BYU and UCLA have played three times this season, in a pair of regular-season matches in Los Angeles (here and here) and in the MPSF conference-tournament final in Provo. The Cougars have taken all three contests, each in four games. In each of these matches, Bruin serving errors have played a seemingly large role in determining the outcome. UCLA committed 15 service errors in the first match, 20 in the second, and 27 in the third. I find this unbelievable, but in the three matches combined, the Bruins missed one-quarter of all their serve attempts (62 misses on 246 serves, which is .252)! (These and other statistics appear in a table below, which you can click to enlarge.)
Of course, a strategy of "just get it in" would help the Bruins only modestly. BYU won nearly two-thirds (.648) of the rallies on UCLA's serve (i.e., when the serve was non-terminal, not an ace or error). If the Bruins floated a bunch of soft, unchallenging serves the Cougars' way, BYU's side-out rate on rallies would almost certainly go up by a sizable amount. The other side of the argument, though, would be that UCLA won zero points on all its missed serves and picking up even a few extra points by winning rallies on less-aggressive serves could be important in a close match.
Tristan Burton and Scott Powers published a thoughtful and sophisticated analysis of the serving-aggressiveness trade-off -- more-effective serves vs. more errors -- in 2015 in the Journal of Quantitative Analysis in Sports (summary). As these authors note, "a balance among [service-ace fraction, service-error fraction] and opponent offensive ability must be considered in order to guide service strategy" (p. 3). Using calculus and other advanced mathematics (e.g., the "Newton-Raphson solution"), Burton and Powers derive graphical displays for determining which players need to serve more or less aggressively. Lacking the volume of data and the brainpower* necessary to apply Burton and Powers' formulations in full, I came up with my own analysis of UCLA's serving vs. BYU, which made intuitive sense to me.
Using play-by-play sheets from the three BYU-UCLA matches (available via BYU's schedule page, by clicking on "Box" for a given match, and then "Play-By-Play"), I recorded the outcome of every serve for each of UCLA's eight main servers (listed in the table above). A serve could result in one of four outcomes: an ace or an error (both considered "terminal" outcomes), a rally (i.e., after a non-terminal serve) won by UCLA, and a rally won by BYU.
Not much was going on with UCLA ace serves (only 18 total in the three matches; 8, 9, and 1 by match chronologically). I therefore focused on service errors. For each of the eight Bruin players, I computed his service-error percentage (number of errors divided by total number of serves) and the percentage of time on that player's serve that UCLA won a rally after a non-terminal serve.
To the extent aggressive serving results in both service errors and (when the serve goes in but does not produce an ace) the receiving team being taken out-of-system in running its offense, we should find a positive correlation between UCLA players' service-error percentage and percentage of rallies won by UCLA. Indeed, we do, as shown in the following graph.
For readers with statistical training, the correlation coefficient (r) = .52. This is a fairly large correlation, but caution is warranted due to the small sample size of 8 players. (Free plotting software is available here.) A couple of players exemplify the trend. Oliver Martin committed only 1 error on 29 total serves vs. BYU during the season (3.4%), but his (apparently) low-risk serving also was easy for the Cougars to field, so that the Bruins won fewer than one-third of the rallies on Martin's serve. At the other extreme, Jackson Bantle had a much higher rate of service errors, committing them 28.6 percent of the time, but UCLA won 44.4 percent of rallies on his serve.
I'll leave the precise optimization of service aggressiveness to Burton and Powers. If you want to determine how risky to be in your serving, taking account of the opponent's ability to launch its offense, you should look at their article. What I've concluded from my little exercise is that UCLA seems to have a good reason to serve aggressively. However, the Bruins' service-error rate does seem excessively high.
UPDATE: A BYU-UCLA match-up in the NCAA men's final never happened, as Ohio State beat the Bruins in a tense five-game semifinal match. The Buckeyes survived three match-points in the decisive game, before winning it 18-16. OSU continued its momentum into the championship match, shockingly sweeping BYU. The Buckeyes outhit the Cougars, .374-.296; not only that, OSU took 20 more attack attempts than did BYU, 91-71, indicative of the Cougars' passing difficulties (box score). BYU's award-winning right-side (opposite) hitter Ben Patch, hitting .383 entering the NCAA tourney, performed well-below that in the final, hitting .091 on 10 kills and 8 errors in 22 swings.
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*I did take a year of calculus as a college freshman 35 years ago and I occasionally watch calculus lectures online to retain as much of it as I can. However, I feel nowhere near confident enough to conduct the analyses reported by Burton and Powers.
