It's over! After surpassing the early 1970s' UCLA men's record 88-game winning streak by two games, the University of Connecticut women had their run of victories halted at 90 by Stanford Thursday night. Give credit to UConn not just for the streak itself, but for scheduling tough nonconference opposition such as Stanford and Baylor.

Purely by the numbers, UConn has the longest Division I basketball winning streak. However, there are other factors to consider when ranking all-time great teams, such as depth of competition (which some might argue is still not as strong in women's as in men's hoops) and the relatively recent information explosion of all-sports cable channels, the Internet, etc. (which seemingly puts contemporary athletes under greater scrutiny than in the past). See the poll question at the top of the right-hand column about where you think UConn's streak ranks in college-basketball history.

The Illinois men's basketball team made its first seven three-point attempts last night, in defeating Iowa 87-77 on the Hawkeyes' home court.

When Kobe Bryant is mentioned on this blog, it tends to be in connection with hot shooting, as seen here, for example. However, last night in San Antonio, Bryant missed 13 straight shots as the Lakers lost to the Spurs, 97-82.

The NBA's Orlando Magic has just completed a rare streak-killing double, ending the Boston Celtics' 14-game winning streak this afternoon after halting the San Antonio Spurs' 10-game string of victories on Thursday. Quoting from the above-linked Orlando-Boston game story, the Magic's accomplishment "marks the first time in 13 years that a team ended two winning streaks of at least 10 games in consecutive outings."

I'm aware of two men's college basketbal games recently, in which one team's fast start coincided with the other's slow start to produce a 20-0 score at the outset.

On December 18, Louisiana Tech took a 20-0 lead over Texas-Arlington. Before scoring its first points, UTA missed six shots and committed six turnovers. Thus, it was a combination of a cold hand and a sloppy hand that put the Mavericks in the hole (play-by-play sheet). Louisiana Tech didn't have that hot of a hand to start the game, for that matter, scoring its first 20 points on 3-of-4 shooting on two-point shots and 4-of-9 on three-pointers (plus a pair of free throws). Despite falling so far behind, UTA hung in there, cut the deficit to 10 points at the half (36-26), and ended up losing by only a single point, 62-61.

Then, today, Northwestern got off to a 20-zip start over Mount St. Mary's and was never challenged thereafter, winning 70-47. MSM missed 15 shots and committed five turnovers before scoring (play-by-play sheet). The Wildcats scored their initial 20 points on 6-of-10 two-point shooting, 2-of-6 on threes, and 2-of-3 on free throws.

The UConn women's basketball team once again routed a nationally ranked opponent, No. 20 Florida State, 93-62, Tuesday night. The win is the Huskies' 89th straight, passing the mark of 88 consecutive wins recorded by the early-1970s UCLA men's basketball program.

Penn State won its fourth straight National Collegiate Athletic Association (NCAA) women's volleyball title over the weekend, sweeping Cal-Berkeley in three games. Penn State lost a few matches during the regular season this year -- in contrast to its undefeated 2008 and 2009 champions, which were part of an overall 109-match winning streak -- but by tournament's end, no one could touch the Nittany Lions.

Trailing 31-10 to the New York Giants in NFL action Sunday, the Philadelphia Eagles scored four touchdowns in roughly the final 7 minutes, 30 seconds to win 38-31. Such comebacks occur every so often. Here is an example from 2006 that I tried to analyze from a probability perspective.

As the graphic to the right illustrates, the University of Connecticut women won their 88th straight game this afternoon, blowing away the nation's No. 10 team, Ohio State, 81-50. UConn has now tied the streak of Coach John Wooden's early 1970s men's teams at UCLA.

Ohio State's Jon Diebler made nine straight three-pointers Wednesday night, in the Buckeyes' 83-55 win over Florida Gulf Coast (play-by-play sheet). He also missed five shots from behind the arc, yielding the following sequence (H = hit, M = miss):

M M H H H H H H H H H M M M

Given that a player has gone 9-for-14 on three-point shots (or achieved whatever hit rate on whatever athletic endeavor), it may be interesting to some to inquire into how many possible ways nine successes can be distributed within 14 attempts. The number would have to be pretty big. For a few examples, which just scratch the surface, a player might have made his or her first nine shots; first eight plus the 10th shot; shots 1-5 and 11-14; or shots 1, 3, 5, 7, 9, 11, 12, 13, and 14. Using the "n choose k" principle (in this case, 14 choose 9), one finds that there are actually 2,002 possible ways (online calculator).

Further, of the 2,002 possible ways to embed nine successes in 14 attempts, only six involve hitting nine shots in a row: Hitting the first nine shots (1-9), shots 2-10, shots 3-11, shots 4-12, shots 5-13, and shots 6-14.

Pretty rare, huh? It should be acknowledged, however, that because I chose to (a) analyze this particular shooting sequence entirely based on its unusual nature; (b) focus on a number of specific details (i.e., asking what are the odds of a player who went 9-for-14 making the nine shots consecutively); and (c) not analyze a representative cross-section of games, I am probably overstating the rarity of the occurrence.

National Football League quarterback Brett Favre had his consecutive-starts streak end at 297, as the Minnesota Vikings declared him ineligible for tonight's game against the New York Giants, due to a shoulder injury.

The streak started on September 27, 1992, as summarized in this YouTube video, with Favre a member of the Green Bay Packers. He started Green Bay's final 13 games of the '92 season. Favre then started all 16 games for the next 17 seasons, with the Packers (1993-2007), New York Jets (2008), and Vikings (2009). This season, he was Minnesota's starter for 12 straight games (see Favre's career statistics).

If you're doing the math, it's: 13 + (17 X 16) + 12, which equals 13 + 272 + 12, which yields 297.

Not surprisingly, given the nature of the game, Favre experienced many injuries during the streak, but always managed to make it for the opening snap. Just this past October, it looked like two fractures in his left ankle might end the streak, but they didn't.

As my symbolic tear-off calendar to the right illustrates, the University of Connecticut women's basketball team is now at 87 straight wins, after tonight's 79-47 victory over Marquette. The Huskies are now just one win from tying the overall Division I college basketball record for longest winning streak, 88 games, set by the UCLA men from 1971-1974.

UConn's attempt to tie the record will have to wait a little while, however, as the team is on a 10-day break for final examinations. The Huskies' next game will be on Sunday, December 19 against Ohio State, in the Maggie Dixon Classic at New York City's Madison Square Garden.

Kenyon College frosh Maureen Hirt, daughter of Indiana University social psychologist Ed Hirt, hit on 7-of-9 three-pointers yesterday.

Happy Thanksgiving to all you Hot-Handers out there!

The San Antonio Spurs mounted a massive comeback at Minnesota last night to extend their winning streak to 12 games (13-1 record overall). Whether this fast start by the Spurs signals a return to the NBA elite remains an open question, in my mind. Looking at San Antonio's game-by-game log, one sees that the quality of opposition during the streak has been, with a few exceptions, pretty weak (including two games against the Clippers).

UPDATE: The Spurs had their winning streak ended Friday night by Dallas.

One of the more exciting men's college basketball games of this young season took place last night, as unranked Connecticut upset No. 2 Michigan State, 70-67, in the Maui Invitational.

One of the reasons it was so exciting, however, is the poor job offensively by both teams in closing out the game. With 5:00 remaining, UConn led 66-61. The Huskies managed only four more points the rest of the way, but that was enough to win, as the Spartans scored only six. In the following table, I've summarized each team's woes, based on this second-half play-by-play sheet.

The University of Connecticut women's basketball team dodged the proverbial bullet tonight in extending its winning streak to 80 games. In holding off No. 2 Baylor, 65-64, in Hartford, the No. 1 Huskies pulled to within eight wins of tying the 88-game winning streak of the UCLA men's program in the early 1970s.

In looking at UConn's schedule, as long as the Huskies keep winning, their chance to capture an 88th straight victory would come on December 19, against Ohio State in the Maggie Dixon Classic at Madison Square Garden.

As the lead to this article on tonight's Denver at Indiana NBA game states, "The Indiana Pacers made their first 20 shots of the third quarter, missing out on a perfect period when Josh McRoberts was off on a 3-pointer with 1.9 seconds left..." These were not just dunks and layups, mind you. The Pacers hit 8-of-9 on 3-pointers in the quarter. The full shot sequence, including estimated distances of the attempts, can be seen in the play-by-play sheet of the third quarter.

This is how close the racehorse Zenyatta came to raising her career win-loss mark to a record 20-0 (you can click on the image to enlarge it). Instead, with tonight's narrow loss to Blame in the Breeders' Cup Classic, Zenyatta sees her 19-race winning streak  -- her "hot hoof," if you will -- come to an end. According to this ESPN.com article, Zenyatta shared the consecutive-wins record of 19 with a horse called Peppers Pride, but the latter's competition was nowhere near as strong as Zenyatta's. A complete-race video of the Breeders' Cup is available, accompanying the above-linked article. I took a screen-shot after pausing the video as close as I could to the finish, and then added the dotted lines to show how close Blame and Zenyatta were to each other.  

The San Francisco Giants have won this year's World Series, defeating the Texas Rangers tonight, 3-1, to finish things off in five games. From a hot-hand perspective, the Giants' pitching staff was the big story, giving up only one run in the Rangers' last 21 and 1/3 innings at the plate (Giants' postseason game-by-game log).

I will be interviewed on Dallas radio station KRLD 1080 today at 3:20 pm (Central), to discuss the Rangers' and Giants' streakiness heading into tonight's World Series opener. You can listen live online at this link. For an idea of the things I may be discussing, see the last several postings below.

In Friday night's 6-1 victory over the New York Yankees to close out the American League Championship Series in six games, the World Series-bound Texas Rangers got a home run from Nelson Cruz in the fifth inning. That home run gave the Rangers at least one homer in all 11 of their playoff games this season, their previous series against Tampa Bay having gone the opening-round maximum five games (game-by-game log).
 
An item in today's Texas preview notes mentioned the team's 10-game (at the time) postseason homer streak, adding that it was the Rangers' "longest home run streak since they homered in 10 straight games from April 6-17, 2009." The notes did not say what Major League Baseball record was for this type of streak. Regardless of whether the World Series opponent for Texas is Philadelphia or San Francisco, the Rangers will have to hit against arguably the toughest pitching staff they have faced all year.

Here are some of Texas Ranger pitcher Cliff Lee's numbers for the 2010 postseason (which consists of two wins over Tampa Bay and one tonight over the Yankees):

Innings pitched:  24
Strikeouts:  34
Earned runs allowed:  2
Walks:  1

Some brief college football news from today's action:

Michigan State has now reeled off seven straight wins to start a season for the first time since the Spartans' famous 1966 campaign.

Oklahoma State won its first game at Texas Tech since 1944. The two schools met only sparingly until becoming Big 12 conference mates in 1996, however, so the Cowboys' losing streak in Lubbock is not as long as the 66-year gap would suggest. I've tried looking up the historical record of games between the teams, but there seems to be some conflicting information. Suffice it to say that Oklahoma State (formerly Oklahoma A&M) had a winless streak in Lubbock of 10 losses and either 1 or 2 ties, before today. Including today's game, Cowboy kicker Dan Bailey is now a perfect 13-for-13 on field-goal attempts this season, which includes two successful attempts from 50-plus yards in OSU's game prior to facing Texas Tech.

Minnesota has had a lot of success making the baseball postseason in recent years. But once there, the Twins have been unable to come up with wins. Last night, the New York Yankees beat the Twin Cities crew, 6-1, to sweep the teams' opening-round MLB playoff series, 3-0.

As stated in this Minneapolis Star-Tribune article:

The Twins have lost 12 postseason games in a row, the second-longest streak in major league history. The Red Sox had a 13-game postseason losing streak from 1986 to 1995, and the Twins now seem to have their own Curse of the Bambino.

Minnesota's skid started in 2004. That year, the Twins actually took the opener of their series with the Yankees (behind star pitcher Johan Santana, who later moved to the Mets), before dropping three in a row. That was followed by a three-game sweep in 2006 at the hands of the Oakland A's, followed by another sweep last year, by the Yankees. This year's repeat sweep by the Yankees thus brought the Twins' playoff losing streak to an even dozen.

Blogger John Tauer has already weighed in on the mathematical aspect of the Twins' losing ways, noting that the probability of 12 straight losses with an assumed .50 probability of winning each time is 1-in-4,096 (.50 to the 12th power). Tauer argues for the plausibility of .50/.50 prior win probabilities in the baseball playoffs because of the narrow range of ability levels between the participating teams (regular-season winning percentages ranging only narrowly, from .556 to .599).

UPDATE (November 7, 2010): I've just returned from attending an academic conference in downtown Minneapolis. Though the Twins have had a lot of postseason difficulty (as detailed above), one thing that should bring a lot of enjoyment to fans in the Twin Cities is the team's new ballpark, Target Field. I walked around the facility, which just completed its first season of play, but it appeared to be closed (except for the gift shop), so I couldn't get close to the playing surface. Here's a montage of photos I took (you can click on it to enlarge). If the Twins could add an up-and-coming Rod Carew-type hitter, that would certainly help!

Defending college football national champion and No.1-ranked Alabama had its 19-game winning streak ended today at South Carolina, 35-21. The length of the stretch falls a little shy of the top 50 college-football winning streaks. However, taking toughness of competition into account, the Tide's roll would have to rank above many longer streaks for overall impressiveness.

The Southeastern Conference (SEC), in which the Crimson Tide participates, is in the midst of what has to be one of the strongest runs by a league in college-football history. Not only have the last four national champions come from the SEC (Florida 2006 & 2008, LSU 2007, Alabama 2009). There are several other SEC teams (varying in quality by year) that can give an opponent a tough day at the office (Arkansas, Auburn, Georgia, Mississippi, Tennessee).

Of Alabama's five straight wins to open the current season, three were against teams ranked at the time: Penn State (No. 18), Arkansas (No. 10), and Florida (No. 7). South Carolina came into today's game ranked No. 19 and will undoubtedly move up!

Texas Tech University's women's volleyball team ended its 64-match Big 12 losing streak tonight, with a five-game win over Kansas (details at my VolleyMetrics blog).

Against Colorado on Saturday night, a game won by the Rockies 10-9, the San Francisco Giants' pitching staff saw its impressive run of 18 straight games with three or fewer runs allowed come to an end. According to this article, it was the third-longest streak of its kind in Major League Baseball history.

Yesterday, the University of Missouri football team missed an extra point after successfully making 252 in a row, going back to 2005 (I assume this mark includes only kicked points-after-touchdown and not going for two, but I could be wrong). According to the linked article, "Missouri ended up 10 shy of the NCAA record set by Syracuse from 1978 to 1989..." A couple of points occur to me.

First, whereas Mizzou's streak involved all or parts of six seasons, Syracuse's took place during all or parts of 12 season. Apparently, the Tigers produced touchdowns a lot faster than did the Orange.

Second, an issue occasionally raised with regard to streaks is awareness on the part of individual athletes or teams that they have a long string of successful (or unsuccessful) performances going. Presumably, a team that has won 20 straight games, a baseball player who has gotten a hit in 50 consecutive games, or a basketball player who has made 70 straight free throws will know what's going on. Whether such awareness might increase the player or team's concentration, sense of pressure, or other psychological state becomes a key question.

On a streak such as made extra points, I'm not sure if the players involved even know about it. Success rates approach 100%, so the short kick through the uprights may well be taken for granted and not register in the minds of the kicker and others involved in the play (i.e., holder, snapper, linesmen). Also, long streaks of made extra points span multiple seasons, with multiple kickers involved (three for Missouri, seven for Syracuse). Any particular kicker, therefore, may only have contributed, say, 50 successful PATs to the streak, so the larger collective streak of over 250 again may not register with the current kicker. It should be noted, though, that a former Tiger kicker contributed 185 of the made PATs, out of what turned out to be the team's near-record 252. 

I'm a little behind the curve on this development, but I wanted to write about it, nevertheless. From September 3-18, Colorado Rockies' shortstop Troy Tulowitzki hit a total of 14 home runs in 15 games. Coinciding with Tulowitzki's barrage, the team won 13 out of 15. With 26 homers on the season thus far, Tulowitzki thus hit more in the 15-game stint than in the enire rest of the season. A trio of sports journalists recently discussed Tulowitzki's offensive outburst and the notion of sports streakiness, in general. In the process, they were kind enough to mention this website. An audio of the segment is available here. As I am wont to do, I made a graphic to illustrate what took place.

With the team winning as well, it looked like shades of 2007 for the Rockies. After Colorado's September 18 win over the L.A. Dodgers (and San Diego's late-August slide; here and here), the Rockies were within 1 game of the first-place Padres (with San Francisco also in the mix; standings tracker). The next day, however, the Rockies blew a 6-1 lead to the Dodgers, losing 7-6 in 11 innings. Colorado has not won since (with Tulowitzki homerless) and has fallen 4.5 games out of the lead, heading into its upcoming game tonight against the now first-place Giants.

Seattle Mariners' outfielder Ichiro Suzuki extended his major-league record for most consecutive seasons with at least 200 hits to 10, with a single Thursday afternoon against Toronto. The longest such streak by anyone other than Ichiro is eight straight years, by Wee Willie Keeler from 1894-1901. Pete Rose had 10 season with 200 or more hits, but not in a row, whereas Ty Cobb had nine non-consecutive double-century seasons.

As seen in Ichiro's career statistics, he in fact has never recorded any fewer than 206 hits in a season (excluding the present one, which still has roughly two weeks remaining) since coming to the U.S. from Japan for the 2001 season. A few times, he has absolutely blown away the 200-hit mark, his best yearly totals reaching 262 (in 2004), 242 (in 2001), and 238 (in 2007).  According to Ichiro's Wikipedia page, in 1994, he "set a Japanese single-season record with 210 hits in 130 games, the first player ever to top 200 hits in one year."

 

Penn State's women's volleyball winning streak has been halted at 109 matches by Stanford, in a three-game sweep at the Big Four tournament in Gainesville, Florida. The Nittany Lions, who have won the last three NCAA titles, last lost on September 15, 2007, also to Stanford.

The San Diego Padres' losing streak is now over. After a weekend sweep at the hands of the Colorado Rockies extended the Padres' skid to 10 games, San Diego finally got a win Monday night, 4-2 over the L.A. Dodgers.

The women's soccer team at Texas Tech, where I'm on the faculty, started the season with five consecutive shut-out wins (over Texas Christian, Texas State, Northwestern State, Rice, and Mississippi). With 90 minutes the standard duration for a soccer game, the Red Raiders had held their opponents scoreless for 450 minutes.

In a 2-0 loss to Notre Dame this afternoon, however, the Fighting Irish scored two quick goals approximately 24 minutes into the game (23:51 and 24:38; stats sheet). Thus, Texas Tech's shut-out streak is now over at 474 consecutive minutes. A game article from Texas Tech's athletic website is available here.

The San Diego Padres have been extremely effective this year at recovering from losses and preventing any serious skids from developing -- until now. Through August 25, with the exception of being swept by the L.A. Dodgers in a three-game series from May 14-16, the Padres had never lost more than two games in a row (game-by-game log).

Now, however, they have lost seven in a row, heading into tonight's game against Colorado. The Padres' lead over San Francisco in the National League West standings, which recently had been as much as 6.5 games, is now down to 3 (day-by-day standings tracker). San Diego's recent cold streak really stands out visually, as seen in the following graphic I created. You can click on the figure to enlarge it.

For three of the games in the Padres' current malaise, they faced one of the best teams in the National League, the Philadelphia Phillies. However, the other four losses were to the last-place Arizona Diamondbacks. In a long season -- 162 games for each team in Major League Baseball -- fairly long streaks of winning and losing are virtually inevitable. The current slide, which could stretch even longer, really seems out of place with how the team has done thus far in the season, however.

(The ticket stub is from a game I attended, while in San Diego for the recent American Psychological Association convention.)

Today's posting is more about the "steady hand" than the "hot hand," as Seattle Mariners' first-baseman Casey Kotchman had a record fielding streak end yesterday. According to this game article:

A wicked, one-hop shot in the eighth inning [off the bat of Yankee Curtis Granderson] caromed off Kotchman's glove and continued into right field. He was charged with an error, ending his Major League-record streak of 274 games without a fielding miscue.

The streak lasted more than two years and covered 2,379 fielding chances.

Another, slightly dated (April 27, 2010) article includes a chart of the records for consecutive error-free games by position. At the time, outfielder Darren Lewis held the overall record at 269 games. The positions of catcher, first-base, and outfield seem particularly conducive to long streaks; shortstop and third-base don't. I would say there are two things that set apart first-basemen from their counterparts on the other side of the infield:

(1) First-basemen get a lot of their fielding opportunities by catching thrown balls (from the other infielders) and relatively few from fielding hit balls. Shortstops and third-basemen (the latter playing at a location known as the "Hot Corner") primarily face balls hit at them.

(2) Shortstops and third-basemen presumably get more balls hit at them than first- or second-basemen, because there are more right- than left-handed hitting batters.

This is not to say that first-basemen never get hard shots ripped at them. The streak-ending ball hit to Kotchman was one that required a difficult short-hop to field, and he couldn't do it (see video associated with the linked article in the first paragraph above). There'll probably be a lot of debate over whether the official scorer's call should have been a hit or an error.

With a 7-2 loss tonight to the New York Mets, the Pittsburgh Pirates saw their record for the season fall to a dismal 40-82. The significance of this record is that, in a 162-game season, the break-even point would be 81-81. The Pirates' 82nd loss thus officially guarantees them of a losing record. And the losing record gives Pittsburgh an unenviable streak, namely 18 straight years without a winning record. As this game article notes about the Pirates:

Their 82nd loss in 122 games extended the longest streak of consecutive losing seasons in major American pro sports history.

They'd never secured a losing season so early, either, accomplishing it on Aug. 20. Previously, the earliest they had done so during the streak was on Aug. 27, 2001.
 
For a team that's been this pathetic for this long, a more thorough autopsy is in order. Fortunately, Sports Illustrated conducted one earlier this summer.

Milwaukee Brewers third-baseman Casey McGehee had his streak of hits in nine consecutive at-bats stopped Friday in the first inning against Colorado Rockies starter Jorge De La Rosa.

As noted in an earlier article marking McGehee's extension of his streak to 9-for-9, "The major league record for consecutive hits is 12, set by Pinky Higgins in 1938 and matched by Walt Dropo in 1952."

I've always felt streaks for consecutive at-bats with hits are underrated. Here, the batter has no margin for error. One out and the streak is over. In a consecutive-games hitting streak (immortalized by Joe DiMaggio), a batter can make outs perhaps a few times per game and still have the streak persist -- as long as he gets at least one hit in a game.

The Arizona Diamondbacks a couple of nights ago became the latest Major League Baseball team to hit four straight home runs. As shown in this chart, Arizona's is the fourth quadruple homer barrage since 2006. Before 2006, the last instance of four straight homers was all the way back in 1964.

As he did once before, in 2005, prolific baseball analyst and writer Bill James has just e-mailed me a write-up he's done on a hot hand-related topic, with permission to post it here, if I choose. The topic this time is pitching, namely the question, "If a starting pitcher has been pitching well in his recent starts, is he more likely to pitch well today?" James describes three separate studies he conducted to investigate this question. Because his write-up is 19 pages long, I'll just summarize the main parts.

Key to the whole endeavor is defining how well a given pitcher is doing, both in a particular game and over his last few starts. Here are some foundational definitions:

Game Scores are a method that “score” each start by a starting pitcher essentially on a zero-to-one-hundred scale. To convert this into a “Hot Pitcher Scale”, each pitcher’s score after each game (and thus, heading into his next start) was 20% of his score from his last start, plus 80% of whatever his score was prior to his last start.

The first study, using all pitchers from 1960-1969, created two dimensions, both coded from A (best) to H (worst): performance quality for a given season (to equate pitchers on prior ability), and "hotness" coming into a game. Pitchers were then evaluated on how well they pitched in their next games. Summarizes James:

...at the conclusion of this I had 64 groups of pitchers, coded AA, AB, AC, AD, AE, AF, AG, AH, BA, BB. . ..HE, HF, HG, HH. AA was high-quality pitchers who came into the game hot; HH was low-quality pitchers who came into the game pitching badly, even by their own standards. We had about 500 starts in each group of games. The essential question was whether and to what extent pitchers would pitch better, relative to the quality of their overall performance, when they were “hot” than when they were “cold”.

They did not pitch better.

The second study, using all starting pitchers from 2000-2009, looked for temporal sequencing; did a given hurler's well (or poorly) pitched games tend to cluster consecutively? (This approach is conceptually similar to a statistical technique known as the runs test.)

"Is there, in general, any tendency for Game Scores to form clusters? None whatsoever."

James's third investigation, again examining 2000-2009, "compared pitchers with identical or near-identical year-to-date records, but one of whom came into the start hotter than the other." There were 504 matched pairs. Finally, in this study, support was obtained for pitcher streakiness:

In this study the pitchers who were “hot” did out-perform the pitchers who were not hot in their next starts, and over the balance of the season —- not by a huge amount, but they did outperform them. The “hot” pitchers, in their 504 “next starts”, had a won-lost record of 199-175, an ERA of 4.28, and an average Game Score of 50.62.

The “cold” pitchers, in their 504 next starts, had a won-lost record of 177-177, an ERA of 4.74, and an average Game Score of 47.94.

James concludes with a piece of practical advice for fans:

...suppose that you are going to a ballgame tomorrow, and both starting pitchers are 11-7 with ERAs of 3.45, but one of them is hot and the other is cold. Is the one who is “hot” more likely to win the game?

Yes.

Northern Ireland's 21-year-old golf phenom Rory McIlroy had an amazing hot spell during today's first round of the British Open, a tournament he leads with his 9-under-par 63. Within a seven-hole stretch, McIlroy bettered par six times, five times by one stroke (a birdie) and once by two strokes (an eagle). Here's the sequence:
 
Hole Result
 
  9 Eagle
10 Birdie
11 Birdie
12 Birdie
13 Par
14 Birdie
15 Birdie

UPDATE: McIlroy fell out of contention on the tournament's second day, thanks to a round of 80 in high winds. He rebounded with scores of 69 and 68, respectively, on the final two days, however, to finish tied for third place, eight shots behind winner Louis Oosthuizen.

The American League's 13-year unbeaten streak in the Major League Baseball All-Star Game (12 wins plus the infamous 2002 tie game) ended tonight, as the National League took a 3-1 decision. As noted on the Wikipedia page on the topic:

"The All-Star Game has seen several 'eras' in which one league tended to dominate. From 1933 to 1949, the American League won 12 out of the first 16. The National League dominated from 1950 to 1987, winning 33 of 42 with 1 tie. This included a stretch from 1963-1982 when it won 19 of 20, including an 11-game win streak [that] went from 1972 to 1982. Since the late 1980s, the American League has dominated..."

You may have noticed the oddity of there being 42 games in the 38-year period from 1950-1987. From 1959-1962, two All-Star Games were held per season.

A couple of streakiness notes from Major League Baseball:

The Texas Rangers had their 11-game winning streak stopped last night, with a 7-4 loss to Houston.

Meanwhile, the Chicago White Sox will be going for their 11th straight win tonight, as the Sox and Cubs continue their intra-city series. Yesterday, the Southsiders beat the Northsiders, 6-0.

UPDATE: The White Sox beat the Cubs Saturday, 3-2, to extend their winning streak to 11, but lost Sunday, 8-6, ending the streak.

In the marathon Wimbledon tennis match discussed in yesterday's posting, John Isner finally defeated Nicolas Mahut, 70-68 in the fifth set.

UPDATE: Some statistically oriented bloggers have attempted to estimate the probability of the Isner-Mahut match having as many consecutive held-service games as it did, here and here.

In Wimbledon tennis action, the men's singles match between John Isner and Nicolas Mahut has been suspended due to darkness for the second day in a row. Wimbledon doesn't use tie-breakers for decisive sets, so at 6 games apiece in the fifth set, Isner and Mahut were left to keep playing until one could secure a two-game lead.

A set getting to 10-10 would probably be pretty rare. Last year's final, in which Roger Federer edged Andy Roddick 16-14 in the fifth, has been called a classic. Back in 1969, before tie-breakers were used at all, Wimbledon saw a 24-22 first set, Charlie Pasarell prevailing over Pancho Gonzalez. Ties at 30-30 or 40-40 would be nearly impossible to comprehend. Well, the umpire has called it a night for Wednesday's action between Isner and Mahut, as the two men are tied 59-59 in the fifth set.

There's a hot-hand angle to this -- I wouldn't be writing about the match if there were not. In the fifth set, the server has won the game (or "held") for 118 straight games!

Stay tuned...

Boston guard Ray Allen made his first seven three-point attempts last night, as the Celtics evened their NBA final series against the L.A. Lakers at one game apiece. Based on the play-by-play sheet, I made one of my sequential shot charts (which I hadn't done in a while) for Allen, as shown below (you can click on the graphic to enlarge it).


If we focus exclusively on attempts from behind the arc, then Allen's hot shooting spans the first and second quarters. He missed some two-point shots in the first quarter, however, so I would say his streak shooting was confined to the second period.

Yes, Garrett Wittels's hitting streak is still in progress -- having been extended to 56 consecutive games in today's NCAA regional action -- but it will be on-hold until next season. His team, Florida International University, was eliminated earlier today by Dartmouth, 15-9. Wittels was only a sophomore this past season, so he can attempt to continue the streak in the 2011 season. He'll need to get at least one hit in each of his first two games next season to tie Robin Ventura's NCAA Division I record of 58. If that happens, we'll then see if Wittels can take his streak to 59 and beyond.

Garrett Wittels doubled today in the sixth inning to extend his hitting streak to 55 consecutive games, as the NCAA college baseball regionals got underway today around the U.S. Wittels's team, Florida International University, wasn't so fortunate, getting crushed 17-3 by Texas A&M at the Miami site. FIU now goes to the losers' bracket, where one more defeat means elimination.

As those who have been following the thread of postings on Wittels know, the NCAA Division I record is 58 games, set in 1987 by Oklahoma State's Robin Ventura. Should Wittels keep getting hits, but his team not rebound to give him three (or four) more games this season for him to tie (or surpass) Ventura's streak, Wittels will be able to resume the streak next season, as he is only a sophomore.

Northwestern had its quest for a sixth straight NCAA women's lacrosse title thwarted in yesterday's national championship game, as Maryland came from 6 goals behind to prevail 13-11.

Garrett Wittels today extended his hitting streak to 54 games, as his Florida International University team won the Sun Belt Conference tournament. FIU now gets an automatic bid to the NCAA regionals, meaning that Wittels will have at least two more games this season (i.e., the regionals have a double-elimination format). The Golden Panthers will need to win twice to give Wittels a chance this season at tying Robin Ventura's record of 58 straight games with a hit. Wittels is only a sophomore, however, so he would have the opportunity to come back next season and extend the streak (provided it doesn't end in the NCAA tournament).

Garrett Wittels of Florida International University extended his hitting streak to 53 games today, as FIU again beat Florida Atlantic to qualify for tomorrow morning's Sun Belt Conference championship game. Wittels was in some jeopardy today as, according to this Sun-Sentinel article:

Wittels, who entered Saturday with a 52-game streak, was 0 for 4 before he rocketed a 2-0 pitch off FAU pitcher Taylor Everist's glove in the eighth inning. He easily beat FAU second baseman Raymond Church's throw to first after the ball ricocheted off Everist.

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One brief non-Wittels note: The Philadelphia Phillies ended a 30-inning scoreless drought last night. This Bleacher Report article slices and dices the Phillies' scoreless streak every which way!

Garrett Wittels got a hit in Florida International's game this morning to stretch his consecutive-games hitting streak to 51 games. FIU won the game, so the team is playing again this afternoon in the Sun Belt Conference tournament.

UPDATE: Wittels also got a hit in FIU's second game today, bringing the streak to 52 games. Florida International edged intrastate rival Florida Atlantic, 18-16, in 11 innings, with Wittels actually pitching toward the end and getting the win! (Correction: This win did not put FIU into the championship game, as the team had to win another game Saturday.)

On a related note, here's a video of current record-holder Robin Ventura being interviewed on ESPN about Wittels's streak.

Florida International University shortstop Garrett Wittels yesterday extended his consecutive-games hitting streak to 49, in dramatic fashion. As described in this game article from FIU's athletics website:

After going hitless in his previous three at-bats in the game, [he] led off the bottom of the ninth with a double over the right fielder[']s head to extend his hitting streak...

The NCAA Division I record is 58 straight games, set by Oklahoma State's Robin Ventura in 1987. Ventura, of course, went on to have a long and successful major-league career, his being punched out by Nolan Ryan notwithstanding.

Wittels's streak is second all-time in length at the D-I level, nine games behind Ventura. FIU is currently involved in the Sun Belt Conference tournament (as we speak, in fact) and conceivably could make the NCAA tournament. Whether Wittels and his team will have nine more games this season is another matter, though. He is currently a sophomore, so he would have the opportunity to come back next season to extend the streak, as long as it isn't snapped this season.

As of this writing, the FIU site shows Wittels's batting average to be .411. Assuming he can get four official at-bats per game, he is extremely likely to get at least one hit, which is necessary to keep his streak alive. One can take his failure rate per at-bat (1 minus .411, or .589) and raise it to the 4th power, yielding a probability of only .12 of going hitless in a game. In other words, given four official at-bats, Wittels would have a .88 probability of getting at least one hit in a game (this calculation also assumes independence of at-bat outcomes, like coin flips or rolls of the dice).

What really puts hitting streaks in jeopardy is when a player only gets one or two official at-bats, due for example to walks (if a player walks every time in a game, a hitting streak is not considered to have ended, however). Wittels doesn't walk very often (18 bases-on-balls in 49 games thus far this season), so it doesn't seem that he'll be shortchanged many opportunities to swing the bat!

UPDATE: Wittels today extended his streak to 50 games. FIU is in action again on Friday morning.

Last night's Game 4 of the Lakers-Suns NBA Western Conference Finals, won by Phoenix to tie the series at two games apiece, featured a couple of outside-shooting bursts. In the second quarter, L.A.'s Kobe Bryant made six straight shots from beyond 20 feet, sandwiched between a miss at the beginning and end of the quarter(I've excerpted the following narrative from ESPN.com's play-by-play sheet).

11:30 Kobe Bryant misses 25-foot three point jumper
8:19 Kobe Bryant makes 21-foot jumper
7:52 Kobe Bryant makes 22-foot jumper
5:50 Kobe Bryant makes 25-foot three point jumper
5:24 Kobe Bryant makes 23-foot three point jumper
3:10 Kobe Bryant makes 22-foot jumper
2:03 Kobe Bryant makes 26-foot three point jumper
0:01 Kobe Bryant misses 27-foot three point jumper

Bryant also went 6-of-9 from the floor in the third quarter. He's had a lot of hot-shooting stretches over the years. It's somewhat hard, however, to classify him as a true streak-shooter, as he rarely exhibits prolonged coldness. Thus, his hot streaks might just be relatively small variations off of his generally high shooting percentage.

At the other end, Phoenix made three treys in a little over a minute (by Channing Frye at the 8:07 mark; Leandro Barbosa at 7:20; and Jared Dudley at 6:47) to key a 9-2 fourth-quarter spurt that boosted the Suns' lead from 89-87 to 98-89. The Lakers never got closer than within six thereafter.

As noted in the above-linked game article, "Frye had made 1-of-21 shots in the series and missed 18 in a row when his second shot of the night [in the second quarter], a 3-pointer, finally fell to the roar of the home crowd."

This past Sunday in Big 10 college baseball action, Northwestern and Michigan produced one of the most unusual box scores you'll ever see:

Northwestern....... 086 000 000 0 - 14 16 2
Michigan............ 006 031 202 1 - 15 18 2

First, the Wildcats had the hot hand, amassing a 14-0 lead after two-and-a-half innings. But then the Wolverines went to work, scoring in five of their next seven offensive half-innings to leave the game tied at 14-all after nine innings. Michigan then won in extra innings. Key to the Wolverine win was relief pitcher Matt Miller who turned the Wildcats' bats cold, allowing no runs (and only two hits) during the final five-and-two-thirds innings.

In theory, the battle between Michigan's hitters and Northwestern's pitchers would have been independent of that between Michigan's pitchers and Northwestern's hitters. However, in this case and in some huge football comebacks, the same team's offense and defense started clicking at the same time.

So great was the magnitude of Michigan's baseball comeback that ESPN showed some video highlights.

The NHL's Philadelphia Flyers tonight became only the fourth team in North American major-league sports history to overcome an 0-3 deficit in a best-of-seven playoff series and win four straight, eliminating the Boston Bruins. Tonight's decisive game was a microcosm of the series, as Boston took a lead of three goals to none, only to see Philly score the final four goals!

Prior to tonight's game, National Public Radio's Mike Pesca did a story on the Flyers-Bruins series, and he was kind enough to interview me regarding what hot-hand research had to say about the situation. Click here to find the archived audio.

For further detail on the three previous successful comebacks from 0-3 -- achieved in hockey by the 1942 Toronto Maple Leafs and 1975 New York Islanders and in baseball by the 2004 Boston Red Sox -- see this summary from the website Who Wins.

The website Blog Interviewer recently conducted an interview with me about the Hot Hand site (done via written communication). Full text of the exchange is available here. In addition to providing background on the Hot Hand site, I also give my advice to anyone thinking about starting a blog.

For the San Antonio Spurs, it was Dragic and it was tragic (to the extent that the outcome of a game can be tragic). The Phoenix Suns' Goran Dragic went wild in the fourth quarter to give his team a 110-96 win and put the Spurs down three games to none in the second round of the NBA playoffs. According to this Associated Press/ESPN.com article:

The backup point guard scored 23 of his 26 points in a brilliant fourth quarter... Dragic hit nine of 11 shots in the fourth, including all four 3-point attempts.

The Orlando Magic used a 19-2 spurt in the fourth quarter to break open a one-point game and defeat the Atlanta Hawks, 112-98, in the teams' second-round NBA playoff series. The Magic has now won 12 straight games, six in the playoffs and six to end the regular season (game-by-game log). Orlando swept the Charlotte Bobcats in the first round of the playoffs and now leads Atlanta 2-0.

Last night's Game 5 of the Phoenix-Portland NBA playoff series definitely was a game of spurts. As shown in this play-by-play sheet, the Trail Blazers blazed to a 14-2 lead, only to have the Suns go on a 12-0 run to tie the game at 25-25 with a minute remaining in the first quarter. Phoenix edged ahead over the next 19 minutes or so, taking a seven-point lead, 65-58, at roughly the six-minute mark in the third quarter. At that point, the Suns caught fire, outscoring the Blazers 26-10 in the span of roughly eight minutes to take a 23-point lead, 91-68, with around 10 minutes left in the game.

I've enjoyed Phoenix's uptempo style in recent years, a style that may be particularly conducive to scoring spurts. The Suns have always fallen short in the playoffs, however, and probably will again this year, although they lead Portland 3-2 in the current series. One thing Phoenix has done to improve, in my view, is to make use of younger players from its roster such as Jared Dudley (age 24) and Channing Frye (26), to complement aging stars Steve Nash (36) and Grant Hill (37).

It's a bit belated, but I definitely want to comment on Phil Mickelson's victory in last weekend's Master's golf tournament, driven by his back-to-back eagles (making a hole in two shots below par) on Day 3. And Mickelson nearly eagled the next hole! According to an ESPN.com blog posting:

Lefty [Mickelson] became only the third player in Augusta National history to make back-to-back eagles -- and came within 6 inches of pulling off another one -- briefly stealing the lead from [Lee] Westwood with one of the most remarkable three-hole stretches Augusta has ever seen.

During Mickelson's remarkable third-round, he made the par-5 13th hole in 3 shots and the par-4 14th in 2. Aggregate statistics from this year's 13th hole, taking the third and fourth rounds combined (to restrict the sample to players who made the cut after the first two rounds), there were 6 eagles out of 96 player visits to the hole. It was the 14th that was really the stingy hole: Mickelson's Saturday eagle was the only one of the entire tournament.

Rather than try to estimate the statistical probability of Mickelson's feat, I would instead fall back on its historical rarity. The Masters tournament has been around since 1934 and, as noted above, back-to-back eagles have been achieved only three times. If one thinks of all the golfers who've participated in the tournament's 77 years and all the rounds and holes they've played, the number of opportunities for consecutive eagles would be astronomical.

In Mickelson's first Master's win (2004) of his three, he got five birdies (one under par) in the last seven holes. Although extensive research has shown a "hot hand" in golf to be elusive, Mickelson has seemed capable of one in at least some years' Masters.

The NHL's Boston Bruins found a hot scoring hand at an odd time this afternoon -- while outnumbered on the ice by the opposing team. As part of a 4-2 win over Carolina, Boston achieved the unpredented feat of scoring three shorthanded goals within the same penalty!

For readers who don't follow hockey closely -- or at all -- it is important to note that goals by a shorthanded team (that has lost a player due to penalty) are extremely rare. Given its precarious situation, a shorthanded team will usually be very defensive-minded, staying near the goal it is defending and hitting the puck to the other end of the rink (i.e., "icing the puck") to kill time and get a reprieve from the advantaged team's offensive attack (icing is not allowed when teams are at equal strength, but is permitted for a shorthanded team).

Statistics for the current season show that even the team with the most shorthanded goals in the league (as of April 9), the Chicago Blackhawks, don't have that many, 13 in 81 games. The Tampa Bay Lightning has scored only two shorthanded goals in 80 games. Thus, Boston today scored more shorthanded goals during a single two-minute penalty than Tampa Bay has scored all season!

As documented in the play-by-play sheet, the following sequence of events took place:

The Bruins' Matt Hunwick got a two-minute hooking penalty with 18 seconds remaining in the first period. Those 18 seconds expired uneventfully, sending the teams to the locker room for a break, but Boston still had to play short-handed with Hunwick in the penalty box for the first 1:42 of the second period (unless Carolina scored, in which case Boston, as the shorthanded team, would immediately be restored to its full complement of skaters).

When action resumed, however, it was Boston doing all the quick scoring, racking up goals with 0:32, 1:21, and 1:36 having elapsed in the second period. Ironically, it must have been Carolina, and not Boston, who was relieved when the Bruins' penalty ended!

UConn Women End Season with 78th Straight Win

The University of Connecticut women exhibited streaky shooting early in their NCAA-championship encounter with Stanford tonight, but not the kind we're used to. UConn missed 16 straight field-goal attempts as part of a dreadful first half that saw the Huskies score only 12 points to Stanford's 20. Fortunately for UConn, it was able to turn things around at the start of the second half, outscoring the Cardinal 17-2. The second-half turnaround was enough to power the Huskies to a 53-47 win.

With the win, UConn has now won 78 consecutive games and the last two women's basketball national titles. The Huskies now need 10 more wins without a loss next season to tie the men's basketball record of 88 straight wins, by John Wooden's UCLA teams of the early 1970s. Connecticut will try to equal and surpass the UCLA men's record the right way, going against top-notch opposition. According to an article about the Huskies' run:

Stanford will be one of the major obstacles the Huskies will face during the non-conference portion of their 2010-11 schedule. They are tentatively slated to host No. 14 Baylor in the second game next season. They will host No. 6 Duke, No. 11 Florida State and No. 12 Oklahoma. They will travel to North Carolina State and meet Ohio State at the Maggie Dixon Classic in New York. That's three Final Four teams and two others that reached the Elite Eight this season.

O-O-Oklahoma on the Baseball Diamond

University of Texas pitchers held University of Oklahoma batters scoreless for 21 consecutive innings this weekend. The Longhorns took the first two games of the series by scores of 5-0 and 2-0. UT then took the finale, 9-3, with OU not scoring until the fourth inning.

The long, season-opening win streaks of the Arizona State and UCLA baseball teams, which were previously discussed here, both came to an end on Friday. ASU lost to Oregon in 12 innings, leaving the Sun Devils 24-1 on the season. Meanwhile, UCLA dropped an 8-4 decision to Stanford, so the Bruins are now 22-1.

It would have been neat if UCLA and ASU could have faced each other with both teams undefeated. Even if both teams had won yesterday, however, considering that the Bruins and Sun Devils don't play each other until a three-game series from April 30-May 2, it wouldn't seem realistic for both teams to go roughly another four weeks without a loss in the very competitive Pac 10 conference.

The icon to the right actually should be modified to say STREAKS (plural) in progress. Two college baseball teams, which both happen to play in the Pacific 10 conference, have gotten well into the season with no losses. No. 1-ranked Arizona State today extended its mark to 23-0, with a win over Cal. Meanwhile, No. 9 UCLA has started the season with a 20-0 record (my thanks to GM in Los Angeles for keeping me posted on UCLA). The NCAA Division I record for longest winning streak is 34, jointly held by Texas in 1977 and Florida Atlantic in 1999. The Texas streak was to start a season, whereas FAU's was not. Interested readers can consult the year-by-year historical data in the Texas and FAU online media guides to get details of the two record streaks.

KLBK Channel 13, the Lubbock CBS affiliate that is providing coverage of March Madness tournament action, came by my office today to do a story on statistical ways of looking at the games. The story was then broadcast on the late local news, following the buzzer of tonight's last game. I spoke about two topics. One was my own hot hand research, on streaks and other statistical oddities; KLBK was kind enough to plug the site, as shown above.

The other topic I addressed, which seemed to be the reporter's primary interest, was the use of statistical equations and the like to predict who would win particular games. I don't do this kind of research, but I was able to refer to the studies of Georgia Tech professor Joel Sokol, who does. In this article, Sokol and his colleague George Nemhauser show how their statistical tool (known as LRMC for Logistic Regression Markov Chain) has exhibited a better record of predicting NCAA tournament games than actual seedings, statistical ratings such as RPI and Sagarin, and media/coaches' polls such as AP and ESPN/USA Today. The LRMC may have worked well in the past, but this year it's laying a major egg.

NCAA Sweet Sixteen Night 1 -- Butler's Streakiness

The No. 5 West-regional seed Butler Bulldogs upset the region's top seed Syracuse, 63-59, in men's NCAA basketball tournament action. In extending their winning streak to 23 straight games, the Bulldogs made use of two within-game spurts, outscoring the Orange 12-1 to begin the game and 11-0 down the stretch to turn a 50-54 deficit into a 61-54 lead (play-by-play sheet).

When last we left the Michigan men's hockey team in early February, the Wolverines had just lost to Wisconsin in an outdoor game at the Badgers' Camp Randall football stadium. Literally, given the 16-degree Fahrenheit temperature at game's end, and figuratively, given their uncharacteristically mediocre 16-13-1 record at the time, the Wolverines were in the midst of a cold spell.

Now, however, Michigan has gotten hot. Behind unlikely goaltending hero Shawn Hunwick, the Wolverines have now won six straight games to capture their conference tournament (Central Collegiate Hockey Association) and head to the NCAA tournament. In fact, it is UM's 20th straight NCAA appearance. As this article on Hunwick and the team points out, "without a CCHA title, [Michigan] had zero chance of getting a tournament invite."

NCAA Hoops Day 4 -- Maryland's Stunning, But Unsuccessful, Comeback vs. Michigan State

Trailing 78-66 to Michigan State with 4:48 remaining in the teams' second-round NCAA men's match-up, Maryland went on a 15-2 run to take an 81-80 lead with 39 seconds left (play-by-play sheet). At that point, there was a bang-bang exchange of baskets -- MSU, Maryland, MSU -- with the Spartans prevailing, 85-83, on a last second three-pointer by Korie Lucious.

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Purdue used a 17-2 second-half run to overcome a Texas A&M lead and set the stage for a close finish. Ultimately, the Boilermakers garnered a 63-61 win in overtime.

NCAA Hoops Day 2 -- Georgia Tech FT Shooting

The Georgia Tech Yellowjackets (also known as the Ramblin' Wreck) finished the regular season ranked 12th (and last) in team free-throw shooting in Atlantic Coast Conference (ACC) men's play at .645 (here and here). One of the great things about NCAA tournament action is that odd things can -- and often do -- happen. That includes Georgia Tech making 24 out of 25 free-throw attempts tonight in a 64-59 win over Oklahoma State.

It is a familiar probability question, known as the binomial expansion, to ask how likely it is for a process with a long-term baserate success probability of [fill in the blank] to succeed in a new set of attempts [blank] times or more out of [blank] attempts. In Georgia Tech's case, we would ask how likely it is for a team with a .645 baserate to make 24 or more free-throws out of 25 (assuming the shots are independent of each other, such as coin tosses). There's even an online calculator for the occasion that, when supplied with the particulars of Georgia Tech's accomplishment, yields a probability of .00026 (26-in-100,000 or approximately 1-in-4,000) of the Yellowjackets doing what they did.

Where does that final probability come from? First, we calculate the probability of Georgia Tech going a perfect 25-of-25. If you think of the likelihood of rolling double-sixes with a pair of dice, it's the probability of a six on a single die, 1/6, raised to the second power (given there are two dice) or 1/36. Analogously in our basketball example, we take the Yellowjackets' probability of success on a single free-throw attempt, .645, to the 25th power, yielding .000017 as the probability of a perfect run of 25 out of 25 made free-throws.

We also have to calculate the probability of 24 made free throws and one miss, which is: (.645 to the 24th power) times .355 (the latter being the probability of a miss). That yields .0000095. However, there are 25 different sequences in which a team could make 24 free-throws and miss one; the one miss could occur on the first, second, third,... all the way through the 25th attempt. We must therefore multiply .0000095 times 25, yielding .0002375.

Lastly, we add .000017 (probability of making all 25 attempts) to .0002375 (probability of making 24 out of 25, taking into account all the different possible sequences of doing so), to get .0002545 (within rounding error of the .00026 from earlier).

A few cautions are in order. First, with all the tens of thousands of games taking place in a single season at all levels of college and professional basketball -- never mind multiple years of play -- a feat like Georgia Tech's will occur every so often. Second, I did not take a random cross-section of games, but rather jumped straight to Georgia Tech vs. Oklahoma State because there was a dramatic accomplishment. Third, it could have been the case that the Yellowjackets had one or two great free-throw shooters (along with a bunch of poor shooters who bring down the average) and that these stellar shooters took a disproportionate share of free-throw attempts against Oklahoma State. As it turns out, however, none of the eight Yellowjackets who played tonight is any better than a .787 free-throw shooter, as seen in the team's statistics.