Friday, December 29, 2006

A couple of months ago, Michigan State set an NCAA Division I-A football record for the greatest deficit overcome (35 points), in a game against Northwestern.

Tonight, Texas Tech reeled off an amazing comeback of its own, overcoming a 31-point deficit (38-7) to stun Minnesota 44-41 in overtime in the Tempe, Arizona-based Insight Bowl. The Red Raiders' rally set a bowl record for comebacks.

Interestingly, Michigan State and Texas Tech started their respective comebacks with similar amounts of time remaining. Northwestern scored on MSU to take a 38-3 lead with 9:54 left in the third quarter, whereas Minnesota went up 38-7 over TTU with 7:47 remaining in the third. It really looked like the Gophers had burrowed too deep a hole for the Red Raiders to climb out of.

One possible way to approach the Texas Tech comeback statistically is via the runs test. If we looked at the temporal sequence of the teams' scoring drives (whether for a touchdown or field goal) in regulation, it would look like this (M = Minnesota, T = Texas Tech):


As can be seen from the color scheme, there were four "runs" in the sequence (a run being a stretch of one team scoring points without interruption by the other team). The fewer the runs, the more streakiness is present. I tested the Minnesota-Texas Tech sequence using an online runs-test calculator, typing in 1's instead of M's for Minnesota and 0's instead of T's for Texas Tech.

As explained in this document from North Carolina State University, the runs test determines how many runs would be expected by chance (which can then be compared to the actual number obtained), "given the proportion of the population in each of the two categories and given the sample size..."

In the Minnesota-Texas Tech analysis, there were significantly fewer runs than would be expected by chance (p < .05). One probably does not need a statistical test to be convinced that Texas Tech ended regulation play on a hot streak and Minnesota, on a cold one. Still, if you had never heard of the runs test before tonight, then the saying that, "You learn something every day," holds true, at least for tonight.

Thursday, December 21, 2006

Every so often, one hears a reference to a coach or manager making a decision according to "the book," as though a definitive catalog of strategy for a given sport existed. Now, however, a trio of baseball authors has come along and written a volume entitled, appropriately enough, The Book, and they have a website to go with it.

The website has a blog component, whose topics include streakiness. It is through this blog that I learned about an online discussion on another board, where a contributor with the moniker "Dackle2" presented some statistics on what happens after baseball teams go through a particularly hot or cold 10-game stretch.

What looks like around 300,000 10-game sequences in Major League Baseball from 1871-2005 were extracted and classified according to teams' records during the stretch (i.e., from 0-10, 1-9, and 2-8 all the way through to 8-2, 9-1, and 10-0). Teams' winning percentages from the five games before and five games after the 10-game stretch were also noted.

If there were anything to the idea of momentum or carryover of streakiness, one would predict, for example, that after languishing through a 0-10 cold streak, teams would have an appreciably worse winning percentage in the five games after the 10-game losing streak than in the five games before. Five games, by themselves, do not constitute a great sample, but aggregating many five-game sequences over many teams and many years, the data would seem sufficient.

As seen in the linked document, however, teams did not play markedly worse immediately after their 0-10 stretches (.347) than they did immediately before them (.358). At the other extreme, teams that achieved 10-0 hot streaks did not play substantially better immediately afterwards (.620) than beforehand (.610). In fact, whichever 10-game breakdown you look at (e.g., 2-8, 5-5, 7-3), the average winning percentages for the five games before and five games after are virtually identical.

Like other studies going all the way back to the original "hot hand" research by Gilovich, Vallone, and Tversky in 1985, the present findings suggest that players and teams have characteristic baseline rates of success, and that short-term hot streaks do not lead to long-term success rates above baseline, nor do short-term cold streaks lead to long-term success rates below baseline.

Saturday, December 16, 2006

One of the more interesting forms of streakiness, in my view, is seeing one team go on a run to build up a big lead, only to see the other team turn the tables and make its own spurt to come back and win the game, or at least make it close.

Last night alone in the NBA, there were at least four games that followed the above storyline:

Phoenix built a 47-22 lead over Golden State in the second quarter, only to see the Warriors rebound for an 80-72 lead (a 33-point turnaround from -25 to +8 on Golden State's part). Unfazed by blowing their huge lead, however, the Suns came back to win the game, their 13th straight victory.

Philly shaved a 17-point Dallas lead to just 3, although the Mavs pulled away again. It was the Sixers' 10th straight loss; Dallas had a 12-game winning streak earlier this season.

Sacramento erased a 16-point deficit to edge Utah.

Finally, in the late West Coast game, the Lakers came back from 21 behind to beat the Rockets.

A week ago, the Nets darted out to an 18-0 lead, but fell to Boston.

This recent lead-blowing even appears to transcend any particular sport. In NHL action last Monday, Washington squandered a 4-0 lead in falling to Pittsburgh 5-4.

The above scenarios were all that I planned to write about. But right now, upon checking the score of the Texas Tech-Arkansas men's basketball game, I see where the Red Raiders have jumped out to an 18-3 lead. Tech, to this point, has missed only one shot, whereas Arkansas has made only one. If the aforementioned games are any lesson, expect a Razorback run to get back into the game.

Update: Arkansas never got closer than eight, with Texas Tech then pulling away to win by 15.

Wednesday, December 13, 2006

Time to check in again on the three-point shooting of the Texas Tech men's basketball team. As noted in my November 30 posting (see below or in November 2006 archives), the Red Raiders were leading the nation in shooting percentage behind the arc, at 50.4. Citing the statistical concepts of extremity of outcomes in small sample sizes and regression to the mean, I predicted the team would drop off some.

It should also be noted that, over the past five seasons, none of the teams that led the nation in three-point percentage exceeded 44%.

2002 Oregon 42.4
2003 Illinois St. 44.0
2004 Birm. Southern 43.0
2005 Oklahoma St. 42.1
2006 Southern Utah 42.9

Since my last posting on this topic, Texas Tech has experienced a small drop in its accuracy from long distance, sitting currently in second place nationally at 47.8.

In the Red Raiders' three most recent games (season log), they had two poor outings from three-point land (4-14, .286 vs. Stanford, and 2-10, .200 vs. Louisiana Tech), followed by an 11-18 (.611) explosion vs. Centenary. I was at the Centenary game and noticed some fans marking each of Texas Tech's made treys by unveiling a succession of cloth signs with 3's on them. With the help of my faculty colleague Bo Cleveland (with later technical assistance by Rachna Mutreja), we were able to take the following photo of the display in full glory at game's end.

I'll continue to track the story. It's important to state that, even if Texas Tech's three-point percentage continues to drop -- as I predict it will -- the team could still lead the nation, as other teams will likely drop too. In other words, Texas Tech's anticipated drop would be in absolute terms, but not necessarily in relative terms.

In terms of individual players, BYU's Austin (Got the Range) Ainge is now down from his earlier 70.6 three-point percentage (which I cited in my previous write-up) to 54.2.

Sunday, December 03, 2006

It was just a few days ago (see November 30 posting below) that I talked about how extreme patterns can occur when looking at a small number of observations (e.g., several batters hitting above .400 early in the baseball season). But, I warned, it's hard to maintain extremely high (or low) levels of performance over larger numbers of attempts.

Yesterday, however, a Division III men's basketball player did as much as can be done within a single game to contradict my assertions. What happened was that Lincoln University's Sami Wylie shot 51% on three-pointers.

If a player were to have shot (roughly) 50% on 10 three-point attempts, I would find that moderately interesting. In 20 attempts? More impressive. And so on as the number of shots from behind the arc increased.

Well, in Wylie's case, he shot 51% on 41 attempts from three-point land. Yes, he shot 41 times from downtown, making 21 treys! All told, he ended up with 69 points in Lincoln's 201-78 win over Ohio State-Marion.'s article likens the game to a scene from the movie Pleasantville, where "every shot from every conceivable angle goes in."

Saturday, December 02, 2006

First, a disclosure: I received my undergraduate degree at UCLA, in 1984.

Going into this year's annual USC-UCLA football game, played earlier today, the rivalry over the past 15 years had been as streaky as is possible for a situation where both teams had enjoyed stretches of dominance.

1991 UCLA
1992 UCLA
1993 UCLA
1994 UCLA
1995 UCLA
1996 UCLA
1997 UCLA
1998 UCLA
1999 USC
2000 USC
2001 USC
2002 USC
2003 USC
2004 USC
2005 USC

With UCLA's eight straight wins, followed by USC's seven, we don't need a statistical test to tell us that the number of observed runs (uninterrupted streaks by one team) is the minimum possible -- two -- given that each team has won at least once.

USC was widely expected to beat UCLA today en route to the (mythical) national championship game, in the process tying UCLA's earlier eight-game winning streak in the Battle of Los Angeles.

But it wasn't to be. UCLA 13, USC 9.