Thursday, February 3, 2011

Free throws and “Luck”

In light of today’s great post on Free Throw Plus by John Ezekowitz, I thought I’d share something I noticed a couple days ago. I had heard some Twitter chatter about Illinois consistently ranking low in Ken Pomeroy’s Luck metric, which essentially tells you which teams have tended to be on the right/wrong side of close games. (They’ve fared no better than 158th in the past 7 years.) It made me wonder if they were doing something specific that would lead to their low ranking. So, I decided to see if any of the stats kept by Pomeroy correlate to “Luck.”

Using 2010 team stats, here’s what I found. I highlighted SOS-related stats in yellow, offensive free throw stats in green, defensive free throw stats in red, and bolded tempo. The bars at the right represent the magnitude of the correlation, but keep in mind that the sign also matters:


A few things jump out:

First, how often you get to the line (o_FTR) has a correlation over twice as high as any other non-SOS metric. Obviously you can’t tell the direction of causation (or even if there is any) from the correlation, but my guess is that this means that offensive FTR is the most skewed by close games. Teams that score well in Luck are going to be those that often have small leads late in games. That’s going to cause opponents to intentionally foul them, which will inflate their Free Throw Rate.

Second, the opponent strength metrics have a higher correlation than any stats which measure what happens on the court (other than offensive FTR). These could me symptoms of the same issue: when you are losing a close game, you foul your opponent, which drives up their offensive rating (and vice versa when you’re in the lead). On the other hand, if that’s what’d driving this, shouldn’t we see a similar effect for the team’s own rating?

Third, tempo is relatively high on the list. Again, late game defensive strategy is to foul quickly, extending the game, and leading to more possessions. This, however, should happen whether you’re ahead of behind, so I’m a little surprised that tempo correlates to good luck.

Now, all these correlations are based off of only a single year, so don’t put too much stock in them. Hopefully soon, I’ll get around to checking other years, to find out how consistent this is. But, let’s assume for a minute that A) it is consistent, and B) the close games are causing the correlation with offensive free throw rate. How much of a difference would this make in the numbers? Well, 95% of teams should have Luck values between –0.1 and +0.1. Using a regression line fit to the points from 2010, the difference between those two Luck values should amount to about a 4 point difference in free throw rate.

Getting back to the original subject of Illinois, if we erased all their bad luck (-0.77) you might expect their FTR to rise from 30.5 to 32.1. That only bumps them up from 316th to 296th, so not a huge difference. Still, the effect of shifting late-game strategy on overall team stats is an interesting topic. Hopefully I’ll get a chance to explore it some more in the future.


In the comments, Nathan Walker pointed out that, given the correlation of the team strength metrics to Luck, I ought to do a partial correlation where I hold these values constant. I think he’s right, so I re-ran the numbers, holding the team Pythag and opponent Pythag constant. That was enough to reduce the correlation of adjusted offense and defense (team and opponent) to near zero, while keeping the number of variables small enough to prevent much over-fitting. I also added Free Throw Production [FT% x FTR], at Nathan’s suggestion. The results look similar, and I don’t think my conclusions from above change. In fact, a couple defensive stats that might be affected by end-game defensive strategy (steal rate and opponent eFG%) jump up near the top, which makes sense:



  1. This is great! I've always noticed Illinois' low luck values (especially when they went 16-19 as the #40 team in Pomeroy in '08). It is pretty intuitive that free-throws are the answer, great job quantifying it! One thing you might want to check is effective Free Throw Rate, that is, FT% times FTR (aka, FTM/FGA instead of FTA/FGA).

    Also, it would be nice to regress the whole thing against Opponent Pyth, offense, and defense (i.e. hold those three constant, because it likely just shows error in Pomeroy's formula rather than true luck).

    Again, awesome work!

  2. Nathan, I updated the post to include both of your suggestions.

    From your comment, it seems like you interpret the results differently than I do. I believe being on the losing side of close games is causing the lowered free throw rate, not vice versa.

  3. Nice post thank you Kristen