APBRmetrics

A concept first brought up to me by Mark Glickman and originally developed for basketball by Sameer Deshpande of Wharton university is the concept of a player's influence on the probability that his team wins an NBA game

A team's probability to win a game is dependent on a) time left in the game, b) current lead (can be negative), c) whether they have the ball and d) the players on the court

To give an example: If your team is down 2 with 1s to go (a scenario where you're unlikely to win), and you hit a 3 as time expires you changed your team's probability of winning the game from <50% to 100%
On the other hand, if you're up 2 with 1s to go, and hit a 3, you only moved your team's probability of winning from ~>95% to 100%
Somewhat obviously, it is more important for your team to go on a run in a tight game, vs when being up by 20+

One can use the standard APM framework to carry out the analysis, but the y-vector - filled with points-per-possession in APM - gets replaced with changes of win probability.
Thanks to the APM framework we can then estimate each player's influence on win probability, controlling for factors a)-d) from above - most importantly controlling for who you're on the court with.

What it does - somewhat in contrast to (R)APM - is rewarding for good performance "when it matters". Scoring points late in a game when you're already up 25 will not lead to a better rating. This is equivalent to "throwing out" observations when the game is already won or lost. It has to be noted that tests that I have carried out several years ago have not revealed any significant benefit of down-weighing (or throwing out completely) certain possessions/observations

Whether this method provides any improvements over RAPM in terms of prediction accuracy remains to be seen, but it's an interesting concept and I wanted to share results.

Single year https://docs.google.com/spreadsheets/d/ ... sp=sharing
This suggests that having Draymond Green on the floor for the entire game raises your probability of winning by 13.2% (assuming 200 possessions, which is actually a little high)
Multi year https://docs.google.com/spreadsheets/d/ ... sp=sharing
Multiyear ratings can reach higher values, an effect of penalization

Results may vary with implementation. Here, I've used Ridge Regression. Sameer is using L1-penalization

Data from basketball-reference.com

Spectacular work!

So, given the crazy WPA in certain specific situations, are the results more highly regressed than normal RAPM? In other words, is the optimum lambda larger?

Alright then here comes another momentum-related post. As the fifth factor and "break" as the possible 6th factor. Analyse below:

234 seconds : Trailing by 16 : Ball Possession : Lineups 1 : 8-0 in the last 54 seconds
234 seconds : Trailing by 16 : Ball Possession : Lineups 1 : 2-3 in the last 54 seconds
234 seconds : Trailing by 16 : Ball Possession : Lineups 1 : 2-3 in the last 54 seconds : Timeout was called 7 seconds ago : 2-3 before TO.
234 seconds : Trailing by 16 : Ball Possession : Lineups 1 : 2-3 in the last 54 seconds : Timeout was called 7 seconds ago : 0-3 before TO.

234 seconds : Trailing by 9 : Ball Possession : Lineups 1 : 10-5 in the last 54 seconds : Technical foul was called 4 seconds ago : 10-0 before Technical Foul.

So I can't agree with this statement:

A team's probability to win a game is dependent on a) time left in the game, b) current lead (can be negative), c) whether they have the ball and d) the players on the court

Edit: Besides the score and breaks in those late short-periods, you should also include power dunks, impossible shots, long 3s, hard fouls, airballs, missed dunks, powerful blocks, crowd noise, injuries as variables that affect the momentum . Those're surely going to make it harder for you to control momentum in any kind of statistical approach.

Interesting idea, but it's subject to the same problem that WPA (win probability added) has in baseball: not all teams, and thus not all players, face the same "potential win probability to add".

E.g. some games are seesaw affairs, as with the Celtics at the Blazers a couple of nights ago (early large-ish lead for the Celts, furious comeback by the Blazers to take a large-ish lead, late furious comeback by the Celts to get a 1-point lead late in the 4th quarter, Blazers come back again, for good, with maybe a minute left).

In such a game there's a lot of opportunities for players to change their team's win probability from say 0.10 to 0.90 (and of course opportunities to see it plummet).

Whereas a more staid game where a team started with a win probability of 0.50 or whatever, jumped out to a lead and so had a 0.90 win prob, and basically maintained that throughout the rest of the game gradually raising it to 1.00 -- well there's only 0.50 of WPA to distribute.

In some cases this is fitting and proper: during the post-Shawn Kemp era, the Sonics depended mightily on Gary Payton. When Greg Anthony arrived, he was not experienced at playing the Sonics' gambling double-teaming defense and was initially a horrible backup PG. With Payton on the floor they'd slowly painfully build a small lead, and when he rested Greg Anthony would come in and the Sonics' lead would evaporate at the rate of a point a minute (so in say 10 minutes of action, Anthony would put up a -10 unadjusted plus-minus). So when Payton came back in the Sonics would have a low win probability and Payton would have to rebuild it again, rinse and repeat in the second half when Payton rested and Anthony frittered the lead away. (I should add that by late in the season he became much better and was one of the better backup PGs in the league, which pretty well describe his whole career: marginal starter, but if he's your backup PG you're pretty happy).

In Payton's case, the repeated dramatic buildup from losing the game to being ahead was an appropriate measure of his importance to the Sonics. But suppose they were a better team, or simply had a better backup PG, so that most of the Sonics games were ho-hum affairs of going from 0.50 to 1.00 win prob. Payton would've been the same player but would've added less win probability to the team.

In short, WPA does a nice job of measuring how much players contributed to victory, but the measures are highly context dependent. A one-man team such as the Sonics with Payton will result in big WPA numbers, but put Payton on say the Spurs and he would have lower WPA.

So WPA measures results, not talent. And almost certainly has less value for predicting how a player will do next season, and maybe even for the remainder of a current season.

But if we want to measure results (e.g. to hand out all-NBA prizes or MVP awards), it might be an interesting measure to use.

@mtamade

Doesn't it work for both ways? There's also same chance of "potential win probability to cost" for those players. I don't know how they do it in baseball but with a regression penalty here, crazy results for certain players can somewhat be controlled.

I just wonder how's it's out-of-sample prediction accuracy for those lineups that minutes come from new additions to teams in NBA games.

Do people still believe that 'clutch factor' is a big thing in pro sports?

Nate wrote:Do people still believe that 'clutch factor' is a big thing in pro sports?

I don't.

Most consider Westbrook and Durant top 5 players. By this one year metric they are 12th and 13th rated on win impact estimate. By multi-year Westbrook is 20th and Durant in the fifties. The tank years probably hurt them but this may reveal a relative weakness beyond that.

Harden is (correction) 74th on 1 year but 22nd on multi-year. One year more affected by randomness? Of course he may have been far less helpful too, but randomness may have heightened it.

J.E. wrote: This suggests that having Draymond Green on the floor for the entire game raises your probability of winning by 13.2% (assuming 200 possessions, which is actually a little high)

So you took Draymond's coefficient and... what? Averaged/integrated through all the values of time left in a game? Assumed the game was tied the whole way through? How do you determine 13.2? If it's simply what the regression spits out for Draymond, I'm not sure how you interpret it.

Statman wrote:

Nate wrote:Do people still believe that 'clutch factor' is a big thing in pro sports?

I don't.

Then you guys don't know a thing about human nature and sports. Don't tell this outside of this community or everyone will laugh at you

Jerry, do you have a good way to compare these results to standard RAPM? I'm sort of trying to do that from memory, but having them side by side to see where players differ would help me.

xkonk wrote:So you took Draymond's coefficient and... what? Averaged/integrated through all the values of time left in a game? Assumed the game was tied the whole way through? How do you determine 13.2? If it's simply what the regression spits out for Draymond, I'm not sure how you interpret it.

You simply replace the scoring margin with changes of the win probability in the response vector (usually named y). And then you run the regression normally. In that way you get win probabilities instead of APM values for each player. The interpretation would actually be that a player would raise/lower the win probablity over average by x percentage points.

I did exactly that for the past 3 seasons already, because, as J.E. will likely get as well (*), it is better as a predictor for overall team success than RAPM. Also, I use that for ranking player careers, because you can directly get the value by how much a player would increase the odds for a team to win a championship (which is the ultimate goal from my perspective).

(*) although my matchupfiles for the past 3 seasons aren't particular good

mystic wrote:...[WPA] is better as a predictor for overall team success than RAPM...

Are you using net WPA / team to "predict" team wins in the season that the data is drawn from?

Nate wrote:

mystic wrote:...[WPA] is better as a predictor for overall team success than RAPM...

Are you using net WPA / team to "predict" team wins in the season that the data is drawn from?

No, that wouldn't be a prediction. I mean out-of-sample prediction, to clarify that point.

mystic wrote:

Nate wrote:

mystic wrote:...[WPA] is better as a predictor for overall team success than RAPM...

Are you using net WPA / team to "predict" team wins in the season that the data is drawn from?

No, that wouldn't be a prediction. I mean out-of-sample prediction, to clarify that point.

Wow. That's not something that I would have expected.