Game theory in playing Black Jack mandates placing higher wagers when the remaining deck is richer than normal with Aces & 10’s. It also requires wagering smaller amounts when it is less so. The only problem? To do this requires what casinos call card counting, and they deem this action to be cheating. Don’t put it past a casino to call anything illegal if it hurts their bottom line, ethical or otherwise. (For those who prefer the side of a metaphor for card counting in Black Jack to that of game theory pertaining to volleyball, this is for you!) Games are intended to be played with strategy, and because there exists an approach to enhance the state of one side, it shouldn’t give the other the right to simply say, “You can’t do that!” Unless of course the other side gets to make the rules, too – Like CASINOS! Thank goodness neither of two volleyball opponents wield that kind of power because it sure would be a lot less fun if one opponent took their ball and went home every time the other produced a successful strategy to improve its chances to win!
The currency in volleyball is win rate – the entirety of point scoring and side-out rate merged together into one. It drives every choice, every action, every moment. Offense is the pursuit to maximize win rate when conditions present an advantage, and defense is the pursuit to minimize the opponent’s win rate when conditions present a disadvantage, metaphorically similar to conditions for when varying wagers in Black Jack optimizes a players’ position. Based on these definitions, swinging at a well placed set is typically an offensive action while serving the ball is more often a defensive one. (In those times they’re not, then one contestant is superior to the other, and all the strategy in the world will not matter one bit as it pertains to the outcome.) Maybe this is a reason why hitting efficiency is measured, to determine the degree to which any advantage is capitalized upon. Meanwhile, minimizing the opponent’s win rate when serving the ball requires executing it in any way to facilitate a possession less likely to be won on their part. Along the way, this pursuit sometimes provides an ace, too. No better way to minimize an opponent’s advantage to win a side-out than by guaranteeing they won’t!
Too often, sentiment by spectators as it pertains to volleyball service goes something like this: “You lose 100% of the points you can’t win – Give yourself a chance by not gifting the opponent a service error.” There is a cost to be paid for this viewpoint because as skill level of an opponent improves, a law of diminishing returns defines it. In 2022 & 2023, I tracked two consecutive seasons of all serves by the same team, mostly the same players one year older. This team’s version of itself the second year was essentially equal in stature, both seasons producing the same 24-8 records with comparable SOS. (Average rank of opponent was approximately 30th in the nation both years.) It even ranked a nearly identical 9th and 10th in the final AVCA Poll for each season, too. For crying out loud, figuratively and literally, they even lost to the same opponent in the first round of both year’s National Tournaments having earned EXACTLY a 48.0% point win rate in both matches, losing by an overall margin of 7 points and then 8 points a year later, with both matches 365 days apart being played in Jersey, no less! But I digress. – Anyhoo… , I tracked many 1,000’s of serves. Those carried out against top 30 nationally ranked opponents most interested me because I believe the level of concern any server has is similarly heightened with a justifiable threat to be defeated by an opponent. Those among the best 30 in the nation would provide this to a team roughly 10th ranked. That, and the caliber in receiving being reasonably commensurate to their skill level in serving, also. As service errors reduced from a 20% error rate to 15% from one year to the next, this team’s point win rate also decreased from 38% to roughly 36.5%, a statistically significant decrease with greater than 90% confidence because of the large sample sizes involved. A decrease that if not met with a side-out rate increase nearly the same, would produce an additional 10% chance to lose a match against one of these top 30 opponents to which I refer.
This study surely contradicts spectator logic cited above, given they erred more in the previous year, but still won points served at a higher rate against like competition. Had the same head coach been there for both seasons, it is probable this difference wouldn’t have been detected. i.e. The drastic change in service error rate is far more likely a function of ideology than any differences in personnel executing the task because those serving were mostly the same players having similar skill sets to those receiving, too. Even the floaters, for which they were the exact same players, errored half as much from the first to the second season while earning a lesser point win rate. All of this suggests a delicate balance tug-of-war between risk/reward favored more aggressive service, even with the increased risk of error to come with it. This implies service aggression prevented higher quality opponents from capitalizing as frequently as they otherwise would have. i.e. Reducing an opponent’s advantage to first possess the ball took place even with a third more errors to start. Understanding this is not to advocate such a strategy is always the best course of action. For example, if any team’s chance to win a match were roughly 90% because it is the higher functioning of the two, this aggressive strategy in the short term almost certainly would reduce match win probability. In fact, the lower functioning team, in this case, would be “served better” by its aggression having less to lose by doing so.
In the last month, I have written two different posts related to the ambiguity in conclusions related to hitting efficiency. The first, illustrating Simpson’s Paradox, showed how accumulating multiple matches of data (what is done for season-long stats) can be deceiving to interpret performance. Remember how Owen hit .100 better in every one of 5 matches but still was hitting .030 worse for the season? The second showed how it was possible to be out-hit by consecutive opponents, but still win both matches to sling-shot to being the #1 ranked team in the country (Wentworth). Earlier in this post, I rhetorically questioned if hitting efficiency is measured to determine how well a team capitalizes on its advantaged situations – Of course it is! Let’s explore how well this purpose is served by that metric in a little more detail below:
Consider three hitters, Domineering Dom, Regular Reggie & Timid Tim. Dom swings 10 times earning 5 kills to 4 errors, Reggie 3 kills to 2 errors in 10 swings, and Tim earns just 1 kill but doesn’t error, also attempting 10. How convenient they each had 10 attempts! LOL All three players are equally efficient (hitting .100), but the team’s win rate in points where these swings took place will only remain equal at 55% so long as all subsequent points not to terminate from their swings eventually end with their team winning exactly half. They won’t. Failure to terminate on any swing takes an offensive opportunity, ripe with potential, to a defensive condition whereby winning half of the subsequent points is not attainable in the long run, at least playing any functionally comparable opponent. If equally efficient hitters can facilitate differing win rates for their teams, then there certainly exist conditions for which less efficient hitters will lead to higher win rates for their teams, too. Since win rate is currency for volleyball performance, then hitting efficiency, as it is currently calculated, might not define its earning power best. Wasn’t it the Oakland A’s who realized guys with lesser batting averages who either walked a lot more or hit more homers were responsible for producing more runs, the real currency in baseball? (Moneyball) Can’t people earn $30K less per year in Buffalo than in Manhattan and still have more purchasing power to produce a higher standard of living for themselves and/or their families? Didn’t we already conclude a lesser rate of serves in play actually can produce a higher point win rate while serving? Maybe therein lies the key to defining exactly when, and by how much, lesser hitting efficiencies can lead to more usable volleyball currency – higher win rates.
These recent thoughts leading to another topic to consider later in the season. Thinking I might call it “More with Less – Conditions Favoring Team Win Rates Even with Lesser Efficiency to Produce Them.” I almost forgot to breathe as I was saying that title to myself! Maybe, “More with Less” is better. Oh, I like that! “More with Less is Better.”