I was reading a blog post about a statistical comparison of men's and women's college volleyball the other day, and I saw a comment that displayed an interesting case of gender bias. The post looked at the difference in how likely an attack was to be dug between the two sides of the sport. The comparison was looking at a potentially useful derived stat called digging percentage. It is equal to digs divided by the difference of opponent's errors and opponent's attempts.
The analysis used a box and whisker plot of women's teams digging percentage and men's teams digging percentage. A box and whisker plot is basically a way to visualize the range of the data points with the median and middle half represented by boxes, and the top and bottom quarter as lines coming off the boxes. The women's percentages were higher than the men's. In fact the two plots had very little overlap, and the overlap was entirely in the men's first quartile and women's last quartile.
This means that usually the women's teams across the board are more likely to get a dig on an attack attempt and extend the rally. With the time I have spent with both men's and women's college volleyball, this is no surprise to me. I have been in Division I practices on both sides of the sport with a radar gun. The speed comparison is not perfect because I was clocking attacks for the women and serves for the men, but I am confident the weaker hitters on the men's team could consistently hit as hard as the single hardest measured hit from the women's team.
The instance of gender bias came in a question about whether this was due to the men being harder to dig or the women being better at defense. The individual asking the question was using a common girl's first name as a username. I think this is a common thought among more casual fans, especially among those not as familiar with the men's game. The difference in the number of men's and women's Division I teams probably helps with this idea. High schools often do not have boy's teams. Volleyball is often thought of as a women's sport because of this.
I found the question kind of amusing because of my background, and also because quality of defense can't really be demonstrated objectively with statistics. On the other hand determining the difference in the difficulty of digging an attack attempt is a more realistic goal. The comparison of digging percentages does a pretty good job, but it isn't the complete picture. It is the best that can be done with the available information. We could have a more complete picture if we had quantitative, comprehensive information on hitting speed and hit location, but we don't have that.
I can say qualitatively that men's teams do hit harder and are more likely to hit at steeper angles toward the floor (meaning the ball hits the floor closer to the net), but again I don't have numbers here. This is largely something that can be explained by physiological differences in men and women. Testosterone leads to more muscle mass, and therefore more hitting power and leaping ability. A harder hit ball is going to come at defenders a lot faster, and a higher jump (along with just being taller on average) allows a steeper angle of attack, meaning more area of the court to cover for the defenders. That translates to less reaction time and the advantage swings heavily in the attackers favor. But since the only numbers we have are the ones in the aforementioned blog post, that can't be expressed as part of the statistical analysis.
The question of whether or not men or women are better defenders is not something we can statistically answer with available data. That question begs the question of how it would be measured in the first place. Raw numbers on blocks and digs don't help. We don't have information on reaction times, movement times, or anything like vision or ability to anticipate hitters. Some of those numbers could be things teams might measure, but they aren't published alongside height and jersey number. Speed might be an indicator of whether or not a player can get into position to make an attempt at playing defense, but we are still stuck with the problem of not having numbers, and in spite of it not being a great measure of overall defensive ability we are such with digs.
A case could be made that men aren't significantly worse, and maybe even better, but that would be my own gender bias showing, even if I have (and I do) a fair amount of firsthand experience in both sides of the sport.
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