Does Momentum from Previous Games Predict Who Wins Game 5?

Happy holidays to everyone!

Today's entry looks at whether, in a five-game match, the winner of the fifth game can be predicted by the pattern of how the first four games have gone. For example, if one team wins the first two games, but the other team wins the third and fourth games, one might expect the latter team to win the fifth game, owing to its momentum from Games 3 and 4. This line of reasoning led many to expect a Stanford win in Game 5 of the recent NCAA women's final against Penn State, but it was the Nittany Lions prevailing.

In the analysis below, I looked at 2007 within-conference matches from four major women's conferences: the Big 10, Big 12, Pac 10, and SEC. As can be seen, in the 34 total matches in which one team (represented by "A") had won the first two games and the other team ("B") had rebounded to win Games 3 and 4, Team A won Game 5 -- and the match -- somewhat more often than did Team B, 19 compared to 15.


Another scenario involves single-game alternation, that is, Team A wins a game, then Team B, then A, and then B. In this case, Teams A and B had virtually identical probabilities of winning the decisive fifth game.

Lastly, a situation can arise in which Team A wins Games 1 and 4, and Team B wins Games 2 and 3. Here, Team A was nearly twice as likely to win Game 5 (15 occurrences) than was Team B (8 occurrences). If the underlying probability of either team winning the fifth game were .50, the probability of one team winning 15 (or more) times out of 23 would be .105, assuming independence of observations, like coin-flipping (see here for an online binomial calculator). This result renders a 15-of-23 result unlikely to arise from an underlying 50/50 distribution, but it does not achieve the conventional .05 statistical significance level necessary for rejecting the null hypothesis of a 50/50 underlying distribution.

The number of matches studied above comprised a relatively small sample, so additional data from the upcoming men's collegiate season and from next year's women's season will be useful for strengthening the analyses.

Another place to look is men's professional tennis, the major tournaments of which use a 3-out-of-5-set format. There are differences, to be sure, between tennis and volleyball, including one being an individual sport and the other, a team sport. Still, momentum-related phenomena may transcend particular sports.

I found an online article that looked at all matches from 1995-2004 in the four Grand Slam tournaments (Australian Open, French Open, Wimbledon, and the U.S. Open).

The tennis article used a different notation than I did, but the formats are analogous. Below are listed the number of occurrences of each outcome:

WWLLW (like AABB-A) 151
LLWWW (like AABB-B) 188
p = .025

The first of the three comparisons was significant, leading us to reject the null hypothesis of a 50/50 distribution of fifth-set outcomes, when one player has won the first two sets and the other, the next two. The player coming back from 0-2 won five-set matches significantly more than 50% of the time. This result is consistent with the "Stanford momentum" line of thinking in the context of the NCAA volleyball final.

WLWLW (like ABAB-A) 135
LWLWW (like ABAB-B) 156
p = .120

Under the single-set alternation scenario, we cannot reject a 50/50 distribution of outcomes, as was the case for volleyball.

WLLWW (like ABBA-A) 186
LWWLW (like ABBA-B) 138
p = .004

As with the volleyball analysis, in tennis the player who has won the first and fourth sets is substantially more likely to take the fifth, than is the player who has won the second and third sets.

I don't know about anyone else, but staring at these notations makes me want to listen to some music by the group ABBA.

UPDATE December 28: After I published the above write-up, I posted a message at the VolleyTalk discussion site to let people know about my analysis. Among the string of messages, a few VolleyTalk readers posted the results of volleyball analyses they had done previously. The following tabulation, by "p-dub," was most on-point (you can click on the chart to enlarge it):


The chart shows what percent of the time Team A wins, under each of the three distributions of wins in Games 1-4. For any given Team-A winning percentage, you can take (1 - p) to see what percent of the time Team B wins under the relevant configuration.

Although the deviations from .500 are small in p-dub's extensive samples, once again the "A" team in the "ABBA" sequence has an increased chance of winning.

Subtlety and Context in Interpreting Volleyball Stats

Over at the VolleyTalk discussion website, user “38 Skynyrd” started a topic the evening of December 15, after the Penn State-Stanford NCAA title match, about volleyball statistics. The initial salvo in the discussion essentially argued for more subtlety and context in interpreting volleyball statistics, given that:

“…absolute raw numbers in the box score do not always tell the true story of how good or bad a player did in a given game or match.”

The full set of messages is available here. A number of suggestions were made by the discussants for new statistics. Given the obvious relevance of this discussion for our mission here at VolleyMetrics, I have excerpted a number of these ideas (with the author of each one credited in parentheses). These are shown below:

“…a hitter may have hit for good numbers overall, but if they made 5-6 hitting errors at critical points in the match, then their overall hitting percentage may still look good in the box score, but they still had a crappy match.

There are also a lot of stats that aren't tracked in the box score. Missed blocking or defensive assignments, poor choices in out-of-system plays, crappy free ball passes. A blocker could not block a single ball during an entire match, yet that player's coach could praise her for having the most incredible blocking match of her career if she made every single blocking assignment and move correctly, and took away what she was assigned to take away, and the back row defenders end up with 300 digs” (38 Skynyrd)

“…a blocked attack is not the same error as an outright hitting error. And there's no way to tell what a "0" attack led to. Did it throw the opposition out of system or did it not stress them at all? Was that hitting error caused by the block?” ([R]uffda!)

“One of the easiest ways to stat an individual player's performance during a match is to assign a +1, 0, -1 scale to each touch that they get on a ball. For instance,

+1 = excellent pass
0 = marginal pass (i.e. passed to 10-foot line)
-1 = bad pass, aced or shank

+1 = kill
0 = ball kept in play by opponent
-1 = hitting error (blocked, out-of-bounds, into net)

If [you] grade each touch a player makes [and average the scores], by the end of the match you'll have a score that is between -1.0 and +1.0.

It can help judge an individual players performance better, but it's not weighted for situational dynamics (i.e. a +1 contact when the score is 0-0 should not be weighted the same as a -1 contact when the team is down 23-29). It also doesn't address bad plays when the player is not touching the ball - such as out-of-position on defense, missed blocking reads, getting in another player's way on the court, etc.” (38 Skynyrd)

“…there are still important many areas of play which are not covered in the stats for volleyball. IMO [In my opinion], the most important of these are passes which do not hit the target, missed blocking assignments (i.e., failure to close the block) and missed digs in the back row” (Traveler5)

“One stat that is completely objective and I think could be useful would be what % of a player’s attacks are handled and then killed for a point by the other team. So if the other team digs your attack, and winds up getting a kill on that 3-touch sequence immediately following your attack, that would count negative, and if they don’t score, either by sending over a freeball or having a legit attack dug up, it counts towards you…

You could also… break down how many blockers were on each of a player’s attacks, and how well they hit against 0, 1, 2, and 3 blockers. This could also be used by setters to see the average number of blockers their hitters had to go against.

Front row vs. back row would also be nice, since a player good enough to get a lot of back row swings is probably going to hurt their % some since that is a lower percentage shot” (Chance)

Suggestions for refinements of dig statistics: “…opportunities matter. Thus, I have calculated the "dig %", which is digs/non-error attacks (it doesn't make sense to penalize a team for not digging a ball that is blocked or out)… [and] digging compared to opponents… difference between digs and opponents’ ” (p-dub)

I and another user, Mike Garrison, both alluded to improvements in baseball statistics that have been fueled by the “sabermetric” movement. Some responses:

“Baseball is helped by the fact that it is such a discrete game. You are either out or safe. You are either at first, second, or third base. A pitch is either a ball or a strike. Etc.

The weakest part of SABRmetrics is the fielding stats… A player can just barely miss a ball or not really come close to it at all…

Most other sports, including volleyball, are more like baseball fielding than hitting or pitching. So I would start by looking more at fielding stat methods than at hitting or pitching methods.” (Mike Garrison)

“Even more important is the independence of events. Whereas the events in baseball are not completely independent, they are far closer than any sport. If a batter is batting with a runner on first, you generally know where that runner is going to be at any time... None of this can be said for volleyball (or most other team sports). Players are all over the place, and offensive sets can vary significantly.

The best example of baseball's stats independence is in offense and defense. Baseball (and like sports) is the only sport where a great defensive play does not improve offensive opportunities. In all other sports, the defense can help the offense. In volleyball, great defense can slow the opponents attack, and we always hear about "transitioning." Shoot, the defense can even score directly on a block...” (p-dub)

“[Unlike baseball, where the pitching rubber and batter’s box constrain the positions of the key players...] Volleyball is a game where the ball is struck from almost anywhere on the court, and there isn't enough information available…

My biggest pet peeve of the [n]umber crunchers are those who tout ridiculous stats or won-loss records without regard for the average competition faced” (Bear Clause)

Where feasible, I will consider gathering the data to produce the statistics suggested above. I invite you readers to do the same!

Top NCAA Women's Programs 2003-07, Relative to National Tourney Seedings

With another women's NCAA Division I season on the books -- Penn State having defeated Stanford in a five-game final -- now is a good time to take stock of how the nation's leading programs have been doing in NCAA play in recent years.

As one option, we could look at which schools have been winning championships and making the Final Four. Looking at the last five years, we would find many "usual suspects," such as Stanford, Nebraska, Washington, USC, and Penn State; even Minnesota, whose icy cold locale doesn't necessarily suggest volleyball greatness, has made two Final Fours in this timeframe.

A more subtle approach, however, is to look at which teams have done best relative to their seedings. Such an analysis can tell us which teams raise their games come tournament time, compared to what their regular-season performance would have suggested. A team that comes into the NCAA tourney as a No. 16 national seed, for example, would be favored to win two matches, until becoming an underdog against the No. 1 seed. If the No. 16 team were instead to win four matches, it would receive a +2 difference score, reflecting the magnitude of its "overachievement" (that a team may have underperformed during the regular season would also be compatible with a positive difference score).

Conversely, a team that compiled a negative difference score (i.e., winning fewer matches than expected from the seeding) would suggest underachievement in the post-season.

Because weird things can happen in any given tournament -- witness this year's early exits by Nebraska, Washington, and Wisconsin -- I felt that aggregation over the past five years would be helpful.

The difference-score approach is not original to me. In the mid-1990s, I saw someone apply it to NCAA men’s basketball. Also, it follows the logic of the chi-square statistic, in terms of taking the difference between actual (observed) and expected counts. Let's start by going over how many matches a team is expected to win in the NCAA tournament, based on its seeding:

The No. 1 national seed is expected to win 6 matches, thus capturing the title...
The No. 2 national seed is expected to win 5 matches, thus making the final...
Seeds 3 and 4 are each expected to win 4 matches, thus getting to the Final Four...
Seeds 5-8 are each expected to win 3 matches, and...
Seeds 9-16 are each expected to win 2 matches.

(If seeding were done down to No. 32, we would know who was expected to win 1 match and who was expected to win none.)

The following figure -- which you make click to enlarge -- summarizes how different schools have fared under this metric, during the past five years (limited to schools that have been seeded at least three times in this period).


As with any statistical analysis, some cautions are in order in interpreting this one:

*Unseeded teams that have had great runs -- such as Santa Clara making the 2005 Final Four -- are not depicted in the chart.

*Teams are, in a sense, "penalized" in these analyses for receiving high seeds. In any given year, the No. 1 national seed cannot exceed its expected number of wins (6), and can only break even, at best. A measurement system that appears to impose an artificial constraint on how high something can be rated is knows as a “ceiling effect.”

No team has faced this situation in recent years any more than Nebraska; the Cornhuskers have received three national No. 1 seedings plus a No. 2 during the five-year span, thus making it impossible or nearly impossible for them to exceed their expected number of wins. On the other hand, there was a lot of room for Nebraska to win fewer matches than expected in a given year. Thus, even with a national championship and national runner-up finish during the years examined, the Huskers still finished with an aggregate minus-6 value. Such a result should be looked at in context and taken with a grain of salt (or in the case of Nebraska corn, with a pat of butter).

To provide some context, I have listed teams' average seedings over the past five years. One suggestion is to compare “+/-” values of teams with similar average seedings. As shown in the top panel of the figure, three teams that have been dealt similar seedings over the five years are USC, Washington, and Hawaii (all of whose average seeds are between 6.2 and 7.0). Clearly, the Huskies have done the best from their starting positions in the field, and the Rainbow Wahine, the worst.

The small sample sizes are another reason for caution, but a five-year window is still preferable to a one-year snapshot.

"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.

-----

*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.

Overview of Setting

Following up on the previous entry about hitting, we now take up another indispensable part of the offense, the setting.

This Daily Californian article from about a year ago describes the setter's role through the eyes of Cal-Berkeley setter Samantha Carter, who at the time was finishing up her four-year career leading the Golden Bears' offense. The following excerpts give an idea of what being a setter entails:

“You have to be one of the better athletes — you’re doing more running and jumping than anyone else on the team,” says Bears coach Rich Feller... “You have to be a sponge and be able to absorb other players’ mistakes and take it upon yourself to make things better.”

...

Before each play, Carter will make eye contact with all of her hitters and signal to them to designate where they’ll each be going and what the play is. Throughout the play, she vocally communicates with her teammates on the court.

“First thing, when I give my calls I basically try to think, ‘Who do I want to set?’ and ‘How can I best get them the ball?’ Then I conjugate the plan and give the signals,” explains Carter. “I will look where the blockers are going and try to set away from them. It’s all about baiting the blocker and try to make them bite the hook.”

The playbook of a setter is extensive. The sets range in height and tempo: A one set is a fast ball to the middle, normally coming off of good passes; a four set is a high ball set for the outside. The list goes on.

“There are endless options of what I could run,” says Carter. “There are so many options, and I have so many hitters, that it makes my job a little bit tougher.”

The toughest part, of course, comes from reacting to unexpected and difficult attacks. A setter, more than anyone else on the team, must react immediately to anything from a bad pass to a surprising move by an opponent and make adjustments to the play accordingly.

The richness of the setter's role, as illustrated in these excerpts, stands in stark contrast to the paucity of quantitative metrics related to the position. The only setting statistic that appears to be widely available in box scores and NCAA compilations is the assist. According to the AVCA statistical definitions, an assist is "awarded to the player who passes the ball to a teammate who attacks the ball for a kill."

As evidenced by this definition -- and also through common sense -- the setter's assist and the hitter's kill are heavily intertwined. A good set, right in the hitter's "wheelhouse," enhances the likelihood of a kill, whereas the presence of hitters who pulverize the ball and have the savvy to overcome the block will increase setters' assist totals. Statistically, a team's number of kills and of assists will be virtually identical; the only discrepancies would occur when a kill came off of something other than a set, such as an overpass by the opposing team.

Within the 2002 book The Volleyball Coaching Bible (edited by Shondell & Reynaud), the chapter on "Scouting Opponents and Evaluating Team Performance" by the late Jim Coleman offers some interesting observations.

Coleman cites the need to go beyond box-score assist statistics and compile one's own, more elaborate, set of ratings (e.g., perfect set, mediocre set, set leading to free ball to opponent, and set giving opponent a direct point or rally). Even these more elaborate stats are not free of problems, however. Among the complications cited by Coleman are, "The perfect set to one spiker is not perfect for another spiker," and "The statistician is often influenced by whether the attacker kills the ball rather than the absolute quality of the set." He also notes that setter ratings are only weakly correlated with winning.

More generally, Coleman feels that, "A statistical system for setting is probably the most difficult system to create," and "The evaluation of setting seems to be more of an art than a science."

A couple of ideas I have for studying setters are as follows:

1. Similar to measuring fielders' range in getting to hit baseballs -- which some sabermetricians are interested in -- setters' range in chasing down passes gone awry could also be assessed. Further, their ability to put up serviceable sets on the run could be evaluated.

2. On an historical basis, collegiate setters' contributions to teams' offensive prowess could be estimated by looking at situations in which most of a team's top hitters return from one season to the next, but with different setters each year. Assuming relative constancy of hitters, difficulty of schedule, etc., from year to year, any difference in a team's aggregate hitting percentage might be attributable to the setter. Year-to-year improvement in hitting ability -- if there is any -- would have to be taken into account.

Overview of Hitting Percentage

For my next few postings, I would like to provide initial examinations of the major volleyball statistics, to try to get a feel for them. Let's start with hitting percentage (also called attack percentage), which can be computed for either individual players or teams.

For a player or a team, one totals the number of kills (i.e., successfully putting the ball away on an attempted attack), then subtracts the number of hitting errors (e.g., attack attempts hit out of bounds or into the net, or that get blocked back into the hitter's face for an opponent's point). The remaining number is then divided by total attack attempts. These terms are defined rigorously on this document from the American Volleyball Coaches Association.

Imagine the following different hypothetical performances. One player, whom we might call "Dana Devastator" has the ball set up for her 10 times and successfully puts it away all 10 times. That would be a 1.000 performance ([10-0]/10). Another player, "Patty Powerless," might be set up for 7 attempts, but only once get a successful kill, her other 6 spikes being fielded by the other team. That would yield a percentage of .143 ([1-0]/7). Then there's "Erin Erratic," who twice scores a kill on her 8 attempts, but also blasts the ball out of bounds 4 times. Because this player has done more harm than good, her hitting percentage enters negative territory, namely -.250 ([2-4]/8).

The hitting percentage formulation, which has been around as long as I can remember, is something I like. The ultimate goal of a team is to win games and matches, which requires getting points for one's own team and denying points to the opponent. Hitting percentage essentially weighs a player or team's balance between kills, which by definition result in points, and hitting errors, which lose you points. Poor efficiency, in terms of hitting a lot of balls that can be played by the opponent, serves to dilute a player or team's percentage.

Viewed from this perspective, it is not surprising that there is tremendous overlap between the nation's "best" NCAA Division I women's teams (as per the September 24 CSTV/AVCA Poll) and the top teams in hitting percentage (as of September 23). As I'll discuss in future postings, other NCAA statistics do not dovetail so well with the poll rankings.

Shown below for the top 10 poll-ranked teams are (left to right) their poll ranking, hitting percentage, and hitting percentage rank:

Nebraska____ 1 __ .338 __ 3

Stanford____ 2 __ .316 __ 4

Penn St.____ 3 __ .347 __ 1

USC_________ 4 __ .287 __ 12

UCLA________ 5 __ .255 __ 37

Florida_____ 6 __ .292 __ 10

Texas_______ 7 __ .298 __ 7

Washington__ 8 __ .341 __ 2

Wisconsin___ 9 __ .284 __ 13

California__ 10 _ .298 __ 6

As can be seen, 9 of the top 10 poll-ranked teams are in the top 13 of team hitting percentage. From the opposite perspective, 7 of the top 10 hitting-percentage teams are in the top 10 of the poll rankings.

There are some anomalies, though. UCLA, ranked as the nation's fifth-best team in the poll, is only 37th in hitting percentage. Texas A&M, on the other hand, ranks 9th in hitting percentage (.293), but is unranked in the poll (not only are the Aggies absent from the top 25, but they're not even among the additional 13 teams receiving some votes to be in the top 25).

Welcome and Introduction

Welcome to my latest blog, VolleyMetrics. The basic aim of this site is to apply the kind of analytical and statistical reasoning that has come to be known as "sabermetrics" to volleyball. The term sabermetrics derives from SABR, the Society for American Baseball Research, but increasingly is used used to refer to quantitative analysis of sports in general. Phil Birnbaum's Sabermetric Research Blog is devoted to all sports, for example.

Three things about me make a sabermetric volleyball site a logical next step:

1. I am a member of SABR and am very much in tune with the sabermetric approach. Another of my blogs, The Hot Hand, is devoted to the statistical study of sports streakiness.

2. I am a professor at Texas Tech University in the Department of Human Development and Family Studies. Although my primary substantive research area is adolescent and young-adult drinking (and personal development during this part of the lifespan more generally), my teaching load regularly involves introductory and advanced graduate statistics classes.

3. My family and I go back a long way with volleyball. My father Leonard played on the U.S. team in the Maccabiah Games in Israel 50 years ago! My dad started taking me to UCLA men's volleyball matches at Pauley Pavilion in the early-mid 1970s, when I was around 10-12 years old. Then, while attending UCLA as an undergraduate, I covered men's and women's volleyball for the Daily Bruin in the early 1980s.

As far as the content of this blog, the immediate focus will be on the currently ongoing NCAA women's volleyball season. However, I'm planning to be flexible and see what looks interesting from week to week. Specific topics that will probably come up are those that have been prominent in sabermetrics research across different sports: which particular performance statistics (e.g., hitting, blocking) seem most predictive of teams' winning percentages, momentum, clutch play, risk-taking, and so forth.

One of the biggest contributions of sabermetrics in its original domain of baseball has been to development more sophisticated and informative statistics than the old stand-by statistics of batting average, home runs, and runs batted in (RBI). These traditional stats suffer from serious shortcomings. Batting average treats all hits (singles, doubles, triples, and homers) identically as just "a hit," with no greater credit for hitting for more bases; slugging percentage does accomplish the latter. Batting average also does not reward players for getting on base via the walk; on-base average (encompassing hits and walks) is thus an improvement. The problem with RBI is that players' totals depend on how many runners are on base when hitters come to the plate, which is not intrinsically part of someone's batting ability. With pitching, a hurler's number of runs allowed has some dependency on the defensive abilities of the fielders.

Through rigorous quantitative analysis, sabermetricians have been able to come up with statistics that better reflect players' performances. For hitters, OPS (On-base average Plus Slugging percentage) is a value that can be calculated without too much trouble (just adding two numbers) from published statistics (the OBA and SLG) and gives a much better idea of players' contributions to scoring runs and winning games. Also, Defense Independent Pitching Statistics (DIPS) have been developed, for getting a more pure assessment of pitching contributions, regardless of the surrounding fielders' defensive abilities.

There are several excellent books available for learning about the sabermetric approach: The Numbers Game, Moneyball, Curve Ball, and The Mind of Bill James (all related to baseball), and Basketball on Paper.

I've done some web-searching and have found very little that might be described as sabermetric volleyball research (although I certainly could be missing some). My blog will thus seek to contribute to building a base of sabermetric knowledge for volleyball. Ideas, suggestions, and comments are always welcome; you can e-mail me via the link to my faculty webpage.