After watching UNC go 21 for 37 from the free throw line yesterday in their ragged victory over FSU, I got to thinking about how important free throw shooting is to team success. On the surface, it makes sense that the more free throws a team converts the more likely they are to win. But what exactly is that relationship? Are commentators correct when they proclaim, "Missing free throws is killing this team!"? I decided to take a look at the numbers and here is what I found.
I got data for the 2003-2004 season on 326 NCAA Division I teams. The data include (winning percentage, FT%, FG%, assists per game, steals per game, 3-point FG%, turnovers per game, team scoring average, rebounds per game and assist-to-turnover ratio). Given all these variables, how important is free throw shooting percentage in contributing to a teams success?
First, let's break down FT% by team winning percentage:
Win pct. Avg FT% by team win>75% 69.7 75%>win>50% 69.6 50%>win>40% 67.5 win<40% 66.5 Total 68.5
Looking at the table, there doesn't seem to be a large difference between the FT% of those teams winning 75% or more of their games (they convert 69.7% of their free throws) and teams winning less than 40% of their games (they convert 66.5% of their free throws).
However if we run a t-test between the FT% of teams winning 75% of their games or more and the FT% of teams winning less than 75% of their games, we find that the FT% for very successful teams (winning 75% or more of their games) is significantly more than the FT% for less successful teams (winning less than 75% of their games). So even though it seems that 70% and 67% are about the same, statistically, they're very different.
Now looking at team FG% by winning percentage we see that teams that win a lot shoot better from the field--no revelation their.
Win pct. Avg FG% by team win>75% 45.8 75%>win>50% 44.8 50%>win>40% 43.1 win<40% 41.6 Total 43.8
Finally, comparing assist-to-turnover ratios (ATR) by winning percentage we again see that teams that win a lot have higher ATR than teams that don't win as much.
Win pct. ATR avg. win>75% 1.11 75%>win>50% 0.97 50%>win>40% 0.87 win<40% 0.79 Total 0.93
What's interesting here is that there seems to be a larger discrepency between the best and worst teams when looking at ATR compared to FT% and FG%. We can run a regression to see exactly what effect these variables have on winning percentage.
After looking at the data, I decided on the following model:
Winning percentage is a function of: FT%, FG%, steals per game, rebounds per game and ATR.
Results
FT% has the smallest effect size of all the variables mentioned above when predicting team winning percentage (TWP). More explicitly:
*for every additional 0.1 assists a team gets per game, TWP will increase by 3.1%
*for every additional steal per game, TWP will increase by 2.6%
*for every 1% increase in FG%, TWP will increase by 2.2%
*for every additional rebound per game, TWP will increase by 1.7%
*for every 1% increase in FT%, TWP will increase by 1%Note: the statistics above assume that all other variables are held constant. For exampe, for every additional steal, TWP will increase by 2.2%, keeping every other variable at its currentl level.
So even though all five variables help predict TWP, improving team free throw percentage by one percent will only increase TWP by one percent. On the other hand, increasing assists and keeping turnovers constant (or better yet, reducing them) has a much larger impact on TWP. For example, if a team goes from an ATR of 2 to 1 to an ATR of 2.3 to 1 (over the course of a season), the model predicts that their winning percentage will increase by roughly 9%.
Given this, maybe teams should spend less time practicing free throws and more time working on ball-handling/passing drills. In the long run maybe recruiting efforts should focus on point guards with high ATR, regardless of how well they shoot from the field or the line. This could be especially pertinent for mid- to low-level NCAA teams who have trouble recruiting blue chip high school players (of course, they may already do that). But what seems to make the most sense, if in addition to recruiting players with high ATR, teams continue to work on free throw shooting (and rebounding and FG% and so on), because in the end, all improvements contribute to winning. But if a team is looking for a quick turnaround, the fastest way to winning may be found in players with high ATR's.
Anyway, knowing all this will probably not prevent me from yelling at Sean May the next time he misses what I think to be a crucial free throw--no matter how many assists he has.
(Note about the data: All models are estimated with some error, so the estimates above are not absolutes--you can always find teams that may have very high ATR's but only win 40% of their games. Why would that happen? These models simplify very complex relationships into a few variables and as a consequence they invariably don't do a good job of predicting extreme examples. But all in all, it's a good way to get an idea about the underlying relationships and a starting point for more research).
