Sunday, March 30, 2008

How dramatically did Joe DiMaggio's major-league record of 56 straight games with at least one hit, accomplished in 1941, stake out the rare extremes of probabilistic territory? Not that dramatically, according to a new analysis in today's New York Times.

The computer-simulation study was conducted by a Cornell University duo, graduate student Samuel Arbesman and applied mathematics professor Steven Strogatz. My first exposure to Strogatz's writings came roughly five years ago, when I read his book, Sync, which I highly recommend. Strogatz has a well-deserved reputation for providing clear explanations of complex scientific concepts for a general, educated lay audience.

Saturday, March 29, 2008

Friday night's NCAA men's basketball Sweet 16 contest between Memphis and Michigan State was one of those odd games for streakiness. In ultimately winning 92-74, Memphis ended the first half on a 15-0 run, stretching a 35-20 lead to 50-20.

The lead got as big as 61-27 early in the second half, when MSU came back with a 17-0 burst of its own. Memphis still held on comfortably, but the Spartan spurt to answer the Tigers' was nevertheless interesting. As basketball analyst Ken Pomeroy wrote:

It's not often you see a team go on a 17-0 [run] in the second half and still never get any closer than 14 points. That's what Michigan State did in this one after falling behind 50-20 at the break and rendering the entire second half garbage time.

Accompanying this article is a Game Flow chart, which plots each team's cumulative point total over time; in it, you'll see a parallelogram, similar to the schematic one I've produced (below).

Whenever one team's point total is staying flat while the other's is rising, you can be certain a run is taking place. Memphis's run seems consistent with its overall superiority to Michigan State; the Spartans' run really seems anomalous!

Wednesday, March 26, 2008

Today is the 35th anniversary of UCLA center Bill Walton's 21-of-22 shooting performance from the field, in the Bruins' 87-66 NCAA title game victory over Memphis State (now the University of Memphis).

As shown in this online video, Walton's attempts in that game were a blend of mid-range perimeter shots and shorter ones -- lay-ups, tip-ins, and alley-oop plays. With this being the immediate post-Alcindor era of the banned slam-dunk, whenever Walton would receive a beautiful pass leading him to the hoop, he had to release the ball gently above the cylinder to score.

I was able to find this compendium of NCAA title game box scores through 2000 (although both FG attempts and makes were not included until 1950). Perhaps the first comparison that would occur to UCLA fans is that with Lew Alcindor (later Kareem Abdul-Jabbar). In three title games, Alcindor was 8-of-12 (1967), 15-of-21 (1968), and 15-20 (1969). Walton played in one other NCAA title game, in 1972, and went 9-of-17 against Florida State.

Statistically, Walton's cumulative title game shooting of 30-of-39 (.769) and Alcindor's 38-of-53 (.717) are not all that different. But on one particular night in 1973, Walton stood above everyone else.

In looking over the box scores for championship games after 2000, the closest performance to Walton's -- though still a ways away -- was the 10-of-11 shooting of North Carolina's Sean May in 2005.

Tuesday, March 25, 2008

The visiting Philadelphia 76ers scored 19 unanswered points last night against the Boston Celtics, en route to a 95-90 comeback victory. Such runs are not that uncommon at the college level, where I've accordingly cut back on trying to document them all. They seem to be much more rare in the NBA, though, especially at the expense of an elite team such as Boston.

Monday, March 24, 2008

A couple of brief items, one related to golf and the other to NBA basketball...

Tiger Woods had his streak of five straight PGA tournament wins (seven tourneys overall) snapped this morning, in the weather-delayed finish of the Doral tournament. For all the excitement surroundings Tiger's streak -- compounded last week by his dramatic 25-foot putt to win the Arnold Palmer Invitational -- I was feeling a little more reticent. I thought that Woods previously had compiled streaks as long as -- or longer than -- his recent one. Indeed, as shown here, Woods's current streak was not his best.


Sunday night in L.A., the Lakers fell behind the Golden State Warriors by 26 points early in the second half, then came back to take the lead, and then let the game get away again. At the end, it was Golden State winning 115-111.

Regarding comeback situations, there's a major question I've pondered with people over the years. Specifically, why in some cases does the team coming from behind keep its rally going and pull away from the formerly leading team to win the game (i.e., a "momentum" scenario), whereas other times the surging team will make the game close (or even take a slight lead) and then fall back down again (i.e., a "regression to the mean" scenario)? The Laker-Warrior game, of course, was an example of the latter.

Sunday, March 23, 2008

Miami Hurricane junior guard Jack McClinton has ended his season with an active streak of 38 straight made free throws. McClinton came into this afternoon's NCAA tournament game against Texas having hit 34 consecutive shots from the stripe. Then, in his team's 75-72 loss to the Longhorns, he went 4-of-4 on FT's (box score).

Saturday, March 22, 2008

During the 2003 NCAA men's basketball tournament, I coined the term "Cool Hand Duke" (a word play on a movie title) to characterize the difficult shooting stretches the Blue Devils experienced in losing to Kansas.

Well, the "cool hand" moniker needs to be dusted off and reapplied to Duke, as it missed 15 straight three-point attempts in losing this afternoon to West Virginia in NCAA tourney play (play-by-play sheet).

As many commentators had noted heading into the tournament, extensive shooting from behind the arc was Duke's modus operandi; the Blue Devils came into March Madness having launched 773 trey attempts, 16th among all Division I men's teams in the nation.

The team's three-point shooting percentage entering today's game was a good -- though not spectacular -- .382. In looking just at the players who shot treys during the 0-for-15 streak and weighting for each player's shot frequency, the adjusted shooting percentage was a similar .394. For simplicity, let's say that Duke's baseline three-point shooting was .400.

How likely is it that a .400 shooting team will miss 15 straight three-pointers? A .400 success rate translates into a .600 miss rate. We then simply raise .600 to the 15th power, which yields .0005 or about 1-in-2,000.

Two qualifications to this statistic are that (a) I was attracted to this event by its unusual nature and surveying a large, random sample of games may make such a phenomenon appear less rare; and (b) the calculation assumes independence of observations, like coin-flipping -- humans are not coins, but athletic performances do seem to be modeled well by random processes.

Tuesday, March 18, 2008

The Houston Rockets' 22-game winning streak has just ended, via a blowout loss to the visiting Boston Celtics.

Sunday, March 16, 2008

The Houston Rockets extended their winning streak to 22 games Sunday afternoon, knocking off the visiting L.A. Lakers, 104-92. There were also several streak-relevant aspects within the game:

*After the Rockets took a 59-44 halftime lead, the Lakers came out after the intermission and outscored Houston 12-0 to make it competitive again.

*With the game still tight until about halfway through the fourth quarter, the Rockets pulled away at the end. Quoting from the above-linked article:

Jordan Farmar's 3-pointer with 6:09 left pulled the Lakers to 86-84, but [Shane] Battier drove for a layup 25 seconds later.

Battier and [Bobby] Jackson sank 3s as Houston surged to a 96-86 lead with 3:20 to play. With [Tracy] McGrady occupying the defense at the other side of the floor, [Rafer] Alston drove for a layup and Jackson swished a jumper from the wing [which] made it 100-86.

*Houston's Alston went 8-of-11 on three-pointers.

In my previous entry (directly below), I came up with a range of estimates of the probability for the Rockets' winning 21 straight games. These estimates wouldn't change all that much after one additional game, so I'll wait a few games each time before updating the calculations.

Next up for the Rockets are the Boston Celtics (52-13), who come to Houston Tuesday night. One thing that should work in the Rockets' favor is that the Celtics must play at San Antonio Monday night, as road games on back-to-back nights exacerbate the draining nature of travel.

ADDENDUM: Also on Sunday, Detroit's Jarvis Hayes had a hot-shooting day in leading the Pistons over the New Orleans Hornets. In all honesty, I had not previously heard of Hayes.

Saturday, March 15, 2008

Houston Rockets' Winning Streak Watch (Full Game-by Game Log)

Length of Current Streak: 21 (following win over Charlotte)

Immediately Prior to Streak: 12-game stretch of 9-3

First Two Months of Season (Roughly): 15-17

Assuming a baseline of .500 play from the team's first two months of play, what is the probability of a .500 team winning 30 of its next 33 games?

Answer: .0000007; if we round up, it's roughly 1-in-1 million. (online calculator)

Another way we could frame the question is to use the 9-3 stretch to provide the baseline and then calculate the probability of a .75 team winning 21 straight. Then, the probability would be .002 (1-in-500).

Gail Goodrich, a member of the 1971-72 Lakers' squad that won 33 in a row, discusses the Rockets' streak and their prospects for seriously challenging the 33 mark.


Two brief items from Friday night's men's conference basketball tournaments:

UCLA defeated cross-town rival USC 57-54 in the Pac-10 semi-finals; in doing so, the Bruins used a 15-2 run at the beginning of the second half to overcome a steady Trojan lead and get in a position to win the game.

Georgia Tech unleashed a 19-2 run to narrow a big Duke lead to two points, but the Blue Devils reawakened to pull away to an 82-70 victory.


Finally, a belated acknowledgement of a double streak-buster in the Mountain West Conference's women's tournament. Utah came in as the top seed with a 16-0 conference record, facing last-place Colorado State, whose record was a mirror image at 0-16. Yes, you guessed it, CSU prevailed 60-52. The euphoria was short-lived, however, as the Rams lost their next game, to New Mexico.

Thursday, March 13, 2008

I seem to have company now, in commmenting upon unusual streaky occurrences. In this AP/ article about Oklahoma State's 76-72 win over Texas Tech in the opening round of the Big 12 men's basketball tournament, the writer observed the following:

In a weird, streaky start to the game, Oklahoma State took a 6-0 lead and then missed its next 10 shots as the Red Raiders went on a 14-0 run for a 14-6 lead.

Oklahoma State, with [James] Anderson hitting the Cowboys' first 3-pointer, then unleashed a 7-0 run for a 14-14 tie.

[Obviously, OSU would have needed an 8-0 run to tie the game 14-14.]


UCLA big man Kevin Love (6-foot-10, 271 pounds) hit three straight three-pointers, all within 1 minute and 16 seconds, to open up the second half, as the Bruins crushed Cal, 88-66 (second half play-by-play sheet).

The Georgetown men used 17-of-28 (.607) shooting from behind the arc in thrashing Villanova, 82-63.

Alabama darted out to a 32-8 lead over Florida in SEC men's action. The Gators, however, put together a 21-2 run in the second half to cut a 55-30 deficit to 57-51. Ultimately, though, the Tide washed out Florida, 80-69

Finally, in Big 10 men's action, Michigan and Iowa each experienced spells of coldness and moderate hotness, with the Wolverines prevailing, 55-47.

And there are still a lot of games remaining tonight!

Wednesday, March 12, 2008

In a first-round game of the Big 12 women's basketball tournament last night, the University of Texas used runs of 19-3 in the first half and 9-0 in the second half in eliminating Texas Tech, 75-63.

Tuesday, March 11, 2008

Saturday, March 08, 2008

A couple of items from this afternoon's Big 12 men's basketball play:

In Baylor's 86-73 win at Texas Tech, the Red Raiders were "Dunn in" by the Bears' LaceDarius Dunn. A solid enough three-point shooter coming into the game (.416), Dunn went 6-of-9 from behind the arc. According to this online binomial calculator, the probability of a prior .416 three-point shooter making 6 (or more) out of 9 is .12 -- not stunningly low, but still fairly rare. Meanwhile, Texas Tech's Alan Voskuil, a .512 three-point shooter coming in, went 0-for-5; the probability of that, given Voskuil's baserate, would be only .03.

On the opposite side of the state from Lubbock, in College Station, Kansas knocked off Texas A&M, 72-55. In their defeat, the Aggies missed 16 of their last 17 field-goal attempts of the game. Beyond a standard "cold hand" explanation (e.g., loss of confidence, poor concentration), another storyline could be that, as a team (such as A&M in this instance) falls further and further behind, it attempts more of the high-risk/high-yield three-point shots and rushes it shots, in general, to try to get points as quickly as possible. Of A&M's late misses, 11 were on two-point attempts and 5 were on threes (play-by-play sheet).

Thursday, March 06, 2008

Break up the Houston Rockets!

The guys from H-town won their 17th straight tonight, with a 113-98 victory at Dallas. The Mavericks were without the suspended Dirk Nowitzki, but I think the Rockets' win is nevertheless impressive because (a) a road win against a good team is never easy, and (b) Houston has been without Yao Ming, who is out for the season.

One thing I learned from this game article is that "Houston's streak is tied for seventh-best in NBA history." The Rockets' turnaround actually goes beyond the current 17-game winning streak, however.

As can be seen on Houston's game-by-game log, the Rockets were floundering at 15-17 around New Year's Day. I (along with a lot of Houston fans, I'm sure) was beginning to wonder whether veteran coach Rick Adelman, in his first year with the Rockets, really was going to get any improvement out of the team.

Houston then went on a 9-3 stretch, before launching the 17-game winning streak. The Rockets thus are now 41-20. To get some idea of how improbable such a turnaround may have been -- albeit in post hoc fashion -- let's say for simplicity that the Rockets were a .500 team before they got hot (roughly corresponding to the 15-17 start). How likely is it, therefore, that a previously .500 team could win 26 (or more) games out of 29?

According to this online binomial calculator, the answer is .000008. About 1-in-100,000.

Monday, March 03, 2008

The National Hockey League's Washington Capitals outscored the Boston Bruins 6-0 in the first period tonight, with the Caps' Alexander Ovechkin getting a hat trick (three goals) in the period. Washington won the game, 10-2.


After Texas Tech's John Roberson hit two straight three-pointers to cut Kansas's big early lead to 30-22, Jayhawk Coach Bill Self called a 30-second time-out. Whatever he said to the team worked, as KU went on a 34-5 spurt to lead 64-27. The final score of tonight's "Big Monday" match-up was 109-51, Jayhawks (play-by-play sheet).


Addendum: Monday night's Dallas-Utah NBA game also had a number of streak-relevant aspects, which I failed to write about at the time (a guy can only follow so many games!). Quoting from the article:

The Jazz scored 16 straight points late in the fourth quarter in a 116-110 win over the Dallas Mavericks on Monday night, coming back after blowing a 21-point lead.

Utah made all 18 free throws in the fourth quarter...

Sunday, March 02, 2008

Kobe Bryant scored 52 points in the L.A. Lakers' overtime win against Dallas Sunday, with a major turnaround in his free-throw accuracy playing a key role. According to this article:

[Bryant,] constantly driving and drawing fouls, was 20-of-27 from the line. He was perfect shooting free throws in the fourth quarter, making 13, and converted the two he took in overtime.

That after he missed five of eight from the line in the first half.


The Tennessee men jumped out to a 20-5 lead over Kentucky this afternoon, only to see the Wildcats fight back tenaciously and make the game close for nearly the entire second half. The game finally ended as a 63-60 Vol win.

Saturday, March 01, 2008

As Johnny Carson used to say, there was some "weird, wild stuff" going on today in Big 12 and Atlantic Coast Conference (ACC) men's basketball action.

Heading the list is how Big 12 rivals Texas A&M and Texas Tech responded against their respective Saturday opponents after Wednesday evening's 98-54 Aggie rout of the Red Raiders. The statistical principle of regression toward the mean would have suggested that A&M's offensive performance would come back down to earth a bit, whereas Tech's would improve to some degree. A&M and Tech indeed saw their offensive performances move in the expected directions, but I don't think anyone could have anticipated how drastically this would happen.

Playing today at Oklahoma, Texas A&M was outscored 28-10 in the first half and 64-37 for the game. According to this article:

The Sooners set what is thought to be an NCAA record for the longest time holding an opponent scoreless, since the advent of the shot clock in 1986, by blanking Texas A&M for 16 minutes and 12 seconds. The record entering this season was 13 minutes and 53 seconds, set by Utah State against Idaho on Feb. 15, 2006.

Texas A&M's 10 first-half points set a Big 12 record for the fewest points scored in a half of a conference game and a school record for fewest points in a half in any game.

In contrast, Texas Tech put on a 16-1 run spanning parts of both halves against No. 5 Texas to turn a 36-30 Longhorn lead into 46-37 Red Raider edge. Texas Tech had to hold off a furious Texas comeback attempt at the end, but did so successfully for an
83-80 upset win (play-by-play sheet).

As if that weren't enough for one conference, Oklahoma State outscored Nebraska 21-5 in beating the Huskers 77-63.

The ACC also saw some interesting streak-related developments...

Down 61-44 at Boston College, North Carolina unleashed a 32-8 spurt to go ahead 76-69; the Tar Heels ultimately won, 90-80 (second-half play-by-play sheet).

Elsewhere, NC State led for much of the second half against Duke, but failed to close the deal as the Blue Devils came back for an 87-86 win. The Wolfpack made its first 18 free-throw attempts and at a later point was 22-of-23. With Duke staging a comeback, however, NC State hit only 3 of its final 6 free throws, thus finishing 25-of-29 from the stripe (play-by-play sheet). Overall, the Wolfpack's free-throw percentage against the Blue Devils (.862, compared to .712 coming into the game) was quite good. Duke only needed a narrow window of opportunity, though, and NC State's final misses provided that window.