Part I of this series[1] featured our first foray into the world of advanced Volleyball statistics. I presented an older, basic method of measuring passing ability along with options for statistical improvement; one presented by Chris Birch, Director of Volleyball Operations for the Virginia Volleyball team, and three inspired by my own basketball analogy.

In the meantime, Chris has settled on an improved passing formula, which I'll recap in this Part II. I'll also present some comments for consideration and attempt to outline what we as amateur Volleyball statisticians can learn from the passing formula development process. As before, we strongly encourage any and all participation.[2]

[Current Passing Formula]

I admittedly had some lofty expectations for Part I. I envisioned a free-flowing exchange of ideas. Input from all levels of expertise. A congenial yet heartily-argued and well-supported debate. Likely as a result of our general unfamiliarity with the nuances of Volleyball,[3] the intended discourse on the merits of each option was, well, pretty much non-existent on this site.[4] But it did elicit some rather strong opinions when Chris posted a link to VolleyTalk.[5]

Chris' score probability option was by far the most popular.[6] Message board posters offered useful suggestions such as accounting for the harm of failed passes while also discussing the size and choice of data samples.

The current embodiment of the passing formula below substantially incorporates these suggestions. You'll recall from the previous post that passes are carefully studied via game tape and rated on a scale from 0-3, where a 3-pass is optimal and a 0-pass directly results in a point for the opponent. Added to the discussion here are overpasses ("OvP"), wherein the intended pass goes awry; heading directly back over the net and missing the opportunity to set-up a teammate.

Previous: FBSP[7] = .452(3-pass%) + .339(2-pass%) + .21(1-pass%)

Current: FBSP = .426(3P%) + .329(2P%) + .176(1P%) +.115(OvP%)

The chart below shows the FBSP stats for each of the UVA Volleyball players through the fall season.[8] For reference, Chris determined an FBSP benchmark as 42.4%; the team average for ACC winners Florida State.





[Current Formula Comments]

The coefficients indicating the likelihood of scoring off of a given pass type have all slightly decreased in the current formula. This is a result of directly relating the scoring play to the pass type, instead of the scoring play to the number of scoring attempts resulting from that pass. If that didn't make sense: e.g., it's now (# of scores[9])/(# of 3-passes) instead of (# of scores)/(# of scoring attempts resulting from 3-passes). So they're lower because most, but not all, 3-passes result in a scoring attempt.

Hopefully Chris can chime in with his rationale for this particular change, but note it would seem to further remove the passing rating from the influence of the player herself. We're opening up the scoring probability for each pass type to the decisions of teammates. If Player 1 makes a 3-pass, should we consider whether her teammate Player 2 decides to go for the "kill?" Theoretically all 3-passes are rated such that they create an equal scoring opportunity from the moment they leave the passers hands[10]. In other words, should the 3-pass rating account only for the position it puts a teammate in to make a kill,[11] or should it also account for the rate of kill opportunities it creates[12]? Something to consider.

The current formula also introduces overpassing. This adds an interesting new dimension, as the FBSP now accounts for all passing scenarios that could actually result in a score for the given player's team, even if the score is the passive result of an opponent error instead of an active kill by the player's team.

But we again run into a familiar consideration. At what point are the influences on scoring too far removed from the player's performance to be considered as part of the player's passer rating? The probabilities in the above formula are the likelihood of a teammate successfully executing a kill after receiving the rated pass. The probability of scoring off that pass is therefore a function of the pass quality, the teammate's kill ability, and opponent defensive ability. Chris noted that the recording of overpasses additionally accounts for opponent attack errors. In an overpass situation, then, the scoring probability is wholly a function of opponent error; defensive error receiving the overpass and error involved in the subsequent offence. Should a player receive even minimal credit for such a pass? Discuss.[13]

[Lessons Learned]

Overall, the original post introduced Volleyball statistical concepts to a wider audience and prompted some useful debate for Chris' formula development. We got from point A to point B. Maybe the path wasn't exactly the intended straight line, but, hey, progress was made and lessons were learned.

It appears that measuring Volleyball stats in terms of scoring probability is overwhelmingly preferred. I can see the appeal. Putting everything in terms of points gained creates an easy visualization and comparison of how that stat actually affects team success. Still, isolating the desired skill is something to keep in mind in future formulas, lest we capture too much information for our intended measurement.

Chris has also recently developed a formula for "digs,"[14] and has asked for our help in improving it. Check back soon for another statistical foray into a whole new aspect of Volleyball.





[1] Which was ... a long time ago; I just wanted to give you a lot of time to mull things over. Yeah, we'll go with that.

[2] In the Comments or on Twitter would be best, but email works too

[3] Or at least I'm certainly a Volleyball n00b

[4] Except for fellow STL-er Brian Schwartz, who put in a solid effort in the Comments

[5] Among the stranger comments is the third, from "alantech," who appears to want to get into some sort of IP debate over the rights behind using "metrics" in relation to sports. It appears even sophisticated message boards are not immune from message board users.

[6] That's putting it mildly. The only one that dignified my options with a response: "math for the sake of math [without] actually telling you anything useful."

[7] First Ball Scoring Probability

[8] for comparison, the old average pass rating stat is the AVG column

[9] or "Kills"

[10] Or forearms, I suppose

[11] the old method: (# of scores)/(# of scoring attempts resulting from 3-passes)

[12] the current method: effectively incorporating both (# of scores)/(# of 3-passes) and (# of scoring attempts resulting from 3 passes)/(# of 3-passes)

[13] This old Mike Myers "Coffee Talk" SNL skit pops into my head every time I hear "Discuss" (see @ 0:54). Seriously. Every. Single. Time.

[14] I'll explain more about exactly what this is in the next post. For now, just consider it the primary aspect of defense.