Saturday, December 17, 2016

Preview of Women's NCAA Final: Texas vs. Stanford

My last posting, on the Final Four teams' success rate this season in five-game matches, turned out to be useless for the semifinals, as neither match went the distance. Maybe tonight's final will...

Things haven't exactly gone as expected. The vaunted Big 10 conference (abbreviated B1G), which had the three highest national seeds -- Nebraska, Minnesota, and Wisconsin -- has no finalist. Also, this year will be the first in the six years I've compiled my Conference-Adjusted Combined Offensive-Defensive (CACOD) measure that a national title winner will be below a score of 1.94. The two finalists are close though, Stanford at 1.91 and Texas at 1.79.

I found Stanford's four-game semifinal win over Minnesota surprising, but the Cardinal had defeated the Gophers, also in four, way back on August 28.

My reaction to the other semi, which also involved a rematch from the regular season, was: What the hell happened? Defending national champion and this year's No. 1 national seed Nebraska had not merely swept, but routed Texas (25-15, 25-16, 25-21) on August 27. In the national semis, however, the Longhorns returned the favor, sweeping the Huskers!

Certainly, improved defense was a major for the Longhorns' turnaround. UT let Nebraska hit .304 in the teams' first match (with only 5 total blocks for the Horns), whereas Texas held the Huskers to .182 in the rematch (with 10 blocks).

Offensively, Longhorn frosh outside-hitter Micaya White struggled mightily in the first Nebraska match (hitting in negative territory, -.143, with 3 kills and 6 attack errors on 21 attempts). However, she improved to a solid, if unspectacular .269 (7-0-26) the second time around.

Another key player for Texas tonight will be fellow OH Ebony Nwanebu. She hit .378 (15-1-37) in Thursday's semifinal match and .333 (13-3-30) in the early-season match against Nebraska. Although now based in different conferences, Nwanebu and Stanford should be pretty familiar with each other. The reason, as close followers of the women's college game are aware, is that Nwanebu began her career at Stanford's Pac-12 rival USC, before transferring to Texas after her sophomore year. As the following chart shows, Nwanebu had some big matches as a Trojan against Stanford and generally committed few hitting errors.

Stanford combines a very youthful line-up (perhaps a reason for the team's slow start this season) with the experience of Inky Ajanaku, a fifth-year middle-blocker who missed last season with an ACL injury. Ajanaku finished sixth in the nation in blocks per game at 1.52. This article describes Ajanaku as the "grandma" of the team, noting also that she's a "wannabe orthopedic surgeon."

The big question, then, is whether the title will go to the wannabe or the Nwanebu.

UPDATE: Stanford takes it in four.

Thursday, December 15, 2016

Final Four Teams' Records in Five-Game Matches

There seem to have been a lot of five-game matches this year, both in the regular season and in the NCAA tournament. Some of the Final Four teams went five in roughly a quarter of their matches this season. Here's how the remaining teams fared in five-game matches:

Texas: 4-3 overall; 2-1 home; 2-2 road

Nebraska: 4-1 overall; 2-0 home; 2-1 road

Stanford: 4-4 overall; 1-3 home; 2-1 road; 1-0 neutral
  • Included in Stanford's record is a win over visiting Cal Poly. How did the Cardinal even let Cal Poly take the match to a fifth game?
Minnesota: 5-3 overall; 4-0 home; 1-3 away

Thursday, December 1, 2016

2016 NCAA Women's Tourney Preview

With this year's NCAA women's tournament getting underway today (brackets), I'm back with my Conference-Adjusted Combined Offensive-Defensive (CACOD) measure to forecast teams' success. The CACOD simply divides a team's own hitting percentage during the regular season by the overall hitting percentage it allowed its opponents, and then multiplies the resulting ratio by an adjustment factor to reward being in stronger conferences (details here). Teams that hit well and don't allow their opponents to do so will get the highest CACOD scores.

I have been calculating the CACOD for the past five years. The following table (which you can click to enlarge) shows scores for all teams making the Elite Eight during that time frame. Again, CACOD scores are based entirely on regular-season play (i.e., NCAA-tourney games are not factored in), so they can be judged for their prognostic efficacy.

The table tells us three main things, in my view:

  • No team below a CACOD of 1.94 has won the national championship during the five years I've computed the statistic. Thus, if your favorite team is well below a CACOD of 2.00, it is unlikely to ascend the victory podium. 
  • Although we're talking small sample-sizes, the CACOD appears to distinguish eventual national-championship teams (mean = 2.43) from national runners-up (1.90), losers in the national semifinals (2.03), and losers in the Elite Eight (1.96). However, it does not differentiate the latter three groups from each other.
  • Only twice in the past five years has the team with the very highest CACOD won the NCAA title (Penn State in 2013 and 2014). One leader lost in the national semis (Penn State, 2012), one lost in the Elite Eight (Washington, 2015), and one even lost in the round of 32 (Nebraska, 2011). 

So which teams have the highest CACOD scores this year? The next table tells us...

No. 1 seed Nebraska leads the way by a sizable margin, with a CACOD of 2.56. Penn State, though seeded all the way down at 16, has the second-highest CACOD (2.10). The Nittany Lions frequently do well on the CACOD, which I take as a sign of its "face validity." Unfortunately for Penn State, it would have to play Nebraska in the Sweet Sixteen. Several discrepancies between teams' seeds and their CACODs are evident. Eleventh-seeded Florida has the third-highest CACOD, whereas fourth-seeded Texas has only the tenth-highest CACOD.

We'll see how well the CACOD performs as the games get underway!

Saturday, September 17, 2016

Hitting Percentages vs. Different Numbers of Blockers Up

How much of an advantage is it for a hitter to go against one blocker instead of two? Or against two blockers who have not closed ranks (i.e., a  split block) instead of two blockers who are side-by-side with no gap between them? The following analysis, a collaboration of Volleymetrics (the blog where you are now) and Volleymetrics (the statistical-analysis consulting firm owned by Giuseppe Vinci), addresses questions such as these.

After several conversations, Giuseppe agreed to share some of his data with me for analysis. Given my location at a Big 12 school, we decided to explore data from women's play in this league (2015 within-conference matches only). Far and away, most spiking attempts occurred against two blockers side-by-side (10,615). The next most swings took place facing one blocker (2,712) or a split-block (1,182). Attempts against zero (409) or three (273) blockers were relatively rare.  Here are the average hitting percentages against each type of blocking scenario:

The primary comparison, in my view, is between hitting against one blocker (with a .315 hitting percentage) instead of two (.203).* The difference of .112 corresponds to 11 additional kills (minus errors) for every 100 attempts hitting against one rather than two blockers.

Ideally, for a truly "apples-to-apples" comparison, all characteristics of a hitting attempt (height and arc of the set, position of the hitter, quality of the hitter, etc.) would be the same, on average, for swings against one blocker and swings against two. That is almost certainly not the case, as sets to the outside tend to be higher than those to the middle and, thus, more likely to allow two blockers to get into position. Caution is warranted, therefore, in interpreting these results.

I told Giuseppe via e-mail that, "I would have thought the hitting percentage vs. 0 blockers would have been higher [than it was]." He replied that, "the reason [hitting percentage against] no blockers might be low can be due to attacks far from the net not having any blockers. If they are attacking just to get it over the net, it won't have a very high efficiency. When we limit attacks against no blockers to being within the ten-foot line, the efficiency against no blockers increases to .3202."

Not surprisingly, spike attempts against three blockers have a very low efficiency (.114). Swings against split-blocks, however, tend to be extremely successful (.423). Apparently, when hitters see a gap between blockers, the former are quite good at exploiting the situation.

Thanks again to Giuseppe; I greatly appreciate this gesture.

*The calculation of mean hitting percentages in the bar graphs was done using statistics at the match level. In other words, let's say a team in a given match hit .300 against two blockers on 20 attempts; another team in another match hit .200 against two blockers on 10 attempts; and a third team in yet another match hit .500 against two blockers on 25 attempts. In this hypothetical example, the unweighted average would be .333 ([.300 + .200 + .500] / 3), not giving the matches differential weight by attempts. The weighted average would give greater weight to matches with more attempts: [(.300 X 20) + (.200 X 10) + (.500 X 25)] / 55 = 20.5 / 55 = .373. The bar-graph shows unweighted averages. The weighted averages (0 blockers: .276; 1 blocker: .300; 2 blockers: .196; 3 blockers: .143; and split-block: .433) were similar to the respective unweighted ones.

Tuesday, August 30, 2016

Volleyball Mag Reviews First Weekend of 2016 Women's College Play

Volleyball Magazine has an excellent overview of the first weekend of women's collegiate play, including who's hot and who's off to a surprisingly slow start. This article will serve as a foundation for the statistical analyses I conduct during the season.

Saturday, August 27, 2016

2016 Olympic Wrap-Up

The 2016 Summer Olympics concluded a week ago in Rio de Janeiro, Brazil, and I would like to offer some statistics and closing thoughts on the women's and men's indoor competitions. The U.S. captured bronze medals in both, but could have, and perhaps should have, won a pair of gold medals.


For women's and men's play alike, there was a 12-team field, with teams divided into two pools (A and B). The U.S. women finished atop Pool B, with a 5-0 record. The top four teams in each pool advanced to an elimination tournament to determine the medal-winners. Accompanying the U.S. from Pool B were the Netherlands (4-1), Serbia (3-2), and China (2-3).

The four teams to come out of Pool A were host Brazil (5-0), Russia (4-1), Korea (3-2), and Japan (2-3). Presumably, the teams were seeded to even out the strength of the two pools as much as possible. However, when the elimination round began -- with the fourth-place team in one pool playing the first-place squad from the other pool, and the second-place team from one pool facing the third-placer from the other -- the pools were shown to have been anything but balanced!

China (fourth-place in Pool B) stunned Brazil (first in Pool A) in five games. Brazil took the opener 25-15, after which China began to play at a level NBC television announcers Paul Sunderland and Kevin Barnett said was "unrecognizable" from how it had played previously in the competition. Outside-hitter Zhu Ting, 6-foot-6 and only 21 years old, took an amazing 58 swings for China against Brazil, amassing 26 kills (with only 6 errors) for a .345 hitting percentage (box score; see this FIVB glossary for differences in terminology with U.S. statisticians).

In fact, all four teams to advance from the quarterfinal round were from Pool B, with all four teams from Pool A losing. After a quarterfinal sweep over Japan, the U.S. women faced a rematch with Serbia, whom the Americans had bested in four games in pool play. Game 1 of the U.S.-Serbia medal-round semifinal started off in much the same fashion, with the U.S. prevailing 25-20. However, U.S. middle Foluke Akinradewo early on was showing signs of injury, only being able to limp around on the court. She left for good midway through the second game.

With Akinradewo out, Serbia took the next two games fairly easily, 25-17 and 25-21, before the U.S. seemed to turn things around with a 25-16 win in Game 4. The U.S. seemed in control for most of Game 5, leading 11-8. Serbia rallied, however. A Serbian service ace gave the team a 13-12 lead, but Serbia committed a service error on the next play, evening things at 13-all. The U.S. then served into the net, giving Serbia match point at 14-13. Serbia won a rally on the next serve to win 15-13.

China, meanwhile, knocked off the Netherlands in four in the semifinals, with Zhu Ting outdoing her performance vs. Brazil with a .443 hitting percentage (31-4-61).

China defeated Serbia in four for the gold medal (Zhu Ting putting together a .386, 24-7-44 night), with the U.S. doing likewise against the Netherlands for the bronze. Unsurprisingly, Zhu Ting captured the MVP award.

The China-Serbia-U.S. order of finish in women's Olympic play replicated exactly the results of last year's World Cup tournament. Brazil wasn't in the 2015 World Cup, as the tournament served as an Olympic qualifier and Brazil was already in as host country. One wonders whether Brazil's absence from the World Cup denied the team some added sharpness heading into 2016.

Fans of a non-championship team -- especially one expected to win  -- often conduct post-mortem discussions on why the team lost. The U.S. bronze finish was naturally a prominent topic on the VolleyTalk boards. One common argument was that the U.S. lacked a consistent terminator on the right and left sides. Below is a graph I created of the hitting percentages of U.S. attackers with at least 10 spike-attempts in a given match, against the team's top opponents. You may click on the graphic to enlarge it (thumbnail pictures from here and here).

Right-side hitter (opposite the setter) Kelly Murphy started strong with a .355 hitting performance against the Netherlands in pool play, but declined in other key matches, until facing the Netherlands again in the bronze-medal match. The other right-side/opposite, Karsta Lowe, came up big in the semifinal vs. Serbia (.429), but not in other matches. The two main outside (left-side) hitters, Kim Hill and Jordan Larson-Burbach, had some strong matches, but not consistently. Kelsey Robinson, in limited action as a front-row OH, went to town against China (.454) in pool play.

Middle-hitters typically record higher attack-percentages than those hitting on the sides, as teams in desperation often send a high set to the outside. The aforementioned Akinradewo and Rachael Adams indeed hit for high percentages. Akinradewo was stellar throughout, including in a comeback effort against the Netherlands for the bronze. Adams appeared to be more effective in pool play than in the medal round.


Things went very differently for the U.S. men than for their female counterparts. The men lost their first two matches of pool play, to Canada in three and Italy in four. Many of the individual games were close -- two lost games against Canada and all three lost games against Italy being "deuce games" (lost by two points) -- but they were losses, nonetheless.

One probably would not have expected the U.S. to get its first win over world No. 1 Brazil, on the latter's home court, but that's exactly what happened, in four games. The U.S. rode the wave it was on, dropping only one game in its next three matches against France (3-1, pool), Mexico (3-0, pool), and Poland (3-0, quarterfinal).

The U.S. faced a rematch with Italy in the semis. After the teams split a pair of deuce games (30-28 Italy and 28-26 U.S.), Italy came unglued in a 25-9 Game-3 loss. The Americans had a good chance to close things out in Game 4, leading 22-19. However, Italy scored the final six points of the game. Unfortunately for the U.S., it experienced a near-total meltdown in Game 5, losing 15-9. A key play near the end that symbolized the American collapse involved an Italian overpass close to the sideline that the U.S. decided to let drop -- and it landed in!

In the bronze-medal match against Russia, 38 year-old Reid Priddy led the U.S. back from two games to none to get the Americans on the medal stand. Priddy hit a remarkable .615 percentage (17-1-26). In the final match, Brazil swept Italy in a trio of tight games, 25-22, 28-26, 26-24, for the gold.

Because the U.S. men seemed to derive much of their success from the block, I examined the team's blocking success rate throughout the tournament. Specifically, I divided the total number of U.S. "kill blocks" (blocks for a point) in a match by the opposing team's spike attempts (minus number of balls hit out of bounds, as there would be no reason to try to block a ball headed out). As an example, the U.S. recorded 7 kill blocks against Canada. The Canadians had 71 spike attempts, including 12 "faults." We know, therefore, that Canada hit 5 balls out of bounds (12 total faults - 7 faults from being blocked). Canada's spike attempts in play thus number 66 (71 total - 5 out of bounds). U.S. blocking effectiveness in this match was thus 7/66 = .106. The next chart shows U.S. blocking effectiveness in all of its matches.

The trend does not track exactly with wins and losses as, for example, one of the better U.S. blocking matches occurred in the loss to Canada. Conversely, U.S. blocking effectiveness was not that high in a win over Poland. Having said this, one can see an upward trajectory in blocking effectiveness, starting with the pool-play loss to Italy and increasing steadily in the wins over Brazil, France, and Mexico.


I didn't examine the statistics of Olympic beach volleyball this year. However, I wanted to recognize the efforts of Kerri Walsh who, after winning three straight gold medals with Misty May (who retired after 2012), stuck around to test her outer limits in trying for a fourth straight gold (this time with April Ross). As readers of this blog would know, Walsh and Ross took the bronze. I did manage to find this one article, which looked into some of the women's beach stats. According to the article, Walsh and Ross were among the women's leaders in attacking (defined as kills/attempts with no accounting for hitting errors), blocks, and digs. They were not among the leaders in aces, however.

Sunday, August 7, 2016

Thursday, August 4, 2016

U.S. Women's Olympic Team for Rio

With the opening ceremony of the 2016 Summer Olympics in Rio de Janeiro just one day away, there is much anticipation among volleyball fans regarding the various competitions within the sport. Kerri Walsh will be seeking her fourth straight gold medal in women's beach volleyball (this time partnered with April Ross, rather than longtime partner Misty May), but we'll save that topic for another day.

The present entry is about the U.S. women's indoor team, which is seeking its first Olympic gold medal in program history. After a shocking setback to Brazil in the final of the 2012 London Olympics, the U.S. women won their first major international title at the 2014 World Championships. The Americans then took third at the 2015 World Cup.

There appear to be several top contenders on the Rio hardwood, besides the U.S., including home-team Brazil, China, Serbia, and Russia. Don't be surprised to see semifinal and final matches coming down to decisive fifth games!

The following chart presents the U.S. women's roster (obtained here), with a focus on the players' collegiate success in making American Volleyball Coaches Association (AVCA) All-America teams.

Player (Position) College All-America Teams (AVCA)
Rachael Adams (Middle) Texas 1st, 2011; 1st, 2010
Foluke Akinradewo (Middle) Stanford 1st, 2008; 1st, 2007; 1st, 2006; 2nd, 2005
Kayla Banwarth (Libero) Nebraska ---
Christa (Harmotto) Dietzen (Middle) Penn State 1st, 2008; 1st, 2007; 2nd, 2006; HM, 2005
Alisha Glass (Setter) Penn State 1st, 2009; 1st, 2008; 2nd, 2007
Kim Hill (Outside Hitter/left) Pepperdine 1st, 2011; HM, 2010; HM, 2009
Jordan Larson (Outside Hitter/left) Nebraska 1st, 2008; 3rd, 2007; 1st, 2006
Carli Lloyd (Setter) Cal 1st, 2010; 2nd, 2009; 2nd, 2008
Karsta Lowe (Opposite/right) UCLA 1st, 2014; HM, 2013
Kelly Murphy (Opposite/right) Florida 1st, 2011; 1st, 2010; 2nd, 2009; 3rd, 2008
Kelsey Robinson (Outside Hitter/left) Nebraska 1st, 2013; HM, 2012*; 2nd, 2011*
Courtney Thompson (Setter) Washington 1st, 2006; 1st, 2005; 1st, 2004
*While playing for Tennessee, before transferring to Nebraska.

Foluke Akinradewo is the leading hitter in the middle, in my view, based partly on the 2015 World Cup. Former Minnesota Golden Gopher Tori Dixon, with whom I've long been impressed, might have been among the team's middle corps, but suffered an ACL injury earlier in the year.

I'm least familiar with the outside (left-side) hitters. Kim Hill played for Pepperdine, which is not in a conference I concentrate on. Jordan Larson's career goes back a ways, only partially overlapping with my time operating this blog. Kelsey Robinson, in her one year at Nebraska (2013) after transferring from Tennessee, hit .318 while taking a very high 29.2 percent (1206/4132) of the Cornhuskers' swings that year.

This Volleyball Magazine article from back in February details the intense competition between Kelly Murphy, Karsta Lowe and Nicole Fawcett for what was anticipated (and indeed turned out) to be two openings for opposite/right-side hitters on the roster. (The term "opposite" comes from being opposite the setter in the rotation.)

Lowe did not perform that well in the 2015 World Cup, but improved dramatically in the January 2016 NORCECA regional qualifying tournament in Lincoln, Nebraska. Quoting from the above-linked Volleyball Magazine article:

"Teamed with [setter Courtney] Thompson in Lincoln, Lowe tallied a combined 22 kills and not a single hitting error in 34 attempts (.647) over less than 10 serving rotations."

Fawcett was named MVP of the NORCECA tournament, but ended up being the odd-woman-out for the Olympic team.

Joining Thompson in the setting ranks are Alisha Glass, key to one of Penn State's run of national titles, and Carli Lloyd (not to be confused with the U.S. soccer player of the same name). In 2010, Lloyd led Cal to the national final and was voted national Player of the Year. I once wrote of Lloyd that "during her senior campaign [in 2010, she] not only ran the high-powered Golden Bear offense, but also hit a respectable .265 on 283 tries (7% of the team's attempts) and contributed 1.08 blocks/set. (... I've come to regard an average of 1.00 or greater blocks/set as a marker for excellence in blocking.)"

All players on the U.S. roster, except former Nebraska libero Kayla Banwarth, earned at least one AVCA first-team accolade, with seven players receiving first-team honors in multiple-years.** Nor did Banwarth play extensively in overseas professional leagues. Her college coach John Cook was quoted as follows in the Des Moines Register:

“What’s really amazing, though, is she stayed with it, without really having much of a pro career," Cook said. "She’s just continued to hone her skills, training in Anaheim (Calif.), training with (U.S. coach) Karch Kiraly and training some days by herself.”

As I reported here, Kiraly gave a forum at Texas Tech University in March 2015, where he revealed many aspects of his philosophical approach to coaching.

We'll continue to track the U.S. women, as they progress through the competition in Rio.

**For each of the last several seasons, AVCA has been bestowing first-team honors to 14 players, so being placed on the first team is more like being on a hypothetical "best roster" rather than "best starting unit."

Thursday, May 5, 2016

NCAA Men's Tourney: If BYU and UCLA Meet in Final, Bruins' Serving Could Be Crucial

We're now down to the Final Four of men's NCAA volleyball, with two semifinal matches tonight -- No. 1 seed BYU vs. No. 4 Long Beach State, and No. 2 seed UCLA vs. No. 3 Ohio State -- and the final on Saturday (link to bracket). In the event of a BYU-UCLA final, which is no certainty, my preview below will be useful. If not, it will have been purely an academic exercise.

BYU and UCLA have played three times this season, in a pair of regular-season matches in Los Angeles (here and here) and in the MPSF conference-tournament final in Provo. The Cougars have taken all three contests, each in four games. In each of these matches, Bruin serving errors have played a seemingly large role in determining the outcome. UCLA committed 15 service errors in the first match, 20 in the second, and 27 in the third. I find this unbelievable, but in the three matches combined, the Bruins missed one-quarter of all their serve attempts (62 misses on 246 serves, which is .252)! (These and other statistics appear in a table below, which you can click to enlarge.)

Of course, a strategy of "just get it in" would help the Bruins only modestly. BYU won nearly two-thirds (.648) of the rallies on UCLA's serve (i.e., when the serve was non-terminal, not an ace or error). If the Bruins floated a bunch of soft, unchallenging serves the Cougars' way, BYU's side-out rate on rallies would almost certainly go up by a sizable amount. The other side of the argument, though, would be that UCLA won zero points on all its missed serves and picking up even a few extra points by winning rallies on less-aggressive serves could be important in a close match.

Tristan Burton and Scott Powers published a thoughtful and sophisticated analysis of the serving-aggressiveness trade-off -- more-effective serves vs. more errors -- in 2015 in the Journal of Quantitative Analysis in Sports (summary). As these authors note, "a balance among [service-ace fraction, service-error fraction] and opponent offensive ability must be considered in order to guide service strategy" (p. 3). Using calculus and other advanced mathematics (e.g., the "Newton-Raphson solution"), Burton and Powers derive graphical displays for determining which players need to serve more or less aggressively. Lacking the volume of data and the brainpower* necessary to apply Burton and Powers' formulations in full, I came up with my own analysis of UCLA's serving vs. BYU, which made intuitive sense to me.

Using play-by-play sheets from the three BYU-UCLA matches (available via BYU's schedule page, by clicking on "Box" for a given match, and then "Play-By-Play"), I recorded the outcome of every serve for each of UCLA's eight main servers (listed in the table above). A serve could result in one of four outcomes: an ace or an error (both considered "terminal" outcomes), a rally (i.e., after a non-terminal serve) won by UCLA, and a rally won by BYU.

Not much was going on with UCLA ace serves (only 18 total in the three matches; 8, 9, and 1 by match chronologically). I therefore focused on service errors. For each of the eight Bruin players, I computed his service-error percentage (number of errors divided by total number of serves) and the percentage of time on that player's serve that UCLA won a rally after a non-terminal serve.

To the extent aggressive serving results in both service errors and (when the serve goes in but does not produce an ace) the receiving team being taken out-of-system in running its offense, we should find a positive correlation between UCLA players' service-error percentage and percentage of rallies won by UCLA. Indeed, we do, as shown in the following graph.

For readers with statistical training, the correlation coefficient (r) =  .52. This is a fairly large correlation, but caution is warranted due to the small sample size of 8 players. (Free plotting software is available here.) A couple of players exemplify the trend. Oliver Martin committed only 1 error on 29 total serves vs. BYU during the season (3.4%), but his (apparently) low-risk serving also was easy for the Cougars to field, so that the Bruins won fewer than one-third of the rallies on Martin's serve. At the other extreme, Jackson Bantle had a much higher rate of service errors, committing them 28.6 percent of the time, but UCLA won 44.4 percent of rallies on his serve.

I'll leave the precise optimization of service aggressiveness to Burton and Powers. If you want to determine how risky to be in your serving, taking account of the opponent's ability to launch its offense, you should look at their article. What I've concluded from my little exercise is that UCLA seems to have a good reason to serve aggressively. However, the Bruins' service-error rate does seem excessively high.

UPDATE: A BYU-UCLA match-up in the NCAA men's final never happened, as Ohio State beat the Bruins in a tense five-game semifinal match. The Buckeyes survived three match-points in the decisive game, before winning it 18-16. OSU continued its momentum into the championship match, shockingly sweeping BYU. The Buckeyes outhit the Cougars, .374-.296; not only that, OSU took 20 more attack attempts than did BYU, 91-71, indicative of the Cougars' passing difficulties (box score). BYU's award-winning right-side (opposite) hitter Ben Patch, hitting .383 entering the NCAA tourney, performed well-below that in the final, hitting .091 on 10 kills and 8 errors in 22 swings.

*I did take a year of calculus as a college freshman 35 years ago and I occasionally watch calculus lectures online to retain as much of it as I can. However, I feel nowhere near confident enough to conduct the analyses reported by Burton and Powers.

Hawai'i Sweeps Long Beach State to Claim Second Straight NCAA Men's Championship

Hawai'i swept Long Beach State last night in Los Angeles to win its second straight NCAA men's championship. Scores were 25-22, 25-...