"Natural Experiment" Compares How Texas Tech Hit Before and After Change of Setters

The women's volleyball team at Texas Tech University, where I'm on the faculty, just finished a Big 12 season that seems hard to describe as anything other than a disaster. After winning their conference opener against Colorado, the Red Raiders lost all 19 of their remaining Big 12 matches (Oklahoma State does not field a team in this sport, meaning that each partcipating school faces 10 opponents, twice each). In Texas Tech's final 11 matches, it only won one game (i.e., 10 times it was swept 3-0 and once lost by a 3-1 score). Above is a photo I took at Tech's home match against Iowa State, relatively early in conference play.

Among the misfortunes experienced by the Raiders, senior setter Emily Ziegler went out -- for the season, it turned out -- after the eighth Big 12 match with a foot injury that required surgery (here and here).

Replacing Ziegler for the Raiders' remaining 12 conference matches was Kourtney Dunnam, whose path to the Texas Tech starting setter's role was unusual, to say the least. After playing for one year at Wayland Baptist University, Dunnam transferred to Texas Tech, where she was the team manager for two years. Certainly, one must admire Dunnam's persistence in working her way up to a roster spot in a major Division I conference.

The research methodologist in me saw an opportunity to take advantage of this "natural experiment" (some might say "quasi-experiment") involving the Red Raiders' change in starting setters, a change that was brought about in more-or-less random fashion.

As shown in the chart below, there were eight opponents (shown in blue) whom Texas Tech faced once with Ziegler as starting setter, and once with Dunnam in that role. That aspect provides experimental balance. Less optimal for research purposes are the facts that (a) Ziegler's matches were in the early part of conference play and Dunnam's in the later part; and (b) identity of the setter was confounded with game location (i.e., for any given opponent, if Ziegler faced the team at home in Lubbock, Dunnam of necessity faced it on the road, and vice-versa).


Still, though, I thought it would be interesting to compare the Red Raiders' hitting percentages under the direction of the two setters, but only against common opponents (Dunnam faced Kansas State and Oklahoma twice each, listed in red above, the data from which are not included in the analyses).

As it turned out, Texas Tech's average hitting percentage was virtually identical against the eight common opponents, .145 under Ziegler and .141 under Dunnam.

What is also apparent from the chart is that the quality of the opponent seemed to be a much more important factor in the Red Raiders' hitting percentage. Nebraska and Texas tied for the Big 12 title, each with a 19-1 record. Against the Cornhuskers, Tech hit .075 and .079 in the teams' two matches, whereas against the Longhorns, Tech hit .047 and .034. Conversely, against the less-dominant conference opponents, the Raiders usually hit in the .10's and .20's.

For each of the eight opponents common to Ziegler and Dunnam, I then averaged Tech's hitting percentages for the two matches, and correlated this with the opponent's Big 12 winning percentage (the idea of comparing a team's hitting percentages against different opponents was suggested in the comments to my earlier posting on hitting percentage).

As shown in the plot below, the correlation was a robust r = -.70 (two-tailed p = .053). In other words, as an opponent's winning percentage went up, Texas Tech's hitting percentage went down. Correlation does not prove causality, but the result makes logical sense.


It would, of course, be a gross exaggeration at this point to say that the identity of a team's starting setter is irrelevant. This analysis was done on only one team, in one year, in a small number of games. Texas Tech's hitting percentages under Ziegler were already pretty low, so even with the less experienced Dunnam, there may not have been much room for them to drop further (i.e., a "floor effect").

If any of you readers know of further examples of a team abruptly switching setters midway through the season, please provide that information in the Comments section. I would be happy to attempt replications of the above findings with other teams.

Perfect Hitting Night for Nebraska's Tracy Stalls

The story coming out of the University of Nebraska volleyball building tonight, quoting from this news release, is that:

Tracy Stalls tied an NCAA record by putting down 13 kills on 13 swings for a perfect 1.000 attack percentage, as the Husker volleyball team sent Stalls and NU's three other seniors out in style Saturday night with a 30-18, 30-10, 30-11 sweep of Texas Tech.

For those not all that familiar with volleyball statistics, what this means is that 13 times the ball was set up for Stalls to swing at, and all 13 times she delivered balls that the Red Raiders could not field. Stalls hit no balls into the net, nor out of bounds, had no balls blocked back in her face by Texas Tech, and did not even have any balls dug up by the Red Raiders in the backcourt.

Now, that's a hot hand!

[Cross-posted at my Hot Hand blog, for the study of sports streakiness.]

Home-Court Advantage in Volleyball

One of the most widely discussed phenomena across a number of sports is the home-court (or home-field) advantage (HFA). According to Cecil Adams, who fields readers' questions on a website called The Straight Dope:

Perusing a comprehensive recent study ("Long-term trends in home advantage in professional team sports in North America and England [1876-2003]," Pollard and Pollard, 2005), I note as follows: (a) since 1900, notwithstanding some year-to-year swings, MLB home-field winning percentages have been remarkably stable at about .540; (b) the NFL HFA fluctuates a lot, no doubt because fewer games means more statistical noise, but home-field wins are usually in the 55 to 60 percent range; (c) NHL home-ice wins have declined from 60 percent in the 70s to a pretty steady 55 percent since the mid-90s; (d) NBA home-court wins dropped from 65 percent in the mid-80s to 60 percent in recent years, still the highest of the U.S. sports studied; and (e) HFA shows up in UK sports too.

How much of a home-court advantage does women's indoor collegiate volleyball confer? Of the sports cited above, basketball shares with collegiate volleyball the environmental features of being played indoors, in a relatively small space, and with screaming fans close to the action (if there are screaming fans in attendance). I thus expected to find a volleyball HFA toward the higher end of those mentioned above.

While browsing some sites in search of historical volleyball statistics, I came across a page in the historical section of the 2007 Pacific-10 women's volleyball media guide (see "Team vs. Team Results") that summarized the head-to-head records between all pairs of conference opponents from 1986-2006, breaking the totals down by location. (The page actually said 1986-2005, but given that each pair of rivals was listed as playing 42 matches, that fits with 21 years, not 20).

With 10 teams, there are 45 head-to-head rivalries. Going alphabetically, we have Arizona, who has rivalries with nine other teams. Next is ASU who, having already accounted for its rivalry with U of A, has eight rivalries. Next is Cal-Berkeley who, having already accounted for its rivalries with U of A and ASU, has seven. Accordingly, 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45. In each of the 21 years, there have been 90 conference matches (two matches, one at each team's home, in each of the 45 rivalries). Overall, then, I had data from 1,890 matches (21 X 90). In the future, I'll analyze other conferences, but a database of nearly 2,000 matches is a good place to start. Also, an essential element in testing HFA's is schedule symmetry, that each pair of teams plays on each team's court during the season, and the Pac-10 has that.*

If you look at the above-linked page in the Pac-10 history section, you'll see a bunch of entries that look like the following:

Oregon vs. Oregon State
Series: OSU leads 23-19
at ORE: ORE leads 12-9
at OSU: OSU leads 14-7

I've put the numbers in green and orange, the school colors of UO and OSU, respectively, to help distinguish the teams. We see that, with 21 matches played at each place, the Ducks won five more at home (12) than away (7), and conversely, the Beavers also won five more at home (14) than away (9). The Oregon-OSU series thus receives an HFA score of 5. Below is shown the distribution of all 45 HFA scores, with another specific example (USC and WSU) highlighted (you can click on the image to enlarge it):


My own characterization is that the home-court advantage is pervasive, yet modest. There were only three instances of teams doing better against a particular opponent on the road than at home, and in each case only by one match (shown above as "-1"). Several more rivalries above had a "0" differential. Many -- though not all -- of these scenarios reflected dominance; for example, Stanford was 21-0 against Oregon State in Palo Alto and 21-0 in Corvallis.

The rest of the histogram shows consistently positive HFA values, indicating that Team A tended to have more wins against Team B on Team A's court than on Team B's. In a few instances, the HFA margin was as large as +6 or +7, but the average margin was close to +2. What that tells us is that, having played a team 21 times on your own court and 21 times on theirs, the average HFA comes to about one excess win per decade due to the home court.

Another way to look at the HFA -- as shown above for North American leagues in baseball, football, hockey, and basketball -- is by simple percentages. What percent of games were won by the home team and by the visitor? Aggregating over the 1,890 Pac-10 matches within the study period, 1,038 matches were won by the home team (.549) and 852 matches were won by the visitors (.451).

Thus, with an HFA of essentially 55%, Pac-10 women's volleyball seems consistent with the other sports. The scenario of loud, screaming fans right on top of the players notwithstanding, this initial volleyball study fails to find an outsized home advantage on average, although a few particular rivalries have them.

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*The Pac-10 media guide said that Cal was 14-8 at home against Washington State, whereas WSU led Cal 12-8 on the Cougars' home court, thus implying that an asymmetric 22 matches were played at Cal and 20 at WSU. I consulted Cal's media guide and found the Golden Bears' HFA to be 13-8 and WSU's to be 14-7. There appear to be other scattered errors throughout the Pac-10 records.

NESSIS Presentation on Volleyball

Just about a month ago, Harvard hosted the inaugural New England Symposium on Statistics in Sports (official site, news release).

In perusing the abstracts of conference papers (which can be accessed through the conference website, where it says "Program"), I came across a study (presented in poster format) entitled, "Skill Importance in BYU Women’s Volleyball: A Bayesian Approach." The authors were BYU statistics graduate student Lindsay Florence and professor Gilbert Fellingham.

The beginning of the abstract gives the basics of the study:

The BYU womens volleyball team recorded all skills (pass, serve-receive, set, etc.), rated each skill, and recorded rally outcomes (point for BYU, rally continues, point for opposition) for the entire 2006 home volleyball season. Only sequences of events occurring on BYU's side of the net were considered.

Florence and Fellingham were nice enough to e-mail me a PDF of their poster. It conveys some basic statistics in the form of two-way cross-tabulated tables, along with more complex, Bayesian analyses.

Each of the simpler, two-way tables shows the relationship between a type of skill performance and outcome of the "possession" (BYU point, continuation of rally, or loss of point). A 6 X 3 table, for example, examines six grades of setting (from "perfect set" down through "set not by setter") in relation to the three possible outcomes.

Three types of sets ("perfect," .53; "low and inside," .52; and "outside and low," .51) were associated with winning the point a little over 50% of the time. Two other types of sets ("high and outside," .47; and "inside and high," .46) were associated with winning the point at a little below a 50% rate, and if the set was not by the setter, BYU won the point only 39% of the time.

Other skills, in the domains of hitting and passing, showed similar results: As long as the task was accomplished adequately (i.e., mid to high grades), the Cougars had around a 50% chance of winning the point. But, if the task were performed well below optimally, BYU only had roughly a 40% chance of winning the point.

As shown on Fellingham's CV on his website (linked above), he has a fairly large portfolio of research that would likely be of interest to quantitatively minded volleyball fans. This includes the following article, co-authored with (now retired) BYU men's volleyball coach Carl McGown:

Fellingham, G.W., Collings, B.J., & McGown., C. (1994). Developing an optimal scoring system with a special emphasis on volleyball. Research Quarterly for Exercise and Sport, 65, 237-243.

If you'd like a copy of the Florence-Fellingham New England poster, just e-mail me via my faculty webpage (link in the upper-right).

Overview of Defense: Blocking and Digging

Continuing our series on the different skills and facets of volleyball, our topic today is defense against opponents' spike attempts, namely blocking and digging. As always, it's a good idea to look at the formal definitions of these plays, for statistical purposes.

According to AVCA guidelines, blocks "are awarded when a player blocks the ball to the opposition's court leading directly to a point without a successful dig." As elaborated in the guidelines, blocks are credited as solo or assist, according to certain criteria. Also, the hitter who is blocked in the manner described above receives an attack error.

A dig "is awarded when a defensive player keeps a bona fide attack in play with a pass."

The central inquiry motivating this blog, of course, is what can be learned through measurement and statistics that tells us about winning matches. Given the suggestion in an earlier posting that a team's hitting percentage seems to be a good marker for general success, it seems plausible that holding down opponents' hitting percentage might also be associated with winning.

Opponents' hitting percentage is not among the statistics displayed on the NCAA statistics page, but it is kept for four major women's volleyball conferences -- Big Ten, Big 12, Pac-10, and Southeastern Conference -- that I looked at recently (see links section on the right).

In looking at team-level defensive statistics, my interest was two-fold: first, what is the correlation (overlap) between teams' blocking and digging statistics and their opposition hitting percentages (OpHP); and second, how do these three variables relate to winning percentage?

I thus computed some correlation coefficients between the four variables, separately for each conference (the data were as of yesterday). To avoid discrepancies within a conference in schedule difficulty due to non-conference schedules, I used statistics only from within conference games. The sample size (number of teams) for each analysis is small, but the replication of results over the different conferences can be instructive.

A positive correlation simply means that both variables travel in the same direction -- as one goes up, so does the other. A negative correlation indicates an inverse or opposite relation -- as one variable goes up, the other goes down. One should not infer a "bad" connotation to the word "negative" in this context; positive and negative simply convey patterns of relationships. A positive correlation approaching its maximum of 1.00 and a negative correlation approaching its (absolute value) maximum of -1.00 each convey a powerful relationship.

The results are shown in the following table (which you can click to enlarge). I just cannot resist the graphical embellishments of PowerPoint!


An "official" block (as defined above) gives the opponent a hitting error; a block that does not immediately rocket to the floor for a defensive point, but is instead played by the original hitting team to prolong the rally also dilutes the opponent's hitting percentage by adding an attempt without a kill. I thus expected to see negative correlations between blocking and opponent hitting percentage (as one goes up, the other goes down). I didn't know how strong the relationship would be, however.

As shown in the above table, these correlations were quite strong, ranging from -.68 to -.87 in the four conferences (these were all statistically significant, even with the small sample sizes). Digs also detract from OpHP, but the correlations were only moderately negative, at best, and not statistically significant (i.e., not reliably different from zero).

How might digs and blocks be correlated? One might expect an inverse (negative) relation, as "airtight" blocking would preclude the need for digs. On the other hand, if a team has a high skill level in general, it should excel at both of these (and other) facets of the game, leading to positive correlations.

In fact, these correlations ranged from moderately negative to moderately positive, with none significant. The one negative correlation, for the Big 10, may well stem from the fact that Michigan (my graduate school alma mater) was leading the conference in digs, but was last in blocks.

Next, for the second part of our inquiry, which defensive element -- OpHP, blocks, or digs -- is most strongly associated with conference winning percentages? In each conference, opponent hitting percentage edged blocks in absolute strength, but both were potent. OpHP is negatively related to own winning percentage because the lower the hitting percentage to which Team A holds Team B, the more likely Team A is to win. Blocks are positively related to winning, as higher numbers of blocks are associated with better winning percentages.

In doing my research to prepare for this entry, I came across two additional sources:

One is a study comparing two blocking strategies: "commit" vs. "read and react." According to this FIVB document:

Teams usually opt for a 'read and react' block (whereby they try to react to the ball leaving the setter's hands) or for a 'commit' block (whereby they decide before the point whether to jump on the quick middle balls).

In their article, "Relationship between the use of commit-block and the numbers of blockers and block effectiveness," researchers J. Afonso, I. Mesquita, and J.M. Palao analyzed four men's national teams in 2001. Quoting from the abstract of their article in the International Journal of Performance Analysis in Sport:

The results show that the use of the commit block [makes?] difficult the formation of double and triple blocks in the wings and does not increase the block effectiveness or the opponent's error in spike.

(As can be seen, a word was omitted from the original version of the online abstract. Based on context clues, my guess is that the word is "makes," but I've added the question mark to denote the uncertainty.)

The other source is an article from Gold Medal Squared by Carl McGown, a highly successful men's coach, on liberos' passing vs. digging. Like my four-conference analysis, the statistical analyses in McGown's article also highlight the uncertain role of digs in winning and losing.

JQAS Article on Serve Reception, Setting, and Attack

A new issue of the online publication, the Journal of Quantitative Analysis in Sports, was announced today. Among the articles was one on volleyball by researchers from Greece, entitled "Does Effectiveness of Skill in Complex I Predict Win in Men’s Olympic Volleyball Games?"

The authors made a terminological distinction between "complex I (serve reception, setting, attack)" and "complex II (serve, block/defense, counterattack)" sequences, and focused on analyzing the former. Raters evaluated videotaped game footage with a software system, issuing grades (on a 0-4 scale) on serve reception and first attack (setting was not graded). Not surprisingly, high-level execution of both reception and attack were associated with winning. The authors used discriminant analysis, which is among the more complex techniques in the data analyst's arsenal. I would have liked to see more basic statistics, such as means and frequencies with, respectively, t-tests and chi-squares to distinguish winning and losing teams.

The article is available at: http://www.bepress.com/jqas/vol3/iss4/3. The journal requires a subscription, although free "guest" privileges are available to view a single article.

Zetou, Eleni; Moustakidis, Athanasios; Tsigilis, Nikolaos; and Komninakidou, Andromahi (2007) "Does Effectiveness of Skill in Complex I Predict Win in Men’s Olympic Volleyball Games?," Journal of Quantitative Analysis in Sports: Vol. 3 : Iss. 4, Article 3.

Overview of Serving and Serve Receipt

Today, let's take up serving and serve receiving, which appear to be two sides of the same coin. Box-score statistics tend to be quite limited, generally reporting only service aces and errors, and serve reception errors. Jim Coleman's chapter in Shondell and Reynaud's Volleyball Coaching Bible (which I've referenced previously) summarizes some schemes for grading serves and serve reception.

The schemes appear to have both a spatial component -- with short serves, in the center of the receivers' court on the left-right dimension, being considered poor for the server and advantageous for the receiver, and deep serves the opposite -- and a component for how likely the receiving team would be to generate an attack for a side-out, given the placement of the ball.

Consistent with calls for better statistical graphics in volleyball, I had been thinking of serve placement/receipt charts, modeled after shot charts in basketball (see examples here and here).

After searching Google Video with the keyword "volleyball," I found an archived full-length video of a 2006 women's Pac-10 match between Arizona and Oregon, from the Ducks' "O-Zone" broadcasts (video, box score). As shown below, I came up with a coding system, which I applied to Oregon's serve receptions in Game 1 (the availability of a freeze-frame option unquestionably increased the accuracy of my plottings). You can click on the graphic to enlarge it...


It would have been good to add the uniform number of the receiver to each little circle, but the resolution of the video clip wasn't sharp enough for me to see the numbers. Adding the server's number might also be helpful. It wouldn't surprise me if some software packages could generate plots similar to what I've done, but I'm not aware of any.

Going back to the Oregon-Arizona chart, the lack of deep serves stood out to me. This pattern may stem, in part at least, from rule changes in recent years that now allow serve receipt with a setting motion (back in junior high in the mid-1970s, I first learned that setting an incoming serve was a no-no). If, as before, a receiver could only field a serve from a digging position, serves presumably would travel further back in the court, as they could not be cut-off with a set at a higher point in their trajectories.