I had a unique opportunity to travel with the Texas Tech Lady Raider basketball team to its February 17 game at Texas A&M. The team charters its transportation, which presumably is a fixed cost; in other words, the planes and buses would cost the same whether 30 people were traveling or 50 people. Thus (again as I understand it), the athletic department can help offset some of its costs by selling travel packages to fans, which is how I got involved.

As far as hot hands, the big story in this year's two games between Tech and A&M was the sharpshooting of the Aggies' Takia Starks. She put up 22 points against Tech in Lubbock, whereas in College Station she torched the Lady Raiders for 29.

More important than basketball, the Lady Raiders' game at A&M was a "Think Pink" event to raise breast-cancer awareness. Nearly all the seats in Reed Arena were covered with pink towels before the game for fans to take, plus many of the College Station locals were wearing pink T-shirts from the awareness campaign. In the picture (below) that I took, the "pink out" can best be seen in the seats behind the basket on the right-hand side, although the entire seating bowl was so festooned. The above-linked article from the game at A&M also has a photograph of the many pink-attired audience members.


The Hot Hand page supports breast-cancer awareness. For further information, please visit the Susan G. Komen organization or the American Cancer Society.

I received an e-mail the other day from Rick Rosser, a "gym rat" free-throw specialist who puts countless hours into refining his craft, and works assiduously to extend his own personal records of consecutively made shots from the stripe. On top of all that, he adds a barnstorming component to his pursuit of free-throw nirvana.

Rick lists his accomplishments as having "... made 100 consecutive freethrows at 205 YMCA's, and over 50 other gyms and outdoor basketball courts [and] ... made 1,000 consecutive 7 times, with a best of 2,118." This newsletter from the South Palm Beach County (Fla.) YMCA documents one of Rick's visits.

Rick also has his own website, on which he writes about his activities and provides links to other free-throw masters' pages.

In men's college basketball action tonight, the Miami Hurricanes opened up a big lead on Duke on the strength of a 15-0 run, then held on for a 96-95 upset victory. If you scroll down a bit on this ESPN.com Duke-Miami summary page, in the "Game Flow" chart you'll see the run near the beginning of the second half. Duke's cumulative scoring line (blue) stays flat, whereas Miami's (green) steadily rises.

Tonight's NHL hockey game between the New York Rangers and Montreal Canadiens featured a streak and a "counterstreak." The Rangers took a 5-0 lead, only to have the Canadiens score five straight goals of their own, producing a tie at the end of regulation. After a scoreless overtime period, the game went to a shootout, where Montreal prevailed.

Given that 10 goals total were scored in regulation, how likely is it that they would be distributed as five straight by one team followed by five straight from the other? Think of 10 boxes laid out side-by-side, numbered 1 through 10, and five pucks with Montreal Canadien logos (representing the 5 Montreal goals). In the actual game, the Montreal goals were the sixth, seventh, eighth, ninth, and tenth goals scored in regulation, thus filling boxes 6, 7, 8, 9, and 10 in our example.

The question then becomes, In how many possible different ways could the five Canadien pucks have been distributed into the 10 boxes? For example, Montreal could have scored the game's second, third, fourth, eighth, and ninth goals; or the first, fifth, seventh, eighth, and tenth. Clearly, there are many, many ways to distribute five objects into 10 boxes.

The mathematical tool we need to use is the "n choose k" principle, in this specific case, 10 choose 5. An online calculator is available for this purpose. The answer is that there are 252 possible different ways to distribute Montreal's five goals into 10 different positions. The actual sequence that occurred, as well as the hypothetical opposite one of the Canadiens scoring the first five goals of the game, would probably be of greatest interest, so the probability would be 2/252 or 1/126.

I did a similar analysis of the 2004 Boston Red Sox' comeback from down 0-3 in the American League Championship Series against the New York Yankees, and I received some criticism for the post hoc nature of the analysis. Applying the critic's reasoning to the present example, it doesn't seem very likely that any fans entered the arena wondering, "What's the probability that the Rangers will score the game's first five goals tonight, only to have the Canadiens answer with five straight?" Accordingly, many statisticians would probably take me to task for undertaking the analysis I performed. Fair enough, but my intent in conducting such analyses is simply to illustrate how various statistical formulas can be used in thinking about sports oddities.

Xavier University hoopster Josh Duncan has now gone two games without missing a field-goal attempt -- and almost without missing any kind of shot attempt at all!

Monday night against Rhode Island, Duncan was 8-of-8 on field-goal attempts overall, 3-of-3 on three-pointers, and 4-of-4 from the free-throw line (box score). In his previous game, against Charlotte, Duncan went 7-of-7 from the field overall, 5-of-5 from behind the arc, and 6-of-8 on free throws (what's up with the two misses?).

A senior, Duncan was amazingly consistent on three-point attempts during his first three years, registering seasonal shooting percentages of .386, .385, and .381 (career stats). Prior to the last two games, Duncan was 32-of-82 (.390) from behind the arc this season, very much in line with his three prior seasonal percentages (adding in his 8-of-8 performance on treys in the last two games, he's now 40-of-90 this season, .444).

According to the online binomial calculator, for a player with a .39 previous three-point-shooting percentage to go a perfect 8-of-8 (combined over his last two outings) has a probability of .0005 (about 1-in-2,000), assuming independence of observations (like coin-tossing).

That's pretty remarkable, and it doesn't even take into account his additional success on two-point attempts and free throws!

Thursday night, I was watching the men's basketball telecast of my graduate-school alma mater, the University of Michigan, playing at Iowa. The Wolverines are in a rebuilding phase under first-year coach John Beilein and things haven't gone very well this season.

After the Hawkeyes raced to a 22-7 lead, I switched the channel and forgot to check back the rest of the evening. Hours later, I figured I'd check the web for the final score and, amazingly enough, Michigan had won 60-52. The key to the turnaround, of course, was the fact that the Wolverines had gone on two major runs to overtake Iowa (play-by-play sheet).

Trailing 25-9, Michigan first outscored Iowa 17-4 to cut the deficit to 29-26. Then, trailing 38-29, the Wolverines went on another huge spurt -- 18-2 -- to pull ahead 47-40.

Kansas State men's basketball coach Frank Martin apparently believes in a robust hot-hand phenomenon -- that when a good shooter is on target early in the game, his or her success on future shots is virtually assured. According to this article, after Texas Tech's Alan Voskuil (now shooting .544 for the season on three-point attempts) went 5-for-6 from behind the arc in the Red Raiders' upset win over the Wildcats Wednesday night, Martin said the following:

"Like all good shooters, when you give him open looks they find the rim," he said. "And once you let a good shooter find the rim, it's over. I don't care how hard you guard him after that, every time he lets it go it's going in."

Vanderbilt ran all over Kentucky tonight 93-52, having built up a 41-11 halftime lead. As seen in this play-by-play sheet, the Commodores darted off to a 15-3 lead. Then, leading 17-6, Vandy unleased another big run, 15-0, to make it 32-6. It was more of the same in the second half, with the Commodores going on a 12-1 run to expand a 43-13 lead to 55-14. Kentucky's overall field-goal percentage in the first half was .200 (3-15).

Heading into last night's Atlantic Coast Conference (ACC) match-up of Clemson at North Carolina, the Tigers had never beaten the Tar Heels in Chapel Hill, losing 52 straight times at UNC. Clemson came oh-so-close to ending the drought, holding an 11-point lead with 3 minutes to play, but Carolina came back to win in double-overtime. The free-throw disparity -- both in number of attempts and in success rate -- really stood out. Clemson went 1-7 (.143), whereas UNC went 31-36 (.861).

***

Team scoring spurts of the kind I've described in numerous prior entries don't seem to occur nearly as frequently in the NBA as in college ball. With only 30 teams, the NBA doesn't have the degree of talent differential in any particular game that a lot of college games do; also, to make the NBA, players generally have to be able to shoot well.

Having said all that, last night the New Jersey Nets went on a 21-0 run against the Dallas Mavericks, en route to a 101-82 rout. According to this ESPN.com article:

The 21-point run bridged the end of the second quarter and start of the third, and it was part of a 36-6 spurt that turned a 36-25 deficit into a 61-42 lead.

I haven't been following women's college basketball as closely this year as in the past, and thus haven't written much about it lately. I did, however, just become aware of a sizable comeback that occurred last night. Northern Iowa, trailing Indiana State 43-28 in the second half, unleashed a 17-1 run to go ahead 45-44. The game remained close from then on, win UNI hanging on for a 68-65 win.

Today's Big 12 men's basketball action featured a couple of "battles of the run."

Texas A&M's 77-69 win over Missouri included a sizable spurt by each team. The Tigers outscored the Aggies 17-3 during a stretch of the first half, but A&M started off the second half 15-0 en route to the victory.

Nebraska went on a 21-2 spree in the first half, and then withstood a 13-2 Texas Tech rally in the second, in defeating the Red Raiders, 73-62.

Elsewhere, Drake University won its 21st straight game, dropping Evansville, 73-65. The Bulldogs are 22-1 overall, the only loss coming at St. Mary's in Drake's second game of the year. Drake is undefeated in the Missouri Valley Conference, defeating several teams that have been good in recent years (Southern Illinois, Missouri State, Creighton). Further, in nonconference play, the Bulldogs claimed the unofficial state championship of Iowa by defeating the Big 12's Iowa State (in a rout) and Big 10 member, the University of Iowa (see Drake's game-by-game log).

In recent weeks, we had been following the consecutive made free-throw streak of the Washington Wizards' Caron Butler (here and here). Alas, it came to an end Sunday at 73. As remarkable as it was, it still was substantially short of the NBA record of 97.

As everyone knows, the New England Patriots came up short in their bid for a perfect 19-0 season, losing in the final minute of the Super Bowl. The victorious New York Giants ended the season on quite a win streak of their own, however.

After losing their season opener at Dallas, the Giants swept their remaining seven road games of the regular season (strangely enough, they were only 3-5 at home, for an overall 10-6 mark). New York then won playoff games at Tampa Bay, at Dallas, and at Green Bay, for an NFL-record 10 straight road wins (if one accepts the idea of combining regular-season and playoff games).

The Super Bowl, of course, represented the Giants' 11th straight win away from home, but it was played on a neutral field in Glendale, Arizona, and not on the opponent's home turf.

This morning's New York Times, reflecting the sports world's fascination with the New England Patriots' quest for a perfect 19-0 season in tonight's Super Bowl, features an article on the mindset of athletes who've recorded some of history's most memorable feats of perfection.

With interviews of athletes from a remarkably diverse array of sports -- from gymnast Nadia Comaneci to speed-skater Eric Heiden to bowler Glenn Allison, who rolled three straight 300 games -- the article notes these performers' virtual unanimity in saying that their minds were always on the immediate task at hand and not on the larger quest for perfection.

There's also a healthy supply of philosophical musings from a familiar source:

“There is no perfect season,” said John Wooden, who coached the U.C.L.A. basketball teams that once won 88 consecutive games. “You can have a season where you win all your games. But that is far from perfect.

“The other teams you played scored points and your team made mistakes. Maybe a lucky bounce actually won you a game or two. No, winning doesn’t make you perfect.”

I went to the Texas A&M at Texas Tech women's basketball game earlier tonight. The visiting Aggies came in ranked No. 23 nationally, but the unranked Lady Raiders were hanging in there, even leading early in the second half. Then Texas Tech stopped scoring points and the Aggies were off to the races. As the Lady Raiders fell further and further behind (they ultimately lost 63-46), the people sitting near me and I were all racking our brains to remember when Texas Tech had last scored. I was also curious about the margin by which A&M was outscoring Tech.

This game article provides answers to these questions: Texas Tech had a roughly 10-minute scoreless gap, and Texas A&M's run was 22-0.

Tonight's Kansas at Kansas State men's basketball game featured a number of streakiness-related storylines:

Even though playing on one's home court typically gives a team an advantage, for 24 straight years K-State had always come up short when hosting KU. Of course, the Wildcats hadn't done very well against the Jayhawks, regardless of venue; the above-linked article notes that, "The Jayhawks had beaten Kansas State 35 of their last 36 overall."

Anyway, K-State's 24-game losing streak to KU in Manhattan, Kansas (the Little Apple) is now over, thanks to an 84-75 Wildcat win.

Another streak ended by this game is that of KU's 20 straight wins to open up the season.

Finally, K-State frosh Jacob Pullen went a perfect 10-for-10 from the free-throw line. Pullen came into the game shooting .707 from the stripe; according to this online binomial calculator, the probability of a .707 free-throw shooter making all 10 attempts is only .03(assuming a player's free throw attempts are independent events, like coin-flipping, which has tended to be a reasonable assumption).

***

Meanwhile, over at West Virginia University, the Mountaineers went a woeful 1-for-22 on three-point attempts, in losing to Cincinnati. WVU entered the game shooting .378 from behind the arc, a fairly strong clip. Using the same online calculator as above, for a .378 team to make only 1 (or 0) out of 22 has a probability of .0004.

A couple of brief items...

Caron Butler of the NBA's Washington Wizards made all 10 of his free throws Sunday against Milwaukee, bringing his streak of perfection from the stripe to 70. Butler is still a ways away from the record, which is 97.

Playing against Vanderbilt, the University of Florida "put together a 23-0 spurt and built a 34-6 lead in the first 12 minutes of the game, then cruised to their 13th victory in 15 games against the Commodores..." (article).

Caron Butler of the NBA's Washington Wizards kept his streak of consecutive made free throws intact today, as his team defeated the Dallas Mavericks in a Martin Luther King, Jr., Day matinee. According to this ESPN.com article:

Butler had five assists and five steals and also went 2-for-2 on free throws to extend his franchise record and NBA season high to 56 in a row at the line.

[I thank Brian Burke for making me aware that Butler was on such a streak.]

In tonight's men's college basketball action, the University of Texas used a 24-2 second-half run to turn around its Big 12 game against the University of Colorado. Trailing 41-28, the Longhorns surged to a 52-43 lead (play-by-play sheet). Texas seemed to have the game under control, leading 69-59 with 4:25 remaining. However, Colorado scored the final eight points of the game to make things close, ultimately losing 69-67.

***

The game between national No. 2 Memphis and Southern Mississippi featured a couple of streakworthy items. The nickname "Southern Miss" was an appropriate description for the team's three-point shooting today, 0-for-14. Also, Memphis closed out the first half on a 20-3 run, en route to an easy victory.

***

George Mason University's Dre Smith set an NCAA record by going 10-for-10 on three-pointers against James Madison. The previous record for most treys in a game without a miss was 9-for-9, which was held by three players.

***

In Florida's overtime win over Kentucky, the Gators' Nick Calathes dominated the extra period (OT play-by-play sheet). He was 10-for-10 from the free-throw line (he was only 3-of-7 in regulation), hit a three-point shot, and got two rebounds. There's no truth to the rumor that he also drew up Florida's offensive plays, taped the players' ankles, and cooked the pre-game meals.

The Washington State men's basketball team continues to show its explosiveness. Coming off of last Saturday's loss to UCLA, in which the Cougars nearly pulled off a miracle comeback by hitting seven three-pointers in the final 1:37 of the game, WSU dispatched Oregon State last night 69-46, thanks to a 20-4 run to start the second half.

Also on the topic of three-point barrages, in last night's Suns-Lakers game in L.A. (won by the visitors, 106-98), the two teams made a combined seven three-pointers in roughly a three-minute stretch near the end of the game (from 4:43-1:27 remaining; see this fourth-quarter play-by-play sheet). Not quite as amazing as WSU vs. UCLA, but still noteworthy.