Fouling at the end of a tie game?

[colts18]

Let's say the opponent has the ball with 20 seconds left in a tie game, would it make sense for the defense to foul the offense in order to get an opportunity at scoring? In the regular scenario, you have no time to match the opponent because they will take the last shot. With fouling, you probably will have to score but you have an opportunity to win it in regulation if the opponent misses a FT.

Someone do the math for me. It's probable that fouling makes no sense, but I want to see the math. I would bet the math says that it would make sense to foul DeAndre Jordan so that you have an opportunity to score.

[J.E.]

Well, you can sketch out the different scenarios
e.g. 1st FT MISS/HIT, 2nd FT HIT/MISS, own buzzer beater HIT/MISS
and assign each event a probability.

But things obviously get complicated once you factor possible offensive rebounds from the opponent team, the fact that the other team might have another shot after your shot, the fact that the other team might employ the same strategy as you are, etc.

Probably easier to just look at it empirically using PbP, checking whether fouling has had a positive effect on winning in tied games with X seconds left


My gut says that buzzer beaters only get hit <35% of the time, while the probability that your opponents hits at least one FT is quite high

[ampersand5]

Let's say the opponent has the ball with 20 seconds left in a tie game, would it make sense for the defense to foul the offense in order to get an opportunity at scoring? In the regular scenario, you have no time to match the opponent because they will take the last shot. With fouling, you probably will have to score but you have an opportunity to win it in regulation if the opponent misses a FT.

Someone do the math for me. It's probable that fouling makes no sense, but I want to see the math. I would bet the math says that it would make sense to foul DeAndre Jordan so that you have an opportunity to score.

I have argued previously that end of quarter fouling adds a higher expected value to your team, so in theory, I could agree with this. However, there is the quixotic ramification that if it worked, then the other team could/would do the exact same thing in response.
Even if the numbers favoured it, it would never happen. The gains of innovation must surpass its quirkiness. The potential gains here are comparatively small and it would be way too "weird" for players and fans to witness.

Lets look at some rough numbers:

if its a bad FT shooter, then lets say there is a 25% chance of making both free throws. Chance of hitting a three and winning the game lets put at 20%. chance of hitting a 2 and tying it, lets put at 30%.
50% chance of them making one free throw and recovering the rebound and 30% chance of making a shot and winning the game.
25% chance of them missing both and then you would have a 30% chance of making the shot.

.05+.15+.075 +.03= 30.5% chance of winning the game if you foul

if you did not foul and they have a 30% chance of scoring on the final possession, you have a 35% chance of winning the game in OT.

[nrestifo]

So i did this for myself the other day, right after ND/Kentucky ended. I used some very broad general/assumptions so my numbers could be very off. Using the assumptions I used, however, I found that ND Win Prob was 30.2% if they fouled, vs. 14% if they didn't. How did I get there?

Assumed 70% ft shooter (slightly better than average college ft shooter).
Assumed odds of making a 3 on a last second play with some time were 20% for both teams.
Assumed odds of making a 2 on a last second play with some time were 40% for both teams.
Assumed odds of going full court distance and scoring with minimal time left after/if UK scored in some fashion was 5%.
Assumed UK would win in OT 80% of the time, and ND would win the other 20%. (Rough pre-game probability projection for each team).

This made for a simple and manageable decision tree that produced that 30.2%/14% difference. Obviously there are some significant over/underestimates here and its a broad simplification, but I was able to do this in 5 minutes. Under these assumptions, fouling becomes disadvantageous if you put Notre Dame's OT chances above 47%. This however, is for college not for NBA, and you would have to change alot of these numbers. Better FT shooter, higher last second percentages, (especially with TO advancement). This is one of the big areas where college is different from pros. Thoughts, criticisms?

[Hoopalytics]

I'm an advocate of it. I strongly believe Notre Dame should have fouled early in UK's final possession Saturday night, just as I felt Michigan should have fouled Kentucky last year. I wrote up a look at that Michigan scenario here http://bit.ly/1ol9N2f

Fouling was discussed by the Michigan staff in the timeout that preceded that final shot, but only if Dakari Johnson (44.7% FT) was on the floor.

[colts18]

Here is some data on end of game shots for the NBA.

10 seconds or less, 4th/OT, 2006-2015, RS and playoffs, tied game

24.5 FG%,28 2P%, 14.6 3P%, 26.4 eFG% (1469 FGA, 384 3PA sample)

11-20 seconds left:

36.7 FG%, 36.5 2P%, 37.5 3P% (only 40 3PA), 40.1 eFG% (218 FGA, 40 3PA sample)

Even extending the sample 10 years back, the sample is pretty small for 11-20 seconds. Teams take 7x more shots under 10 seconds than 11-20 seconds left in a tied game. The results show that teams are very inefficient late in the game. Here are the top 10 in FGA with 20 seconds or left in a tie game:

FG FGA eFG%
LeBron James 9 36 0.250
Kobe Bryant 7 32 0.219
Joe Johnson 8 32 0.250
Dirk Nowitzki 15 31 0.516
Kevin Durant 7 28 0.321
Dwyane Wade 8 27 0.315
Carmelo Anthony 8 26 0.308
Paul Pierce 4 25 0.160
Jamal Crawford 5 25 0.220


Dirk is the outlier in these situations. Of the 43 players with 10 FGA in these situations, only 3 have a 50 eFG% or better (Dirk, Nash, and Turkoglu) and Dirk is the only with more than 11 FGA to do it. Dirk did it with 31 FGA. Amazing feat.

[boooeee]

Using my Win Probability Model

Assuming a league average ft% of 76% and a league average free throw offensive rebound rate of 19%:

For evenly matched teams:
Win probability with possession, tie game, and 0:20 on the clock: 62%
Win probability with two free throws to shoot, tie game, and 0:20 on the clock: 71%

If the team with possession is a 10 point favorite:
Win probability with possession, tie game, and 0:20 on the clock: 73%
Win probability with two free throws to shoot, tie game, and 0:20 on the clock: 80%

If the team with possession is a 10 point underdog:
Win probability with possession, tie game, and 0:20 on the clock: 48%
Win probability with two free throws to shoot, tie game, and 0:20 on the clock: 60%

The gap shrinks if the team with possession is a heavy favorite, which makes sense. Favorites tend to win in overtime, and fouling lessens the probability of overtime. But it still isn't a better option to foul (at least according to my modeling).

[Mike G]

... league average free throw offensive rebound rate of 19% ...

Is it really that high?
The overall OReb% is .251, and I'd thought that on missed/reboundable FT it was less than half of that.

[boooeee]

... league average free throw offensive rebound rate of 19% ...

Is it really that high?
The overall OReb% is .251, and I'd thought that on missed/reboundable FT it was less than half of that.

Whoops. You're right. It is not that high. I grabbed that number from a stale set of code. The number I have (that is actually used for the model) is 13.4% for free throws and 30.4% for field goals.

[Kevin Pelton]

Ken Pomeroy has written about this at length in regards to the college game:
Part 1
Part 2
Part 3
Specifically on Saturday's game

[willguo]

I would bet the math says that it would make sense to foul DeAndre Jordan so that you have an opportunity to score.

1) I would suspect OREB% on missed FTs is inversely proportional to how good the FT shooter is, even more so controlling for that poor FT shooters are typically good rebounders.
2) Given how often a DREB in this situation would lead to a TO, a coach can be even more inclined to crash the glass.