,C,D,E,F" has a +/- of -1. "A,B,C,D,E" = +4 per 10 mins OR +0.4 per min "A,F,G,I,J" = -1 per 5 mins OR -0.2 per min This is then contrasted to how well the other 4 players in these line ups do when they are on the court at the same time without player A. "x-A,B,C,D,E" represents all the line-ups with players B,C,D and E that DO NOT include player A. We will also look at "x-A,F,G,I,J". The fictional +/- in this example for the line ups without player A that we are interested in are: "x-A,B,C,D,E" = +0.5 per min "x-A,F,G,I,J" = -0.3 per min This means that line ups with B,C,D,E did better without player A (by 0.1 per min), while line-ups with F,G,I,J did worse (by 0.1 per min) without player A. "A,B,C,D,E" - "x-A,B,C,D,E" = -0.1 per min "A,F,G,I,J" - "x-A,F,G,I,J" = +0.1 per min To calculate his PI: -0.1*10 + 0.1*5 = -0.5 His player impact is thus -0.5 in 15 minutes of play. We can say that his team on average scores 0.5 points less per game when he is on the floor, even though traditional +/- tell us that the rotations he plays with score 2 points more per game. Variants of this PI stat can include PI/min and PI/48mins, which for player A will be -0.03 and -1.6 respectively. Obviously PI has lots of limitations, and is not meant to be a "holy grail" stat that by itself tells us how valuable a player is. It doesn't take into account strength of opposition (which can vary, esp. for scrubs that only play in garbage time), and unlike the VORP stat in baseball that tells us the value of a player compared to the average MLB player, this PI stat only applies to the player's value over his team mates that replace him. For example, if player A is a starting PG whose backups are absolutely trash, it would skew his PI upwards. This also assumes that if player A does not play, his replacements would be able to sustain their level of performance without him in the line-up for longer periods of time which is unlikely. That said, PI still gives us a better picture of his individual impact on his current team than tradtional +/- does. At least that's what I think atm. Thoughts?
wanted to add that "We can say that his team on average scores 0.5 points less per game when he is on the floor" this is probably the most important part of PI. Am I wrong in saying this? If I can't say PI says this... then it probably won't be very useful stat.
What you are describing sort of a simplified version of adjusted +/-, or APM. If you go to basketballvalue.com, run by Aaron Barzilai, you can see calculated APM for players. He keeps them up to date over the course of the season. Methods discussed here: http://82games.com/ilardi2.htm And, in fact, adjusted +/- can be split into offensive APM and defensive APM, which I think makes it very intriguing. Steve Ilardi recently put some low-noise offensive and defensive APMs on the web, which you can look at here: http://spreadsheets.google.com/ccc?key=0AnGzTFTtSPx_dFVrZXdHNlNZQUJadllKUm1Ld294WkE&hl=en Lots of discussion on APM, methods, and results over at the APBRMetrics board.
Thanks for the links durv. Unless I'm misunderstanding what APM is, I think this is different from what APM does. Correct me if I'm wrong, but besides using possessions instead of per48minutes, isn't APM just using data for multiple seasons and weighting traditional +/- for more recent results to give a larger sample size? Is APM more than that? I think my proposed method would also benefit from using possessions instead of per48 and weighting multiple seasons, but even if you do that I think you would end up with very different scores from APM.
No, APM is trying to capture how much a player contributes to his team's scoring margin, adjusting for the other 9 players on the floor. Here's the idea in a nutshell. You can think of every game consisting of a number of distinct 5 vs 5 matchups. For example, in the first 5 minutes of a game, you could have players A1, A2, A3, A4, A5 from the Rockets facing players B1, B2, B3, B4, B5 from the Spurs or something. In that span where there are no substitutions, how much do the Rockets outscore the Spurs by? Then, on the next substitution, you have another 5 vs 5 matchup. What is the resulting scoring marging there? And so on. APM basically takes all those matchups and the resulting point differentials, over every game in a season (and, optionally for reducing noise, looks at mutliple seasons worth of information) to deduce how much each player contributes on average to those margins. And, you're right, there will probably be significant divergence between your results and what APM might show. But the basic principle of what you're trying to capture (a players contribution to the +/-, adjusted for other players on the floor) is the same. One other thing. APM isn't easy to calculate (I never attempted to do so myself), so there is definitely value in coming up with an adjusted +/- variant that is relatively easy to compute. I'd be interested to see how well your results correlate to APM over a large sample of players.
So, is APM isolating a player's +/- by comparing how the average replacement player performs with/against the same other 9 players? If it does, how does APM determine how much the differential for each set is weighted towards a player's 100 possessions?
I think you should post your idea over at the APBRmetrics board. There will be more people who can help you over there.
Durv: Sorry ignore my last post, I missed your edit, I thought you were saying they were the same thing. sbyang: Yeah, never heard of APBRmetrics board b4, or at least don't remember it. I'll probably start lurking there.
Maybe it will be clearer with a very simple case. Say we just have 1 game, and its 2 vs 2. Each team has 3 players (A1, A2, A3 and B1, B2, B3). Let's say, over the course of the game, we have the following matchups and results: A1 & A2 vs B1 & B2 for 20 possessions, +5 A1 & A3 vs B2 & B3 for 15 possessions, -4 A2 & A3 vs B2 & B3 for 20 possessions, +4 A2 & A3 vs B1 & B3 for 22 possessions, -3 A1 & A2 vs B1 & B2 for 19 possessions, +6 We want to calculate APM for each of the 6 players, based on this information. So, we set up the following model: a1 + a2 - b1 - b2 + e = 5/20 * 100 poss a1 + a3 - b2 - b3 + e = -4/15 * 100 poss a2 + a3 - b2 - b3 + e = 4/20 * 100 poss a2 + a3 - b1 - b3 + e = -3/22 * 100 poss a1 + a2 - b1 - b2 + e = 6/19 * 100 poss Then, you find values for a1, a2, a3, b1, b2, and b3 such that e is minimized. These are your APMs for each respective player. Obviously, for such a small sample of matchups, the results aren't going to tell us very much. That's why to get meaningful values without large errors, you need thousands upon thousands of these equations. And, preferably, you want data on each player playing in many different contexts (i.e. with many different team and opponent lineups) to accurately isolate the impact of individuals.
I THINK I understand now (maybe haha). I will definitely read up more on it. Thanks a lot once again.
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Very nice board with statistical analysis out the wazoo. Dean Oliver and other statheads post there. If you need a link : http://www.sonicscentral.com/apbrmetrics/
