Fun With Numbers
Sean Keeler of the Register wrote an article for today's paper in which he analyzed Iowa and Iowa State's use of their possessions during Friday night's game. Knowing how many possessions each team had and how efficiently they used them are excellent tools for understanding a basketball game. I played around with something similar this past week that I got from Dean Oliver - I think it's a little clearer than Keeler's model (which he got from Dean Smith).

Let's get the obvious points out of the way first. Only one team can have possession of the ball at any time. Equally simple, one team's possession ends when the other team obtains the ball and begins their possession. Therefore, if teams alternate control of the ball for the entire game, they will finish the game with an equal number of possessions (give or take one or two because of beginnings and endings of halves). Contrast this with one of Keeler's points -

(a.) It wasn't that the Cyclones didn't have opportunities - they had the ball
more often and did less with it than the Hawkeyes.

Determining possessions in a game (without manually counting them) isn't an exact science, but we can get pretty close if we stop to think about which events cause possession to change between teams. Before going further, I should mention that Oliver treats an offensive rebound as a continuation of a possession since the offense maintains control of the ball, even though it misses its shot.

There are three events that account for the majority of possession changes. The first is any field goal that the offense does not rebound. Possession changes any time the offense scores or the defense rebounds a miss. This term is represented by (FGA - Oreb). Turnovers (TO) are another obvious way to give the other team the ball. The final possibility is a free throw that ends a possession, whether it be a make on the second of a pair or the end of a three-point play, or a miss that gets rebounded. This term is difficult to determine from the box score, but Oliver's years of research led him to believe that about 40% of free throw attempts end a possession (0.4*FTA).

So our formula for possessions becomes -

P = FGA - Oreb + TO + (0.4*FTA)

(This is fairly similar to the stat the Big Ten Wonk ran out the other day, although this uses offensive rebounds and turnovers to fully account for team possessions.)

The first thing the number of possessions in a game tells you is the pace of the game, since, clearly, the more possessions you have, the more often the teams are running up and down the court. So yes, I was a little confused to read -

Smith's method isn't perfect. It doesn't account for the pace of the game. . .

Pace is the exactly what possessions represent. Iowa, the Big Ten's most up-tempo team so far, is averaging 72 possessions a game. Northwestern plays a much slower brand of basketball, and works with 60 poss/game.

Keeler highlights an important point when he covers efficiency. Points/possession (PPP) is a handy stat to compare teams of different styles by measuring how efficiently each team uses its possessions. A team that shoots 60% on 60 possessions might score less than a team that shoots 40% on 80 possessions, but the former team is more likely to win because its opponent will also have only 60 possessions to use, and that opponent will be hard-pressed to score enough to overcome that 60% shooting.

Using straight points/possession usually leaves you with a 1 and several decimals, so it's convenient to multiply it by 100. Now our formula for points per 100 possessions, or offensive efficiency, becomes -

((Pts) / (FGA - Oreb + TO + 0.4*FTA)) * 100

Since the free throw term is not exact, it's best to average each team's possession number to approximate the number of possessions for that game. By that I mean use team A's stats once in the formula, use A's opponent once, and average the two results. Also, you can use a team's points allowed to figure their deffensive efficiency.

Not too difficult, but in just in case you don't think you're up to a little math right now, I went ahead and made a table to summarize the Big Ten teams' offensive and defensive efficiency.

Big Ten Efficiency Ratings (thru 12/13/04)

Team	Poss/Game	Off. Eff.	Def. Eff.
Illinois	67	123	94
Michigan State	71	122	92
Iowa	72	115	99
Ohio State	67	114	90
Penn State	66	108	103
Minnesota	67	106	96
Wisconsin	63	105	95
Michigan	66	100	95
Northwestern	60	99	97
Indiana	64	92	99
Purdue	66	90	102
Average	67	108	97

Again, offensive efficiency is measured as points a team scores per 100 possessions, and defensive efficiency is points allowed per 100 possessions.

Interesting things to note - (1) Michigan State's defense only ranks 8th in points/game allowed, but they're very tough on a more accurate points/possession measure. Also, they're leading Illinois in points per game, but are taking an extra 4 possessions to score the extra points. (2) Iowa's offensive efficiency is comfortably above the conference's average, despite playing one of the most difficult schedules. Of course it would be nice to see that tied-for-third-worst defense improve. (3) Perhaps Ohio State is overlooked by some, as suggested by the Wonk. Their 2 losses were close ones to decent teams (Creighton and Clemson), but none of their 6 wins have been close. And their numbers in that table look pretty nice too.

Well, let me know if you think this kind of stuff is useful or at least interesting, or if I made any major errors along the way. Definitely let me know if it was confusing - my professors have fully informed me that I could use more clarity and organization in my writing. And please note that none of these ideas are mine - if they interest you I suggest taking a look at Oliver's Journal of Basketball Studies.

Since Iowa doesn't play again until Saturday and since I'll be tied up with finals until Friday night, posting this week will probably be limited to tables of Big Ten leaders in some non-traditional stat categories. Stop back and see how you like them.

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