## Monday, May 12, 2014

### Should the Thunder have fouled?

 Scott Brooks and Maurice Cheeks
If my Twitter feed is any indication, the following are universally held opinions:
1. The Thunder's Scott Brooks is a bad coach
2. Not fouling the Clippers with 27 seconds left and trailing by 2 was a bad decision and evidence of 1. above
In this post I will use my win probability model to evaluate whether the Thunder would have been better off fouling the Clippers instead of playing for the stop (recap and win probability graph for the game in question).

### Game State

After Westbrook's layup, the Thunder were down by 2, and the Clippers with possession. To evaluate this decision, I will set a low bar for Scott Brooks to clear. Let's assume that the Clippers held the ball for the full 24 seconds and allowed a shot clock violation. How does the win probability of a team down by 2 with possession and three seconds compare to the win probability of a team down by 2 with ~twenty seven seconds left and their opponent on the line with two free throws to shoot?

According to my win probability model, having the ball down by 2 with three seconds to go has a win probability of 9.1%. What is the corresponding "deliberate foul" win probability?

### Six Possible Outcomes

Putting a team on the line leads to six possible outcomes, each with its own associated win probability. For the calculation below, I am using league averages for both:
• Free throw percentage (75.6%)
• Offensive rebound percentage of missed free throw (13.4%)
The first foul shot has just two relevant outcomes: make or miss. The second foul shot, however, has three: make, miss + offensive rebound, miss + defensive rebound. The table below summarizes the probability of each of the six outcomes along with the corresponding Thunder win probability that would have ensued. Note that below I am assuming that it takes ~2 seconds for the Thunder to foul, so the end states are calculated with 25 seconds to go.

1st shot 2nd shot probability win probability
missed missed, oreb 0.8% 10.7%
missed missed, dreb 5.1% 26.0%
Total 100.0% 10.7%

As you can see from the table above, fouling would have led to a total win probability of 10.7%, which is above the "low bar" probability I set of 9.1%. So Scott Brooks is an idiot, right? Not necessarily.

### League Averages

I called out above that I am using league averages for both free throw percent and rebound rate in the win probability calculation. But who did the Clippers have on the floor when the Thunder faced their decision? Chris Paul, Darren Collison, Danny Granger, Jamal Crawford, and Blake Griffin. With the exception of Griffin, the remaining four are ~86% free throw shooters this season according to basketball reference. What if we reran the win probability calc assuming an 86% free throw percentage? See below:

1st shot 2nd shot probability win probability
missed missed, oreb 0.3% 10.7%
missed missed, dreb 1.7% 26.0%
Total 100.0% 9.2%

At 9.2%, now we're at nearly break even with the "no foul and play for a stop" strategy. But I'm probably overselling the "no foul" strategy by assuming it can only end with no score and a shot clock violation. I think there is more downside for the Thunder than upside: an inadvertent late foul or last second successful field goal seems more likely than the Clippers turning the ball over or stupidly taking an early shot. You can argue that Griffin should have held the ball rather than shooting with 4 seconds to go on the shot clock, but it's not clear cut at that point, especially if you have a decent look.

You also have to contend with the "chuck the ball in the air and burn a few more seconds of regulation" strategy, but even that is not always foolproof.

### Conclusion

I went into this calculation "knowing" that Brooks had made the wrong decision. I was somewhat surprised that the numbers were not more decisively on my side. I still think that fouling would have been the right decision, but perhaps only marginally so, given the strong free throw shooters the Clippers had on the floor.