Over at the VolleyTalk discussion site, frequent contributor "P-Dub" raises an interesting question about hitting percentage, defined as: (kills-errors)/total attacks.
Player A: 6/3/15
Player B: 3/0/15
Both players have hit .200, but the first has done it with more kills and more errors. Which of these contributions is better?
To answer the question -- in theory, if not in practice -- P-Dub suggests looking at what the defensive team does with the balls the offensive team has neither put away (kills) nor failed to place in-bounds on the other side of the net (errors); in other words, what happens to the balls that remain in play?
For example, if a team is really good at converting opponents' non-kills into its own kills, then the aforementioned Player B's 3/0/15 line isn't good, because it gives the other team 12 opportunities to produce its own kills. This seems like a productive line of thinking, but it would be good to add some actual data to the debate.
The full discussion thread, which has now reached three pages, can be accessed here.
UPDATE (9/28): Tristan Burton, whose work has been cited before on this blog, sent me the following comment on evaluating hitting performances (with his permission to reproduce it).
I just saw your post about hitting efficiency. My paper defines "hitting effectiveness", which includes the outcome of any non-terminal swings by a hitter. So if I attack and the opponent digs me and then immediately gets a kill of their own then it counts against my hitting effectiveness. In English (instead of mathspeak), hitting effectiveness is hitting efficiency minus (the fraction of my swings on which the opponent gets their own attack) times (their hitting efficiency on those attacks). Usually, hitting effectiveness is lower than hitting efficiency and for those hitters who make a living just putting the ball in play it might be substantially lower (depending on whether or not the opponent is good at converting). I've looked at data for Pac-10 women where two OH's had virtually the same hitting efficiency but drastically different hitting effectiveness numbers because one of the players was aggressive and had a higher kill% and higher error% but the opponent could not easily convert her "in-swings" while the other player was putting more balls in play and the opponent was converting easily. There seems to be a focus in the volleyball community on minimizing errors but that's not what you are really trying to do, you're actually trying to increase the score difference between yourself and your opponent as much as possible with every swing (this is what hitting effectiveness actually tells you) . An in-swing that the opponent converts for a kill is no different than a hitting error as far as the score is concerned. As with so many things in life, there's a risk vs. reward relationship that needs to be considered.
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A team having the service will score a point by two different sequences indicated by 0j +i
or –j where ( 0 )is a neutral attack
(minus ) – an error attack and
(+) a kill and i j indices for the two teams
In case of consecutive double negative errors following sequences can be added
0 00+, 0 0000+ etc and 00-, 0000- etc
The terms 0i 0j are for the two teams i and j and are for simplicity presented as 00
For certain cases , often near equal strength teams the yields for first attack and on defense may have the same efficiencies 0 – and + may hence be considered as constant over the rally and the terms constitute a geometrical series the sum of which will be
0+ plus - /(1 – 0*0)
A numerical example follows
team + 0 -
i 50 30 20
j 40 35 25
For team i the probability of scoring a point will be( 0.25*0.50 +0.25)/(1- 0.30*0.35) = 0.47 for the second team j this will be ((0.30*0.0.40) +0.20)/ (1-0.30*0.35) =0.36
For the expected average result of the match will be taken into account that the number of side outs for both teams will be equal This is the case when the team starting the service wins the set .
(25 – 25-0.47)/ (1- 0.36) = 20.4 hence 25 – 20
In case one of the tow teams makes more neutral attacks the result can now be calculated. In following example the ratio of kill attacks to errors is assumed to be constant. Results are as follows
0.35 20.4
0.40. 19.8
0.45 19.0
0.50 18.4
0.55 17.7
0.65 16.7
For each 5 % more neutral attacks the team loses one point.
In case yields are much different for first attack and on defense , than the calculation has to be performed in two parts , one for first ball and the remainder making same assumptions of equal efficiency for attack on defense.
0+ plus 0+/(1-0*0) and – plus -/(1-0*0)
In case data are available for breakpoint ( points scored on service ) than the values can be compared after correction for service aces. It is often found that those value may be 0.8 to O.9 times the original non corrected values.
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