Tuesday, April 09, 2013

There is no such thing as a "game-winning" shot.

Reading Kahneman's Thinking Fast and Slow really changed how I look at the end of basketball games. We spend so much time remembering/talking about the end of a close game, as if that last shot or that last blown call was more important than the others-- they're not. Two points is always just two points. The blown calls at the 8:13 and 12:45 mark were just as consequential as the one at 39:49. The last shot taken doesn't "win the game," the final score is a cumulative outcome of all shots made. If you lost by one point, then any of your missed field goals or free throws would have made the difference. Kahneman calls this obsession with the final moments "the tyranny of the remembering self."

Kentucky fans (myself included) suffer the '92 Laettner shot every year. There's no need. Had he missed any of his shots, or Kentucky made just one more shot or free throw the outcome would have been different. The final play was just one of a large number.

The Michigan economist @justinwolfers reminded me during the championship game that Michigan's benching of Trey Burke after picking up his 2nd foul in the first half was also illogical. It doesn't matter if Burke plays the first 30 minutes or the last 30 minutes of a game, two points are two points whenever they're scored. (This would have taken away the captivating Spike Albrecht show. It was illogical to keep playing Albrecht in second half, something called regression to the mean-- he's not a good player and it showed.) There is no such thing as "crunch time." The end of the game is no more important than the beginning. Invite an economist to watch a game with you whenever you want it ruined.

A booke related to the subject that I'd highly recommend:

Dean Oliver now works for ESPN.com, this book is dated but still the bible of statistical analysis of basketball.


Justin Tapp said...

One can make an argument that you want to save your best players for the last few minutes (ie: make sure they haven't fouled out) because strategy becomes more deliberate in the last few possessions of the game (as time and potential possessions become easier to calculate) and you want your best players to execute it.

Adam Fernbach said...

This is just not correct. A buzz-beater is a game winner not only by definition but also because the opponent can't react to it. It's not just how deliberate end-game strategy is.

NFL demonstrates this more clearly. Let's say my Bills lose a game by two points. They missed a FG with 10:20 to play in the first quarter. Would they have won if the kicker had made the attempt? No way to tell. The other team might have played for touchdowns instead of field goals later on if the Bills had hit the FG. Maybe they go for two instead of a PAT. But if they Bills also missed a FG as time expired, that's clearly something that would have made the difference in the game.

If the game is close, you want your best players on the court at the end because those minutes are actually more valuable. Difference in win probability up 3 at 15:00 1H is much different than win probability up 3 at 00:15 2H

JN said...

The points count the same, but their impact on winning is greater in late-game situations than with 12:00 left in the 1st half. The point isn't to accumulate the most points possible, it's to win.

To illustrate this, imagine if Burke scores on the possession immediately following his benching. Michigan entered that possession up 20-17 with 11:09 left. The game was basically a toss-up, with Michigan about 51% to win. If Burke had scored a layup instead of the turnover his teammates produced, Michigan's odds of winning increase to ~54-55%. With the turnover, they actually fell to ~48%. So that play would've been about 6-7% better than what happened in real life.

Compare that to if that layup had happened inside of a minute in the 2nd half when Michigan was down 4. That would've been worth 16% in win probability. Same shot, same points, but twice as valuable.

Now, you're not guaranteed a close game at the end, but with Michigan leading, the game outcomes when Burke was benched skewed towards at least being close (if not Michigan winning comfortably). The fact that Michigan grew their lead to 12 with ~4 minutes left reinforced this. Beilein may have put Burke back in if the game was tied at the 3:33 media timeout, but with Michigan up 12 it's even more likely that they'll at least be in a close game at the end where Burke can significantly impact the finish.

Justin Tapp said...

Adam: The final score is determined by the sum of all shots-- therefore, no one shot is the "game winner" or they all are-- your choice. Also, see my comment above.

I recommend the website Advanced NFL Stats to help you think through your Bills scenario. He has an algorithm for calculating expected points and win probability of a potential play based on game factors you describe.

JN: Since the final score is cumulative of all scores, it doesn't matter when a player gets his minutes. "saving him for the end" doesn't make sense because you've reduced his minutes and productive contribution to his team.
Why is it important to "impact the finish" as opposed to impacting the other possessions that also determine the finish?

Nate Kratzer said...

Points scored are not independent phenomena. If something happens in the first 5 minutes of the game, both teams react to that new situation. This makes the question "what would have happened if he missed that shot?" very difficult to answer. By contrast, on the last shot, we actually know with reasonably certainty what would have happened.

Natália Perez said...

There is actually a perfectly good reason to sit players when they get into foul trouble: they tend to play more tentatively when they're in foul trouble, and thus become less effective. Here's a paper about it from some researchers at NYU.


Bryan said...

A team wants its best players on the floor for the most possessions, not for the most time. Its rational to expect that there will be more possessions in the last two minutes of a game than in any other two minute stretch, as teams will press and intentionally foul to draw out the game (and thereby increase the number of possessions per minute). Pulling a player with 2 fouls out of the game for 4 minutes in the first half may cause him to miss 5 possessions for his team, but his team may have 10 possession in the last 4 minutes of the game. So its a good trade.

Justin Tapp said...

Natalia, thanks for the paper. I'll pass it along.

Bryan, interesting thought as well.

keithwalters.org said...

I agree. As a player who fouled out a lot in highschool I am a big fan of using those fouls. If you loose who cares if your best player only has three fouls because he was benched. It would be smarter to let him play, possibly fouling out, and get some good points then bench him and get no points. Those fouls are a resource dont be afraid to use them all! :P