Despite falling to William Smith in the Liberty League championship game, Vassar women’s soccer finished the season with a strong 11-8-1 record. The Brewers’ defense was particularly tough, forcing opponents into poor shots. Only 44.5 percent of the shots taken by Brewer opponents were on goal, the second-lowest percentage since 2000.
Wait. If the defense was so strong, then why did they allow their 7th highest goals per game among their last 17 seasons? I theorized that the low shots on goal percentage (SOGP) the Brewers held their opponents to might correspond to a high number of total shots allowed. World-class teams playing against vastly inferior ones can maintain accuracy while taking tons of shots, because they can get point-blank looks at the goalmouth at will. Alternatively, vastly inferior teams can manage very few shots, and they tend to be desperate 35-yard prayers because they can’t get closer to the goal. However, in evenly matched games like your average Liberty League contest, the more shots you take, the higher your divisor is for SOGP, and the lower your percentage of shots on goal will be. You are less likely to be accurate on any given shot, but more likely to score a goal over the course of a 90-minute game chock-full of shots.
The data support my theory (Vassar College Athletics, “Women’s Soccer Cumulative Statistics,” 02.16.2020). Opponents’ shots per game significantly predicted their SOGP, explaining 16.8 percent of the variance in their SOGP (r2 = .168, p = .10). For every extra shot taken, SOGP decreased by one percent on average. While opponents’ SOGP did not predict the amount of goals they scored per game (r2 = .005, p > .50), the amount of shots opponents took per game did, explaining 11.3 percent of the variance in opponents’ goals per game (r2 = .113, p = .19). For every extra shot taken, opponents’ goals per game increased by 6.5 percent on average.
It’s a simple case of expected value: If adding one shot decreases the accuracy (in terms of a shot being on goal) of all other shots, then the expected value of the new shot should be equal to or greater than the expected value taken away by reducing the accuracy of all other shots. For example, say a team takes 50 shots one game at a SOGP of 40 percent. According to the model, if they were to try and take 51 shots the next game, their accuracy would likely decrease to 39 percent for all of those shots—is the expected value of another shot at an accuracy of 39 percent worth the one percent accuracy (and thus, expected value) it takes away from the 50 other shots?
Another SOGP tidbit: Number of corner kicks per game significantly predicted SOGP, but not in the way you might think. For each extra corner kick, SOGP decreased by .16 percent on average (r2 = .113, p < .10). Taking an accurate shot off of a corner kick is hard!