Wednesday, October 29, 2014

Hitting Value Relative to Average

In baseball "sabermetrics," various statistics have been developed to quantify a player's contribution to winning games, such as Bill James's Win Shares. Other, related statistics incorporate a comparison to possible replacement players (e.g., Wins Above Replacement and Value Over Replacement Player).

Some of these statistics have been carried over into other sports (e.g., Wins Shares for basketball). However, to my knowledge, these kinds of statistics have not been developed for volleyball. Winning at volleyball encompasses many skills: serving, passing, setting, hitting, and blocking. There has not been enough volleyball statistical work, in my judgment, to attempt an all-encompassing metric analogous to Win Shares, WAR, or VORP at this time.

With the aim of eventually taking us toward Volleyball VORP (or some such term), I have decided to focus on one skill for the moment, the important ability to hit for kills without committing attack errors (hitting the ball out of bounds or getting blocked for an immediate point by the opponents). These aspects of attacking are, of course, operationalized in the formula for hitting percentage: (Kills - Errors)/Total Hitting Attempts. Hitting percentage is strongly correlated with winning, so this seems like a good place to start.

My new statistic involves taking a given player's hitting percentage and subtracting some reference value of hitting percentage (akin to that of an average replacement player), The resulting difference is then multiplied by 100. As an example, if a player ended up with a value of 5.0, it would mean that, per 100 swings for each player, the focal player's kill-minus-error number is five higher than the hypothetical reference player's. Stated differently, the focal player would generate five more kills per 100 hitting attempts than would a reference player (having subtracted hitting errors from each player's number of kills).

Because middle blockers tend to have higher hitting percentages than outside hitters, I conducted all analyses separately for middles and outsides (opposite/right-side hitters, who were not always distinguished on teams' roster pages, were combined with traditional outsides who hit from the left-hand side). Thus, the new statistic will evaluate middles in comparison to a reference middle blocker, and outsides in comparison to a reference outside hitter.

I chose the Big 12 conference (which only has nine volleyball-playing schools) for this first effort, as I am based at one of the schools (Texas Tech). Also, each team has played eight conference matches so far, marking the halfway point of league competition,*

To get at the "above replacement" aspect, I wanted to take the average hitting percentage of all players at a given position who did not start for their respective teams as the reference value. However, not all schools included matches-started totals in their statistics and, even if they had, there were not that many usable reserves out there. Many non-starting OH and MB players had very small numbers of total hit attempts, so I didn't want to use their hitting percentages. Imposing minimum criteria for inclusion, for which I settled on at least 20 Total Attempts in conference play or at least 40 TA for the entire season, the number of "replacement players" appeared to be small.

Therefore, instead of averaging all reserve OH and MB in the conference, I averaged all the OH in the conference (starters and reserves) with the necessary minimum of hitting attempts (yielding an average hitting percentage of .197), and all the MB in the conference with the necessary minimum (yielding an average of .274). The "reference player" I alluded to above is now the same as the "average player" at the given position (OH or MB).

Below are the results. You'll notice that Haley Eckerman of Texas leads outside hitters with a +11.3 value. This tells us that, given 100 swings, Eckerman would generate 11.3 more kills (deducting hitting errors) than the average OH/OPP in the Big 12. Most of the results are not so dramatic. Many players will only get you an extra kill or two (or even just a fraction of one kill) per 100 swings, or lose you an equivalent amount.

Outside Hitters
Increased or Decreased Kills (Minus Errors) Per 100 Attempts (Relative to Average OH)

Eckerman (UT) +11.3
Attea (WVU) +8.5
Ward (OU) +7.7
Albers (KU) +7.1
Holland (TCU) +5.9

Anderson (WVU) +5.4
Holst (OU) +5.0
Sassin (KSt) +4.7
Victoria (UT) +3.5
Bigbee (ISU) +3.2

Ybanez (TTU) +2.7
Neal (UT) +2.5
Malloy (Bay) +1.8
Cerame (UT) +1.7
Hurtt (ISU) +1.6

Pickens (TCU) +1.6
Zumach (KSt) +0.9
Smith (TCU) +0.6
Gardiner (OU) +0.4
Stacy (TTU) +0.2

Keating (KSt) -0.6
Staiger (Bay) -0.6
Baker (UT) -0.7
Fragniere (TTU) -0.9
Dockery (KU) -1.0

Mikels (TCU) -1.2
David (TTU) -2.0
Sackett (WVU) -2.6
Capezio (ISU) -3.1
Kurht (ISU) -3.1

Allen (TTU) -3.5
McClinton (KU) -4.3
Rigdon (KU) -6.1
Montgomery (WVU) -7.2
Bardali (Bay) -10.7

Jones (Bay) -12.5
Munch-Soe. (Bay) -15.2

Among the middles, the leader was Mia Swanegan of TCU. The Horned Frogs' volleyball statistics page does not list Total Attempts, but I inferred that she likely has had at least 20 swings in conference play, because she has 16 kills (and a .433 hitting percentage).

Increased or Decreased Kills (Minus Errors) Per 100 Attempts (Relative to Average MB)

Swanegan (TCU) +15.9
Payne (KU) +11.1
Ogbogu (UT) +10.1
Bell (UT) +9.2
Jones (KSt) +9.1

McCage (UT) +5.9
Douglass (TTU) +5.5
Soucie (KU) +5.3
Conaway (ISU) +3.3
Hazelwood (OU) +2.7

McGuire (TCU) +0.4
Reininger (KSt) -0.6
Hill (Bay) -1.3
Mills (TTU) -1.4
Burleson (TCU) -1.9

Richburg (Bay) -2.8
McCoy (WVU) -2.8
West (ISU) -3.6
Spann (OU) -4.6
Wells (WVU) -4.8

Vondrak (ISU) -6.1
Shreve (WVU) -6.1
Itiola (Bay) -6.2
Knuth (ISU) -12.4
Grant (TTU) -23.0

As usual, some cautions apply to these results. The quality of passing and setting is obviously not uniform across teams, so any player's value of kills added/lost would likely be different if she played for another school. Also, as noted earlier, a player who does not appear to add value through hitting may nevertheless do so through blocking, serving, or other skills. I will try to develop new measures of these skills (relative to average) in the future. At that point, an across-the-board Volleyball VORP may be within reach.

*The plan was to use only conference matches in the analysis, but only full-season statistics were available for Iowa State, Texas Tech, and West Virginia.


Taylor said...

I am curious if these numbers end up being monotonic transformations of standard attack efficiency. Don't get me wrong, I love the idea of a zero baseline, I just wonder if these rankings will necessarily preserve the order of a rank of hitting efficiency. Nice work!

alan said...

I think you're right -- the rank-ordering of players by hitting percentage and by value relative to average would be the same. Subtracting the sample mean from everyone's hitting percentage would not change the rank-ordering. Neither would multiplying each result by 100. I think the main contribution of the new statistic is the interpretation relative to an average hitter. Also, the "per 100 swings" frame of reference is easier to visualize than conventional hitting percentage, in my view.

Anonymous said...

To confusing