Preview of Penn State-Pepperdine NCAA Men's Final

In anticipation of tonigh't NCAA men's volleyball final between No. 1 Penn State and upstart Pepperdine (which only made the field via a late surge through the Mountain Pacific Sports Federation tournament), user "nomas" on the VolleyTalk discussion board offers this analysis of the match-up.

One of the salient issues is that Penn State has not played that tough of a schedule during the season, thus likely inflating the Nittany Lions' statistical prowess. As seen on Penn State's schedule, the Lions have played only a few matches against traditionally strong teams from the Pacific (Hawaii, UCLA, and Long Beach State), and two of those three matches were back in early January.

Preview of Men's NCAA Final Four

This coming Thursday and Saturday, the men's volleyball version of the NCAA Final Four will take place in Irvine, California (tournament website). The semi-finals will match Penn State against Ohio State, and Pepperdine against Long Beach State.

Men's collegiate VB is much more of a low-key affair than women's, with fewer schools fielding teams, less media coverage, etc. Accordingly, I have not posted nearly as much on the men's season as I had done for women's play last fall.

The Final Four is actually all there is of the men's "tournament." Three teams earn automatic berths via conference tournaments of the Mountain Pacific Sports Federation, Midwest Intercollegeiate Volleyball Association, and Eastern Intercollegeiate Volleyball Association. The field is rounded out by one at-large team, inevitably from the MPSF. The at-large choice is often controversial, and this year's was no exception.

The two contenders were BYU and Long Beach State, the regular-season MPSF co-champions at 18-4. Each lost in the conference tournament to eventual champ Pepperdine (which tied for fourth in the regular-season conference race at 12-10), thus giving the automatic bid to the Waves.

This Salt Lake City Deseret News article attempts to break things down scientifically:

The NCAA manual gives some criteria for selection the fourth at-large team — which didn't help clear up matters.

One of the first matters is won-loss records. Both finished tied atop the MPSF regular-season standings with identical 18-4 league records. Long Beach won the rights to host the MPSF Tournament, to be the top seed and to have the quarterfinal bye because of beating BYU twice in the regular season.

However, BYU had a better overall record, finishing 25-5 to LBSU's 23-6 — that's two more wins and one fewer loss than the 49ers.

Also considered is the strength of schedule, head-to-head competition, results against common opponents and results against Final Four qualifiers and other teams under NCAA tournament consideration.

LBSU had faced the other three Final Four teams in regular-season play, winning twice at Ohio State, losing at home to Penn State and going 1-2 all year against Pepperdine. The 49ers were also 1-1 against Cal State Northridge, who finished a game behind BYU and LBSU in the final league standings and lost to the Cougars in the MPSF semis.

BYU's five '08 losses were to Stanford (at home), twice to Long Beach (on the road), to UCLA (on the road) and to Pepperdine in the MPSF finals.

Long Beach's six losses were twice to Pepperdine (a regular-season defeat in Malibu and the MPSF semifinal loss), at hoem to Northridge, Penn State and UCLA and on the road at UC Irvine.

To me, the issue comes down to this. With NCAA tournament bids extremely scarce, why does the MPSF choose to have a conference tournament at all? The result this year is a regular-season co-champion staying home, while a team that finished six games behind in the standings will be playing in the Final Four. Perhaps the NCAA requires these conference tournaments to be held. It doesn't in other sports, however, so it probably doesn't in men's volleyball.

Tradeoff of Serving Aggressively (or Cautiously): Service Errors vs. Aces

The other night, I caught a replay of UCLA hosting USC in men's volleyball, on Fox College Sports. It was the second match of the season between the Bruins and Trojans. In the first match, as the TV announcers pointed out, the teams had combined for 51 service errors, so it was suggested they would be toning down their aggressive service in the rematch. Indeed, UCLA and USC cut their combined service errors in half, to 25, in the second match.

That got me to thinking about coaches' decision-making strategies involved in choosing whether to have their teams serve aggressively or cautiously. The most aggressive type of delivery would seem to be the jump serve, as illustrated in these brief video clips I found on the web (here and here).

Such a serve has the potential to generate an ace or, if not that, a ball that the receiving team struggles to retrieve and thus takes the team out of its offense. Trying to pulverize the ball on the serve also, however, creates the potential for a missed serve, either into the net or out-of-bounds long. Jump-serving truly seems to be a high-risk/high-yield proposition (see here for a general discussion of risk/return tradeoffs, from the perspective of investing).

Additional web-searching turned up a 2000 American Volleyball Coaches Association (AVCA) newsletter article on serving, written by Melissa Stokes, who this past fall completed her 12th year as women's coach at Missouri State (formerly known as Southwest Missouri State).

The article by Stokes covers serving strategies and practice drills, with a healthy supply of statistics thrown in (probably from 1999). Using stats from the Missouri Valley Conference (in which her team plays), Stokes reveals that though her team was not among the league leaders in aces per game, it kepts its service error rate very low, resulting in virtually a 1-to-1 ratio of aces and errors. In contrast, there were a few MVC teams whose error-to-ace ratios were roughly 2-to-1. Stokes commented that:

Every team will have a different serving philosophy. This chart shows you that these statistics support our serving philosophy. We may not have posted as many aces, but committing fewer errors allowed our players the opportunity to score points at the net or by playing defense.

My curiosity sufficiently piqued, I then went and found the boxscores for the two UCLA-USC men's matches (both of which, incidentally, were won by the Trojans).

UCLA at USC (January 23, 2008, 5 games)
UCLA: 11 aces (2.2/game), 30 errors (6.0/game)
USC: 3 aces (0.6/game), 21 errors (4.2/game)

USC at UCLA (February 6, 2008, 3 games)
UCLA: 3 aces (1.0/game), 11 errors (3.7/game)
USC: 4 aces (1.3/game), 14 errors (4.7/game)

Speaking in approximate terms, UCLA's rates of aces and service errors each were cut in half from the first to the second match. This kind of proportionality is what I would have expected. USC doubled its rate of aces (albeit from a low baserate), but only experienced a slight proportional rise in errors.

These are just some limited examples, but I hope this posting can spur an expanded discussion of serving tradeoffs.

Ferocity of Men's vs. Women's Spikes at the Elite College Level: Rates of Being Dug

As collegiate volleyball in the U.S. switches from women's play in the fall to men's in the winter/spring, so too does VolleyMetrics shift its focus. Fittingly, given this transition, there was a recent discussion topic on the VolleyTalk boards about the differences -- and relative enjoyability -- between the men's and women's games.

The discussion appeared to focus on the greater power of men's spiking than that of women's. In fact, one discussant characterized the men’s game as “Pass, set, boom.” Whether one finds beauty in these rocketing blasts or prefers the (assumed) longer rallies in the women's game is in the eye of the beholder, but the consensus that this difference exists was wide.

Here at VolleyMetrics, however, we want hard numbers. As an initial step, we can look at men's and women's team hitting percentages. Keep in mind that (as best I can tell), there are far more women’s volleyball programs in Division I alone than there are in men’s Divisions I, II, and III combined.

Having said that, it turns out that only five women’s Division I teams exceeded a hitting percentage of .300 this past season (Penn St., .350; Texas, .343; Nebraska, .327; Stanford, .316; and Florida, .303; a link to NCAA women's statistics is available in the upper-right of this page).

In contrast, at least 11 teams in the combined D I-II configuration surpassed .300 in the most recently completed men's season (the men's top 10 list stops with two teams tied for 10th at .307).

That's pretty good evidence, but me and my computer wanted more. Conveniently, as part of a separate VolleyTalk discussion thread on statistical refinements (which I excerpted a couple of entries down), user "p-dub" had suggested computation of:

"dig %", which is digs/non-error attacks...

I like the idea, which to elaborate a little, takes Team A's dig total and divides it by Team B's (total number of attacks - errors). More colloquially, we might call this measure "dig-ability" -- of the spike attempts coming at a team, what percentage of them do they dig up? (Note that a spike attempt blocked back in the face of a hitter is considered an error, so blocked balls are accounted for.)

Another thing I wanted to do is study the same schools' men's and women's programs, thus holding constant the strength and prestige of athletic programs, quality of facilities, etc. (assuming the men's and women's volleyball teams get equal access to these facilities).

Given the nature of the above formula, dig-ability can only be computed on a match-by-match basic, and not with aggregate seasonal stats. Given my roots as a former UCLA Daily Bruin men's and women's volleyball correspondent (1980-82), I selected the four UCLA-USC matches (two men's, two women's) played during 2007. For any given match, the dig-ability of both teams' spikes are calculated separately, so these four matches would generate eight data points. Further, to augment and diversify the sample, I also used the four Penn State-Ohio State matches of 2007 (the Nittany Lions and Buckeyes are in the same conference, the Big 10, in women's play, but in different men's conferences). The eight matches and 16 dig-ability data points are summarized as follows (with box-score links):

Women's: #4 USC vs #5 UCLA (Oct 05, 2007) 4 games
UCLA Dig 66 / (USC Attempts 150 - USC Errors 25) = .528
USC Dig 63 / (UCLA Att 170 - UCLA Err 30) = .450

W: #9 UCLA vs #6 USC (Nov 02, 2007) 4 games
UCLA Dig 89 / (USC Att 207 - USC Err 34) = .514
USC Dig 87 / (UCLA Att 183 - UCLA Err 29) = .565

Men's: USC vs UCLA (Jan 27, 2007) 3 games
UCLA Dig 28 / (USC Att 92 - USC Err 4) = .318
USC Dig 28 / (UCLA Att 112 - UCLA Err 26) = .326

M: #4 UCLA vs #12 USC (Mar 31, 2007) 3 games
UCLA Dig 24 / (USC Att 100 - USC Err 23) = .312
USC Dig 20 / (UCLA Att 94 - UCLA Err 12) = .244

W: Ohio State vs #3 Penn State (Oct 10, 2007) 3 games
OSU Dig 32 / (PSU Att 93 - PSU Err 8) = .376
PSU Dig 39 / (OSU Att 112 - OSU Err 27) = .459

W: #1 Penn State vs Ohio State (Nov 21, 2007) 3 games
OSU Dig 42 / (PSU Att 103 - PSU Err 10) = .452
PSU Dig 45 / (OSU Att 121 - OSU Err 29) = .489

M: #11 Ohio State vs #7 Penn State (Feb 01, 2007) 4 games
OSU Dig 30 / (PSU Att 131 - PSU Err 21) = .273
PSU Dig 45 / (OSU Att 133 - OSU Err 22) = .405

M: #6 Penn State vs #8 Ohio State (Apr 4, 2007) 5 games
OSU Dig 24 / (PSU Att 118 - PSU Err 26) = .261
PSU Dig 29 / (OSU Att 116 - OSU Err 24) = .315

It is plainly evident that spike attacks in women's matches have a higher dig-ability rate than those in men's, which will not surprise many observers. Whether the magnitude of difference is greater or less than expected, or about as expected, may differ among members of the volleyball community.

This analysis seemed to provide a good occasion to introduce the box plot, a graphical statistical tool. At a glance, the box plot displays the following aspects of a statistical distribution: the median (Mdn; point at which half the scores are greater and half are less than), the lower quartile (1Q; the point that cuts off the lower 25% of scores), the upper quartile (3Q), and the lowest and highest individual values in the distribution. This online calculator allows one to type in individual data values and automatically generates the necessary statistics for a box plot (and more).

The mean and median, respectively, were virtually identical within the men's distribution (.307, .3135) and within the women's (.479, .474); this is not always the case in analyzing data. Here are the two boxplots (you may click on the image to enlarge it).


The usual cautions about small sample size are applicable. Still, across the four men's matches and across four women's matches (each set taken from two regions of the country), the results appear to exhibit considerable consistency. Yes, women's spike attempts were more dig-able than were men's in the matches studied, but the magnitude of difference was less than .20 (roughly .48 - .31).

Whether these statistics indicate (to paraphrase a popular book title from several years ago) that the men's game is from Mars and the women's from Venus, or (to paraphrase a colleague of mine) the men's is from North Dakota and the women's from South Dakota, I don't know, but at least some statistical information can be added to the discussion.

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.