Recent thoughts which lead to another topic to consider later. Thinking I will 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 out loud to myself! Maybe, “More with Less” is better. Oh, I like that! “More with Less is Better.”
The end of the 2/22/24 Post – “Maximizing Volleyball Potential to Earn Volleyball Currency – A Spectators View of Strategy”
To remind readers from where this vein of thought originated, a couple excerpts from the aforementioned post:
“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 …“
“ 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 theirs, too. Since win rate is currency for volleyball performance, then hitting efficiency, as it is currently calculated, might not define its earning power in the best manner. … 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.“
NOTE: The precursor to this post was intended to be less analytical and appeal to a larger audience as it related it to Black-Jack, and gave anecdotal evidence for supporting serving aggression plus more. It was a game theory point of view for a macro-view of the game itself. This follow-up is more aligned to a game theory approach of a micro-view intended to answer the question, “When is less efficiency actually more beneficial to a team.”
When an entrepreneur produces a business model, one objective is to maximize profit. Later, if changes to reduce revenue become warranted, it would be ill-advised to assume profit would also decrease, too. Sometimes a precursor to revenue reduction incurs significantly less cost, and in those cases the profit can go up, even while revenue decreases. (Think corporate downsizing…) The hitting% statistic in volleyball is like revenue and the point win rate (W%) in volleyball similar to profit. If the goal is to maximize W%/Profit, then whatever is required to do so will be beneficial to that objective. Even should that thing be reducing revenue, or to complete the metaphor, playing volleyball in a manner which might reduce efficiency (H%), if it can achieve the goal to maximize point win rate.
Last month I was talking to a prominent coach in the D3 landscape who mentioned to me he wants his pin hitters to be aggressive enough to live with an error rate of 16%, knowing if they do this, the expectation would be for their kill rate to be as productive as possible, at least 40% I believe he said was the general goal there. This would make it so efficiency goals were no less than .240, after subtracting. This seemed to be a retrospective standard for how he communicates the degree of aggressiveness he wants his players to have when swinging. Over time each one likely gravitates to the best version of himself, but only if all hitters are created equal.
The conversation started with a comment I made about former St. John Fisher OH, Josh Bigford, who last season had an error rate less than 6%, exactly 5.5%, as I just took note. A number so low it was a full standard deviation beneath the second lowest in the country, and would still be if compared to today’s stats as well. I always marveled at this, partly because he coupled it with a 39% kill rate, but being who I am, I was most enamored with it being greater than 4 standard deviations from the mean of the best 200 in the country. That is an event so rare, check back in 100 years and it will not have happened again! Even a 5-setter match like NYU & Baruch with every set a 2 point margin, 4 going to extra points, will have happened a few times by the time any OH playing D3 does that again. Assuming volleyball is still being played in the 22nd century, that is.
I’ve written posts about the paradoxical nature of a hitting efficiency statistic, already. H% = (Kills – Errors)/Attempts The earlier ones related to combining data to create season long statistics which can lead to short-sighted conclusions. This paradox is different and comes about by virtue of case studies, like the one below, to prove it is possible for more aggressive hitters with marginally less efficiency to provide their teams with higher win rates.
CASE STUDY: Consider an ultra-passive hitter with 1 kill & 0 errors in his first 10 swings who then becomes ultra aggressive, generating 5 kills and 5 errors in his next 10 attempts. This hitter’s efficiency is cut in half going from .100 after 10 attempts to .050 after 20, even as his team won 5 of the last 10 points, something only achievable in the first 10 swings, if it subsequently won no less than 4 of the 9 transitions to follow the non-terminal swings. It likely isn’t going to happen if the opponent is a 70th percentile D3 Men’s VB team now having possession of the ball!
I will be using a 70th percentile D3 team as the standard opponent for all demonstrations to follow for a few reasons. [1] This is an opponent who achieves a 40% kill rate with a 16% error rate. (Usually ranked in the mid 30’s in the T100 with a rating close to 13 points, too.) [2] Not only was this a general goal created by a coach of a top 25 program for his own team, but the averages of the best 200 hitters in the nation are fairly close to these standards, [3] Many of the ranked teams in the landscape play a schedule whose average rank of opponent is relatively close to 30-ish. Perhaps most importantly, [4] Since I am going to be contrasting multiple hitters to make a point, it is advisable to let the opponent act as a control for any mindful study.
Note: The model seen below is for a team’s expected point win rate when any individual hitter swings against a 70th percentile D3 opponent, and it can be modified by changing the state of Kill % rate and the Error % rate for any opponent. This is done using a method called a Markov Process. However, it won’t be altered for the remainder of this post in order to compare “apples to apples” on the following slides.
Seen above is a point on the grid for Owen Wickens of Nazareth, determined by his Kill% and Error% for the 2024 season to date. It informs there is a 64+% chance Nazareth will earn any point in which he swings against this top 30-ish team Nazareth would be playing. Nearly 52% right away as he is credited with a kill, and the rest of which is determined by a Markov Chain forecasting its “absorption rates using its transitional rates,” known to volleyballers as terminal & transitional. i.e. The sum of his kills and errors is a little beyond 70%, so there is still close to 30% yet to be accounted for – This is where Markov comes in to determine his team should still win close to 12% of his 30% transitional swings not arriving at either a kill or an error.
This point represents Owen’s current state, just like any other point I could place on this grid represents any hitter’s current state. Consider the answer to the question, “What happens if he or any hitter becomes more aggressive than his current state?” More aggression certainly will increase both kills and errors to some degree, forcing any hitter’s current data point to shift in some manner to the lower left from where it starts. Owen’s current state is already significantly to the lower left on this grid, so increased aggression may or may not improve his team’s point win rate, and most assuredly would reduce his efficiency.
If he increased his aggressiveness to improve both his kills and errors by just 1%, his team is certainly better off because the table shows a 64+% win rate improving to 65+%. This is a consequence from winning half (1 more kill to every 1 more error) of a portion of those remaining transitional swings. This is better than his team would otherwise be expected to win against this level of opponent. (This is the 1.0 E/K gold line threshold well above, and far to the left of Owen’s data point.) In fact, if you scan to the left from his data point, the first gold line seen is 1.2 E/K which simply stands for a presumed additional 1.2 errors for every 1 additional kill, apparently resulting from his increased aggressive behavior – Also synonymous with 20% more errors than kills, equivalent to mean a 45% probability of winning what otherwise would have been a transitional swing had he not shown more aggression. The team would win more points with that aggression while Owen’s efficiency begins to take a hit, but as his data point moves closer to the 1.2 line it is approaching a threshold for which any additional aggression will fail to increase win rate. So for Owen, when his added aggression can’t produce at least 5 more kills to every 6 errors, it turns into a liability for the team having longer been a liability for his efficiency statistic. (1.2E/K ratio is 5 kills per 6 errors.)
A series of slides with current hitters data points and the meaning behind them related to the concept above:
The rest of this post is for those truly interested in dissecting a little bit further. At this point only hoping you made it to the slides above which I believe to be the most informative part of this post, unless you happen to be a coach.
Going back to Owen with this vector analysis.
For coaches and players consideration, below are 4 hitters who may likely benefit from higher aggression in their hitting behavior. Even Player 4 who is obviously a great hitter who presently is hitting .375 and earning his team points at least two-thirds of the time he swings at a ball. It wouldn’t be surprising to find out this is a Middle Hitter by comparing its position on the grid to every hitter from above who was a pin hitter. Each player below falls directly to the right of a different E/K marginal threshold. This essentially means Player 1 really needs to ramp up his aggression, Player 2 maybe a little less, Player 3 even less than that, and Player 4 just a smidge! The farther left and down a data point goes, the closer to his sweet spot any hitter becomes. This gold shaded “sweet spot” in the shape of a circular sector will always drive a lesser efficiency for any player, but serves the team’s best interest by increasing point win rate.
As you scan right to left, looking closely, you will see the size of that gold sector sweet spot is getting smaller. This is because there will be a law of diminishing returns for aggressiveness as a player becomes better skilled in the art of hitting. All decent D3 hitters over time with increased aggression will move to the lower left, but not all will be approaching the same exact spot on this grid. It will be different for Middles and Outsides, and it will certainly be dependent on a player’s temperament, comfort level in accommodating to higher degrees of aggression, and experience. It might be interesting to plot 10 hitters on this grid, 5 each from those playing in a conference final next month to see which team is likely to be the aggressor of the match, among other things. There I go again. I can’t look under one rock to see what’s there without finding another 5 rocks to look under as well. A blessing and a curse!
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