Sunday, January 6, 2008

Ferocity of Men's vs. Women's Spikes at the Elite College Level: Rates of Being Dug

As collegiate volleyball in the U.S. switches from women's play in the fall to men's in the winter/spring, so too does VolleyMetrics shift its focus. Fittingly, given this transition, there was a recent discussion topic on the VolleyTalk boards about the differences -- and relative enjoyability -- between the men's and women's games.

The discussion appeared to focus on the greater power of men's spiking than that of women's. In fact, one discussant characterized the men’s game as “Pass, set, boom.” Whether one finds beauty in these rocketing blasts or prefers the (assumed) longer rallies in the women's game is in the eye of the beholder, but the consensus that this difference exists was wide.

Here at VolleyMetrics, however, we want hard numbers. As an initial step, we can look at men's and women's team hitting percentages. Keep in mind that (as best I can tell), there are far more women’s volleyball programs in Division I alone than there are in men’s Divisions I, II, and III combined.

Having said that, it turns out that only five women’s Division I teams exceeded a hitting percentage of .300 this past season (Penn St., .350; Texas, .343; Nebraska, .327; Stanford, .316; and Florida, .303; a link to NCAA women's statistics is available in the upper-right of this page).

In contrast, at least 11 teams in the combined D I-II configuration surpassed .300 in the most recently completed men's season (the men's top 10 list stops with two teams tied for 10th at .307).

That's pretty good evidence, but me and my computer wanted more. Conveniently, as part of a separate VolleyTalk discussion thread on statistical refinements (which I excerpted a couple of entries down), user "p-dub" had suggested computation of:

"dig %", which is digs/non-error attacks...

I like the idea, which to elaborate a little, takes Team A's dig total and divides it by Team B's (total number of attacks - errors). More colloquially, we might call this measure "dig-ability" -- of the spike attempts coming at a team, what percentage of them do they dig up? (Note that a spike attempt blocked back in the face of a hitter is considered an error, so blocked balls are accounted for.)

Another thing I wanted to do is study the same schools' men's and women's programs, thus holding constant the strength and prestige of athletic programs, quality of facilities, etc. (assuming the men's and women's volleyball teams get equal access to these facilities).

Given the nature of the above formula, dig-ability can only be computed on a match-by-match basic, and not with aggregate seasonal stats. Given my roots as a former UCLA Daily Bruin men's and women's volleyball correspondent (1980-82), I selected the four UCLA-USC matches (two men's, two women's) played during 2007. For any given match, the dig-ability of both teams' spikes are calculated separately, so these four matches would generate eight data points. Further, to augment and diversify the sample, I also used the four Penn State-Ohio State matches of 2007 (the Nittany Lions and Buckeyes are in the same conference, the Big 10, in women's play, but in different men's conferences). The eight matches and 16 dig-ability data points are summarized as follows (with box-score links):

Women's: #4 USC vs #5 UCLA (Oct 05, 2007) 4 games
UCLA Dig 66 / (USC Attempts 150 - USC Errors 25) = .528
USC Dig 63 / (UCLA Att 170 - UCLA Err 30) = .450

W: #9 UCLA vs #6 USC (Nov 02, 2007) 4 games
UCLA Dig 89 / (USC Att 207 - USC Err 34) = .514
USC Dig 87 / (UCLA Att 183 - UCLA Err 29) = .565

Men's: USC vs UCLA (Jan 27, 2007) 3 games
UCLA Dig 28 / (USC Att 92 - USC Err 4) = .318
USC Dig 28 / (UCLA Att 112 - UCLA Err 26) = .326

M: #4 UCLA vs #12 USC (Mar 31, 2007) 3 games
UCLA Dig 24 / (USC Att 100 - USC Err 23) = .312
USC Dig 20 / (UCLA Att 94 - UCLA Err 12) = .244

W: Ohio State vs #3 Penn State (Oct 10, 2007) 3 games
OSU Dig 32 / (PSU Att 93 - PSU Err 8) = .376
PSU Dig 39 / (OSU Att 112 - OSU Err 27) = .459

W: #1 Penn State vs Ohio State (Nov 21, 2007) 3 games
OSU Dig 42 / (PSU Att 103 - PSU Err 10) = .452
PSU Dig 45 / (OSU Att 121 - OSU Err 29) = .489

M: #11 Ohio State vs #7 Penn State (Feb 01, 2007) 4 games
OSU Dig 30 / (PSU Att 131 - PSU Err 21) = .273
PSU Dig 45 / (OSU Att 133 - OSU Err 22) = .405

M: #6 Penn State vs #8 Ohio State (Apr 4, 2007) 5 games
OSU Dig 24 / (PSU Att 118 - PSU Err 26) = .261
PSU Dig 29 / (OSU Att 116 - OSU Err 24) = .315

It is plainly evident that spike attacks in women's matches have a higher dig-ability rate than those in men's, which will not surprise many observers. Whether the magnitude of difference is greater or less than expected, or about as expected, may differ among members of the volleyball community.

This analysis seemed to provide a good occasion to introduce the box plot, a graphical statistical tool. At a glance, the box plot displays the following aspects of a statistical distribution: the median (Mdn; point at which half the scores are greater and half are less than), the lower quartile (1Q; the point that cuts off the lower 25% of scores), the upper quartile (3Q), and the lowest and highest individual values in the distribution. This online calculator allows one to type in individual data values and automatically generates the necessary statistics for a box plot (and more).

The mean and median, respectively, were virtually identical within the men's distribution (.307, .3135) and within the women's (.479, .474); this is not always the case in analyzing data. Here are the two boxplots (you may click on the image to enlarge it).

The usual cautions about small sample size are applicable. Still, across the four men's matches and across four women's matches (each set taken from two regions of the country), the results appear to exhibit considerable consistency. Yes, women's spike attempts were more dig-able than were men's in the matches studied, but the magnitude of difference was less than .20 (roughly .48 - .31).

Whether these statistics indicate (to paraphrase a popular book title from several years ago) that the men's game is from Mars and the women's from Venus, or (to paraphrase a colleague of mine) the men's is from North Dakota and the women's from South Dakota, I don't know, but at least some statistical information can be added to the discussion.