Jay piqued my curiosity with his comments on free throw shooting in the Northwestern State game summary. So, per reader request, I will now present my study of the relative impact of Dean Oliver’s so-called “Four Keys.” Let me go ahead and issue a warning: if you’re put off by a little math, you might have trouble with this part, so just skip to the conclusions. Otherwise, brave reader, trudge on.

The idea behind the four keys is that controlling each of these aspects of a basketball game will lead your team to victory. Accordingly, there is a flip side to each key: your team needs to perform well in that area, while at the same time forcing the opposing team to perform poorly in that area. I measure this net impact using the team’s percentage of performance above or below the opposing team’s performance in that area.

**The four keys are:**

1. *Shooting well from the field* – Oliver measures this with field goal percentage, but it seems like true shooting percentage is really the better way to measure this. TS% properly accounts for 3-pointers and free throw shooting, essentially measuring the number of points scored per shot.

2. *Controlling the offensive glass* – You can get more shot attempts if you do this well, so it is clearly an important part of the game. The stat I use to measure this is offensive rebound percentage, which is the team’s offensive rebounds divided by total rebound chances (team’s offensive plus opponent’s defensive rebounds).

3. *Ball control* – If you don’t turn the ball over, you get more chances to make a shot, so I use turnover ratio (the percentage of turnovers per possession) to track this.

4. *Getting to the free throw line and making your shots* – This is one of the most efficient ways to score points, so according to Oliver, it is important to get to the free throw line (and, of course, make the shots). I use free throws made per possession to track this key.

I compared the net values of these stats to net efficiency, which is the best way to tell who won the game (and how decisively). Basically, offensive efficiency is the number of points per possession (not per shot), while defensive efficiency is the same for the opponent. Offensive minus defensive efficiency gives you net efficiency. This method is superior to using margin of victory, which does not account for the pace at which the game is played, leveling the playing field between fast-paced and slower-paced teams.

**The Results:**

To start, I checked the variances of the individual keys when compared to net efficiency. The variance stat (also known as the correlation squared) basically tells us how much of the change in the dependent variable (net efficiency) can be explained by the independent variable (the four keys). Variances range from 0 to 1, with 1 being a perfect correlation. The individual variances are as follows:

TS%: .707

OR%: .113

TR: .118

FTM/P: .041

This tells a lot of the story. True shooting percentage is clearly the best indicator of the bunch, and it really is the only one that is strong by itself. Free throw shooting, as suspected, is the weakest of the bunch.

Next, I used a technique called stepwise regression to determine the variances of several of the four keys at once. Here are the variances of some of the combinations:

TS%-TR: .856

TS%-OR%: .764

TR-OR%: .220

Even using the turnover ratio and offensive rebounding components together does not explain much of the variance in net efficiency, but using either along with true shooting percentage makes TS% somewhat stronger. The next logical step was to combine all three:

TS%-TR-OR%: .904

That is a significantly strong variance. Now, here’s the kicker about free-throw shooting:

TS%-TR-OR%-FTM/P: .908

Adding in free-throw shooting only helps the variance by a very small amount. If it wasn’t clear before, it is clear now that this is the weakest of the four key areas. It is, however, statistically significant at the .01 level, so I wouldn’t have a problem leaving it in.

**The Conclusion:**

Free-throw shooting is a significant part of the game, but as Jay said in his comment, there are factors that contribute to a lot of “noise,” leaving it only marginally significant. Different offenses, late-game situations, and referees all play a large role in free-throw shooting, taking away from the impact of that skill from game to game. Offensive rebounding and ball control are more significant, but shooting is clearly the most important factor.

Shooting covers a very broad range of basketball strategy, encompassing defensive strategy (to keep the other team from shooting well), particular styles of offense, and varied levels of shooting proficiency by the players. Some offenses are prone to getting easier shots, while others shoot a lot of threes to help their TS%. Other teams do well in this category by smothering the other team on defense and just getting by on offense.

**Making Predictions:**

My regression model also provides a formula to “predict” the winner of a game, based only on the net +/- values of the four keys (the values I typically display to the right of the four keys in my game summaries). To get those values, you take one team’s perspective and divide each stat value for that team by the other team’s corresponding value, then subtract 1 (so that it’s based on 0, not 1). The formula (with a little rounding to make the numbers more manageable) is:

Net Efficiency = ([TS%] x 79) – ([TR] x 20) + ([OR%] x 6.5) + ([FTM/P] x 1.5) – 4

So, you ask, how did this formula fare at predicting the 165 games in my sample? It got 155 of them correct, for a 155-10 record. That’s slightly better than you’d expect for stats which, as a whole, explain just under 91% of the variance in net efficiency (you might expect 150-15). This may not tell us a whole lot about how a team should play the game, since most of the game is already focused on getting good shots and stopping your opponent from doing the same, but it does give us some numbers to back that up.

My next task: find potential additions to the four keys by adding stats to the regression model. If I come up with anything interesting, I’ll pass it along.

[EDIT 12/24: A little change in the methodology here yields much better results, which are forthcoming tomorrow, if I don’t have better things to do on Christmas Day.]