Win Probability Graphs and Box Scores for the 2013 Season

[deepak]

So there was an interesting play last night in the game between the Rockets and the Knicks, and I'm wondering what this model used here for Win Probability can tell us.

The Knicks (the road team) had the ball with the score tied towards the end of the game. They got an offensive rebound on a missed shot and swung the ball to the top of the key where J.R. Smith was wide open for a 3-pointer, but the shot clock was also off. Smith took the shot and missed, and he was pretty much universally chastised for the decision to not hold for a final shot. He even claimed that he thought the Knicks were down two after the game.

If we breakdown the probabilities, what is the smarter decision in this scenario? Take the wide open shot that can put you up 3 and give you a decisive advantage, or hold for a last shot with a strong likelihood of heading into overtime (where, presumably, the home team would be at an advantage)?

[boooeee]

So there was an interesting play last night in the game between the Rockets and the Knicks, and I'm wondering what this model used here for Win Probability can tell us.

The Knicks (the road team) had the ball with the score tied towards the end of the game. They got an offensive rebound on a missed shot and swung the ball to the top of the key where J.R. Smith was wide open for a 3-pointer, but the shot clock was also off. Smith took the shot and missed, and he was pretty much universally chastised for the decision to not hold for a final shot. He even claimed that he thought the Knicks were down two after the game.

If we breakdown the probabilities, what is the smarter decision in this scenario? Take the wide open shot that can put you up 3 and give you a decisive advantage, or hold for a last shot with a strong likelihood of heading into overtime (where, presumably, the home team would be at an advantage)?

Oddly enough, a spanish language NBA website did just that (using my win probability model):

Recap from the Couch

My espanol isn't so good, but the Google translation is passable. Their conclusion: JR was right to take the three and I think I agree, but I may do the math myself just in case.

If you want to try your hand at it, you can use my Online NBA Win Probability Calculator.

[deepak]

If you want to try your hand at it, you can use my Online NBA Win Probability Calculator.

Thanks.

Supposing there was a 40% chance of that 3-pointer going in (it was a wide open look off an offensive rebound), and a 30% chance they get the offensive rebound in case of a miss. There's an 88.2% of them winning if the 3-pointer is good, and a 45.6% chance of them winning if its no good (the latter is probably a bit high, since its not factoring that the Knicks were the road team). So, this comes to a 62.6% chance of the Knicks winning the JR shooting the shot. On the other hand, the calculator gives the Knicks a 60.8% chance of winning when they have the ball with 19 seconds left and the game tied (again, probability a bit high since the Knicks are the road team).

If instead we give JR a 34% chance of making it (his season average), then the probability of the Knicks winning with him taking the shot drops down to 60.1%.

From this, it seems like it was a close call and Smith was unfairly blasted for it.

[Mike G]

In this Century, the home team has won .536 of 1090 overtime games.
In playoffs, it's 36/70, or .514

[Mike G]

If you want to try your hand at it, you can use my Online NBA Win Probability Calculator.

Hey, thanks for the access to this.
Is this a bug? Chance of winning with score tied and the ball, 12:00 remaining in:
1st Q - .507
2nd Q - .509
3rd Q - .518
4th Q - .507

Shouldn't your 4th Q odds be better yet than opening the 3rd with possession?

I'd expect to have the same odds with the score tied to end a quarter, knowing my team has the ball next. But with zero seconds showing at the end of the quarter:
1st Q - .511
2nd Q - .513
3rd Q - .517
4th Q - .549

That last entry is conflicted. You don't know you have the ball to start overtime. Odds with 0 pt-diff and 5:00 to play in OT are .536

How safe is a one point lead as the seconds wind down? Again, you have the lead and the ball.
Sec - W - L
10 - .864 - .136
8 - .876 - .124
6 - .886 - .114
4 - .896 - .104
2 - .905 - .095
1 - .910 - .090
0 - .913 - .087

The certainty seems to approach .913 rather than 1.000, as would be intuitively expected.
I'd also expect the certainty to accelerate towards 1.0, rather than slowing down as the seconds tick away.

[boooeee]

Such as declaring Chris Paul the 'least valuable player' in a game, which is the most erroneous conclusion possible?
It's essentially like watching the game 'highlights' vs watching the whole game. Which really tells more about 'what happened'?

It would be more interesting if it were like a plus-minus summary of all players on the floor, rather than just the one who made/missed the shot. It may well be that equal/more credit should go to the guy who set the pick, or made the pass, or the previous pass, or who got the offensive rebound and kicked it out ...

The MVP and LVP designations should be taken with a grain of salt. There is a lot that I am not measuring when it comes to WPA (it ignores assists and rebounds). But as others have remarked, this is a story-telling stat, not necessarily a tool for prospective player evaluation. I had toyed with including other stats in WPA, or even a plus/minus as you suggested, but I would prefer to keep things simple. I'm not looking to create a "master stat", rather I'm looking to measure one aspect of the game as cleanly as possible. I prefer to have several cleanly defined metrics to review, as opposed to several competing "master stats" that have different methods of weighting rebounds, missed shots, assists, etc.

[boooeee]

If you want to try your hand at it, you can use my Online NBA Win Probability Calculator.

Hey, thanks for the access to this.
Is this a bug? Chance of winning with score tied and the ball, 12:00 remaining in:
1st Q - .507
2nd Q - .509
3rd Q - .518
4th Q - .507

Shouldn't your 4th Q odds be better yet than opening the 3rd with possession?

I'd expect to have the same odds with the score tied to end a quarter, knowing my team has the ball next. But with zero seconds showing at the end of the quarter:
1st Q - .511
2nd Q - .513
3rd Q - .517
4th Q - .549

That last entry is conflicted. You don't know you have the ball to start overtime. Odds with 0 pt-diff and 5:00 to play in OT are .536

How safe is a one point lead as the seconds wind down? Again, you have the lead and the ball.
Sec - W - L
10 - .864 - .136
8 - .876 - .124
6 - .886 - .114
4 - .896 - .104
2 - .905 - .095
1 - .910 - .090
0 - .913 - .087

The certainty seems to approach .913 rather than 1.000, as would be intuitively expected.
I'd also expect the certainty to accelerate towards 1.0, rather than slowing down as the seconds tick away.

The model still needs some work for beginning and end of quarter situations, but for different reasons.

The anomalies you point out for the beginning of the quarter is probably a data sparsity issue. The ESPN play by play data usually doesn't tell you which team has possession to start the quarter, so the probabilities at the beginning of the quarter are probably dominated by a handful of data points in which a team lost possession early in the quarter. In theory, I should be able to derive which team has possession to start the quarter and then insert a row into the play by play data, but it's a coding exercise I haven't been able to get to.

The end of the quarter, particularly the fourth, is just difficult to model using regression. I try to tighten my smoothing window as the game gets closer to the end, but even with that, there are still the anomalies you point out. I'm thinking a tree based method is more appropriate once you are down to the final seconds, but I'm not sure how to blend that cleanly with my regression approach for normal game situations. I could also just manually adjust the probabilities, but I'm really hesitant to do that. Once you start adjusting the numbers to what you think they "should" be, it's hard to know when to stop.

Thanks for taking a look at the model, this is helpful in refining the methodology.

[boooeee]

In this Century, the home team has won .536 of 1090 overtime games.
In playoffs, it's 36/70, or .514

I suspect that is because home teams tend to be favored, as opposed to something intrinsic about home court and overtime. I took a look at overtime win percentages for various sports here: Underdogs Shouldn't Play for Overtime.

The Knicks were 11.5 point underdogs against the Rockets that night. Based on data from the last ten years or so, NBA underdogs of 10 points or more have won just 32% of the time when they force overtime. Underdogs of 5 to 10 points have only won 34% of the time.

Which makes JR's shot look even better. If you're the underdog, you don't try to extend the game. You end it quickly if you can.

[Mike G]

The MVP and LVP designations should be taken with a grain of salt. There is a lot that I am not measuring when it comes to WPA (it ignores assists and rebounds). ... I prefer to have several cleanly defined metrics to review, as opposed to several competing "master stats" that have different methods of weighting rebounds, missed shots, assists, etc.

Thanks for the replies. I wasn't suggesting you try and weigh the rebounds, assists, and etc. Now that we have pbp, and you are apparently using that to read "game clock" and "who scored" -- doesn't it seem like one could create a great merger of Plus-Minus and Play Significance?
Not saying you ought to be the one to do it, but somebody ..

Whether a scoring specialist is helping his team outscore the opponent, or if his liabilities outweigh his positives, then his points will be (in the long run) scaled to the context of both efficiency (vs opponents) and effectiveness (in leading to a win).

If you steal the ball at midcourt and pass it to me for a game winning layup -- and the only reason I was near that basket was that I was lazy -- I shouldn't receive full credit for the change in win likelihood. Just distribute that parcel of WPA to all 5 guys we had on the floor -- and debit the opposing 5, also by 1/5 shares.

Garbage time would be reduced toward zero import. Early plays retain their importance in a game that is close all the way.

[deepak]

For those that are interested, I now have Win Probability Graphs and Box Scores (Win Probability Added at a player level) for every game of the current NBA season (through Christmas).

Graphs and Box Scores
Introductory Post

Any feedback on presentation, features, or methodology would be welcome. I plan on keeping this updated throughout the season. A longer term project will be to add previous seasons (I believe play by play data is available all the way back to the 1996-97 season).

Is it possible to provide something like a "garbage time" curve? The x-axis would be time remaining in the game, the y-axis would be absolute scoring margin. The curve would be those margins for which a team has N% chance of winning the game given x minutes remaining, where N is set to some really low number like 5% or whatever.

[boooeee]

The MVP and LVP designations should be taken with a grain of salt. There is a lot that I am not measuring when it comes to WPA (it ignores assists and rebounds). ... I prefer to have several cleanly defined metrics to review, as opposed to several competing "master stats" that have different methods of weighting rebounds, missed shots, assists, etc.

Thanks for the replies. I wasn't suggesting you try and weigh the rebounds, assists, and etc. Now that we have pbp, and you are apparently using that to read "game clock" and "who scored" -- doesn't it seem like one could create a great merger of Plus-Minus and Play Significance?
Not saying you ought to be the one to do it, but somebody ..

Whether a scoring specialist is helping his team outscore the opponent, or if his liabilities outweigh his positives, then his points will be (in the long run) scaled to the context of both efficiency (vs opponents) and effectiveness (in leading to a win).

If you steal the ball at midcourt and pass it to me for a game winning layup -- and the only reason I was near that basket was that I was lazy -- I shouldn't receive full credit for the change in win likelihood. Just distribute that parcel of WPA to all 5 guys we had on the floor -- and debit the opposing 5, also by 1/5 shares.

Garbage time would be reduced toward zero import. Early plays retain their importance in a game that is close all the way.

I can see some value in a plus/minus WPA at the player level. Unfortunately, I currently have not gone through the process of deriving who was on the floor just yet (it sounds like a coding nightmare from the descriptions here). Ultimately, you would have to take the stat for what it is: a very noisy, imperfect representation of player contribution (although I suppose that applies to pretty much any basketball stat). But I have a feeling plus/minus WPA would be particularly noisy.

[boooeee]

For those that are interested, I now have Win Probability Graphs and Box Scores (Win Probability Added at a player level) for every game of the current NBA season (through Christmas).

Graphs and Box Scores
Introductory Post

Any feedback on presentation, features, or methodology would be welcome. I plan on keeping this updated throughout the season. A longer term project will be to add previous seasons (I believe play by play data is available all the way back to the 1996-97 season).

Is it possible to provide something like a "garbage time" curve? The x-axis would be time remaining in the game, the y-axis would be absolute scoring margin. The curve would be those margins for which a team has N% chance of winning the game given x minutes remaining, where N is set to some really low number like 5% or whatever.

That's definitely doable and a good idea. I just need to set aside the time to do it.

[boooeee]

Player win probability added totals for the season now available.

[italia13calcio]

Really interesting stuff.
It's interesting how Kevin Durant is so low, compared to other rankings. Could it be because his team is winning most of their games fairly comfortably and he hasn't had to hit many game winning shots that would spike his WPA?
I also think it would be interesting to see maybe a team ranking of comebacks and of excitement - maybe this way you could statistically solve Bill and Jalen's question of which team is the best league pass team.

[Bobbofitos]

I find it fascinating Love is 5th in WPA added, despite the TWolves something ridiculous like 0-11 in games decided by 4. I guess it's just not his fault, eh?