Sunday, January 4, 2009

Another post on rebounding

Georgetown lost to the Pitt Panthers yesterday, for the Hoyas' second loss of the season, due in large part to a massive discrepancy in rebounds: 48 to 23. That's a rebounding margin of -25, or two more than the total number of rebounds that the Hoyas secured.

A few weeks ago, SFHoya99 wrote a prescient article explaining a pair of slightly more sophisticated statistics (Off. Reb. % and Def. Reb. %), which we tend to use around here rather than rebounding margin. I won't explain here why we prefer them (do read his article if you'd like to know why, it's very good), but I will re-post the equations to calculate each.
. Off. Reb.
Off. Reb. % = ----------------------------
. (Off. Reb. + Opp. Def. Reb.)

. Def. Reb.
Def. Reb. % = ----------------------------
. (Def. Reb. + Opp. Off. Reb.)

These are simple calculations - we're just looking at the number of rebounds gathered divided by total opportunities to get those rebounds. We'd expect teams to get about 1/3 of their own misses and 2/3 of their opponents', and we treat offensive and defensive rebounds separately. Again, re-read the above linked article for more information.

About a year ago, I also wrote a note about Georgetown rebounding difficulties, added to the end of a recap of an ugly road win against Rutgers. I'd like to return to it, and update the underlying statistics in an attempt to put the Pitt game into some perspective.

I mentioned then, and again in yesterday's recap, another rebounding stat called Total Reb. %. This is also a simple-to-calculate metric that serves as the stat-head analogue to rebounding margin, and is merely the average of Off. Reb. % and Def. Reb. %. That is:
. (Off. Reb. % + Def. Reb. %)
Tot. Reb. % = ---------------------------
. 2

If two teams perform equally well in a game at rebounding, each should end up with a Tot. Reb. % = 50%. Here's an example you might find in a typical box score:
Team A vs. Team B
14 20 34 10 28 38

If you were to simply look at rebounding margin, you'd say that Team B out-rebounded Team A by four. However, if you were to calculate rebounding percentages, you'd see that the teams were even on the glass. For example, Team A's OR % = 14 / (14 + 28) = 33.3; that is, while Team A was on offense there were 42 (= 14 + 28) rebounding opportunities, and they got 14 of them, or one-third. Here are all the numbers for our hypothetical game:
. Team A vs. Team B
OR % DR % TR % OR % DR % TR %
33.3 66.7 50 33.3 66.7 50
Of course, this is not to say that rebounding margin always gives misleading information. In yesterday's game, Georgetown ended up with a Tot. Reb. % = 32.2, which looks nearly as bad as the -25 rebounding margin I mentioned at the top.

After all this introduction, allow me to roll out another in a never-ending series of overly busy plots, looking at Georgetown's Tot. Reb. % for this and the last two seasons (click to enlarge).

The points represent individual games, the solid black line indicates the 50% rebounding rate (a draw with the opponent), the solid blue, red and gray lines represent moving averages of the data (n=5 for 2006-7 and 2007-8; n=3 for 2008-9) and the dashed lines are linear fits to each year's data.

A few comments and observations:
  • Tot. Reb. % is not a stat that is adjusted for opponent, so playing a run of great or lousy rebounding teams can make your team look better or worse than they may be over the course of the season. For the sake of argument, we'll assume that the relative rebounding ability of teams played at the same time of year is roughly equal season to season.
  • The three-year trend from comparing the linear-fit lines from each season indicates that this team is the worst of the three, and by a substantial margin. Do keep in mind that there is quite a bit of uncertainty for these fits which I don't indicate, so the differences would not be considered significant in the true sense of that word.
  • More interestingly (to me) are the observed seasonal trends from comparing the moving averages for previous years, and which may be repeating again this year:
    1. After starting the season essentially neutral or noisy, the team rebounding improves strongly in December. I suspect this is from a diet of "cupcakes" during the exam period.
    2. The Big East conference season begins, and it is a shock to the Hoyas. Rebounding performance drops dramatically.
    3. By February, the team has recovered - or more likely worked hard in practice - and is rebounding nearly as well as during the December stretch.
    4. By March, the rest of the league has caught up, and Georgetown is now rebounding equally well as their opponents.
  • Just by looking at the moving averages, this year's team, while starting much more poorly than previously, looks to have recovered to roughly last year's level, before the beating from Pitt. However, it should be pointed out that about this time last year, the Hoyas took the same type of pounding on the boards in the aforementioned Rutgers game.

The question to be answered in the next few weeks is whether this team can follow the lead of its predecessors and make the same type of commitment to rebounding by February.

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