The Hot Hand in Sports

With Boston's win over Cleveland last night, the New York Yankees have officially been eliminated from the postseason picture. The Yankees' streak of consecutive playoff appearances now ends at 13, one short of the Atlanta Braves' record of 14. The Bronx Bombers got more out of their postseason appearances, however, with four World Series championships to Atlanta's one.

The Houston Astros, whose hotness I wrote about in the posting immediately below, have now gone cold. In two games against the Cubs, the Astros were no-hit last night by Carlos Zambrano and then were held without a hit for six innings today by Ted Lilly. To provide some historical perspective, MLB.com reported several items of no-hitter trivia. The following appears most applicable to the Astros' latest futility:

According to the Elias Sports Bureau, the last time a team pitched or succumbed to a streak of 15 consecutive no-hit innings was June 2-3, 1995, when the Expos held the Padres without a hit for that span. On Sept. 25-27, 1981, the Astros held the Dodgers without a hit for 16 consecutive innings.

As they almost always seem to do, the Houston Astros are again pulling off a late-season hot streak. With a 6-0 win today against Pittsburgh, the Astros have now won 14 out of 15. As this ESPN.com/AP article notes:

Houston was 66-66 and 11 games back of Milwaukee, the NL wild-card leader, before the run began Aug. 27. The latest win closed the Astros within three games of the Brewers...

One method statisticians use to help determine if a given team's (or athlete's) streakiness is more than just a chance occurrence is to see if the team/athlete has shown any ability to repeat the special performance year after year. I recall the Astros' having had strong finishes in recent years, so I decided to look at the numbers for the last four completed seasons. Shown for each year are the Astros' records as of the last day of July, for the month of August, and for the month of September (plus any regular-season games played in October). You can click on the year to see the Astros' game-by-game log.

YEAR........THRU JULY..........AUGUST.........SEPT/OCT

2004........52-52 (.500)......17-11 (.607).......22-7 (.759)

2005........57-48 (.543)......13-14 (.481).......18-11 (.621)

2006........49-56 (.467)......17-12 (.586).......16-12 (.571)

2007........46-60 (.434)......15-14 (.517).......12-15 (.444)

Thus, with the exception of 2007, in recent years the Astros indeed have regularly put together strong finishes in August and/or September. Brewers, look out!

Leave it to those L.A. Dodgers to, once again, put together an amazing cold-to-hot pattern. In 2006, as I wrote about at the time:

The Dodgers started off the second half of the season, right after the All-Star Break, by losing 13 out of 14. They've now rebounded by winning 17 of 18...

Now in 2008, beginning August 22 with a loss at Philadelphia and culminating with today's 5-3 win at home against Arizona, the Dodgers have immediately followed up an eight-game losing streak with a winning streak of the same length (game-by-game log).

Given that a team has gone 8-8 during a 16-game stretch, how likely is it that such a record has been accomplished by losing eight straight and then winning eight straight (or vice-versa)?

Perhaps the easiest way to think about this problem is to imagine 16 boxes (representing the number of games) and eight cards, each of which has a "W" on it, for wins. Then we can ask: In how many ways can the eight wins be distributed into the 16 boxes? Obviously, there are lots of ways for this to happen. In addition to winning either the first eight or last eight games, a team might win games 1-2-4-5-7-10-11-12 or games 3-4-5-8-10-13-14-15, for example.

Fortunately, there's a relatively simple formula for determining how many ways eight wins can be distributed among 16 games. It's known as the "n choose k" formula, where in this case, n = 16 and k = 8. Using this online calculator, we find that there are 12,870 possible ways to distribute eight wins in 16 games.

So, indeed, the Dodgers' particular pattern is quite rare. Of course, it was the unusual nature of the sequence that drew me to analyze it in the first place, after the fact.

Perhaps it's a case of post-Olympic fatigue, but whatever the reason, the gold-medal beach volleyballers Misty May-Treanor and Kerri Walsh have had their 112-match winning streak snapped, in an Ohio tournament.

W.M. McEntire posted a message on the SABR members' e-mail discussion list, noting that the Cleveland Indians' current 10-game winning streak gives the team both 10-game losing and winning streaks this season (the losing streak occurred during late June and early July, whereas the more recent log of games is available here). According to McEntire, this is the 21st time since 1900 that a team has exhibited such a pattern.

A couple of major streakiness items from the Olympics:

The U.S. beach volleyball duo of Kerri Walsh and Misty May-Treanor won the gold medal for the second straight Olympiad. Overall, the pair has won 108 straight matches.

Another U.S. women's juggernaut, the softball squad, had its reign of three straight Olympic golds snapped by Japan. The gold-medalist pitcher, Yukiko Ueno, had quite a last two days. After pitching eight scoreless innings (seven innings is the regulation length) against the U.S. on Wednesday before losing in the ninth, Ueno came back later the same day to pitch all 12 innings of a 4-3 win over Australia. Then today, in a rematch with the Americans, she limited them to one run, the Japanese winning 3-1.

Given that Ueno gave up several runs during this stretch, I'm not sure we can say she always had the "Hot Arm," but I don't think anyone would dispute awarding her the title of the "Durable Arm!"

The Chicago White Sox hit four homers in a row Thursday afternoon, in a 9-2 victory over Kansas City. Such a feat has been accomlished six times in MLB history. Interestingly, half of these occurrences have taken place between 2006-2008 and the other half between 1961-1964 (see the linked article for a chart listing all the teams and players involved).

Baseball fans are still buzzing about Boston's 19-17 win over Texas last night, a game in which it looked like the Sox's 10-run first inning might go for naught. Obviously, several batters had big nights. The hottest hitter, though, appears to be the Rangers' Marlon Byrd who, according to this article, "went 5 for 6 and is 21 for 34 in his past eight games."

Trailing 10-11 early on against China, the U.S. women's Olympic basketball team closed out the first quarter on a 23-0 run (article, play-by-play sheet).

Deja vu, all over again. Similar to how he won the British Open last month, Padraig Harrington had the hot putter down the stretch to win the PGA Championship today.

"Manny's being Manny!" intoned legendary L.A. Dodger broadcaster Vin Scully in this MLB.com video, as the team's celebrated new acquisition Manny Ramirez belted a ball into the bleachers for a home run last weekend.

Ramirez's hot start in Dodger Blue has now continued on for several games. At the close of Wednesday night's play, according to this ESPN.com article, Manny "is batting .600 (12-for-20) with three homers and six RBIs in five games since joining the Dodgers."

Unfortunately for the Dodgers, they've had to face St. Louis the last few nights, and the Cardinals have some hot-hitting sluggers at the moment, as well. Quoting from the same ESPN.com article:

[Ryan] Ludwick tied a franchise record with a homer in his fifth straight game, only four pitches after [Albert] Pujols' grand slam, and the St. Louis Cardinals beat the Los Angeles Dodgers 9-6 on Wednesday...

Ludwick was 3-for-5 with three RBIs and Pujols finished 4-for-4 with a walk, while insisting being on the same field as Manny Ramirez served as motivation.

Tuesday night, Ludwick had homered in the 11th inning to give the Cards a 6-4 win over the Dodgers.

With Tiger Woods's absence from the golf scene due to injury, and other stories such as the upcoming Summer Olympics and the Brett Favre/Green Bay Packers saga garnering most of the sports media attention, relatively little has been made of the annual PGA Championship beginning tomorrow.

To the extent that commentators have addressed the PGA tournament, a good deal of the discussion has focused on how Phil Mickelson's career (in major touraments, at least) has turned on a dime, for the worse. What seemed to be a rise to greatness fell, just that quickly, into his being mired in mediocrity.

Having won the 2005 PGA and 2006 Master's, Mickelson appeared to be on the verge of making it three straight majors, as he neared the end of the '06 U.S. Open. However, as characterized by the Wikipedia, Mickelson ended up with:

...one of the most memorable final hole collapses in major championship golf. Leading by a stroke with one hole to play, he chose to hit driver on the final (72nd) hole of the tournament, and hit it well left of the fairway... He decided to aggressively go for the green with his second shot rather than play it safe and pitch out into the fairway. His ball then hit a tree... He was unable to get up and down from there, resulting in double bogey and costing him any chance of winning the championship outright or getting into a playoff... and also ending his bid to join Ben Hogan and Tiger Woods as the only players to win three consecutive professional majors...

Reflecting on his performance afterwards Mickelson admitted: "I still am in shock that I did that. I just can't believe I did that. I'm such an idiot".

In the nine majors he's played since then -- the '06 British Open and PGA, all four majors in '07, and this year's Master's, U.S. Open, and British Open -- he has finished in the top 15 only once (a tie for fifth in this year's Masters; see aforementioned Wikipedia link for his career finishes).

It's certainly tempting to say that Mickelson's collapse at the '06 U.S. Open threw his career into a tailspin, compared to how well he had been playing. Prolonged -- and unexpected -- slumps are not new for him, however. After recording three straight high finishes spanning 2001-2002 (second in the '01 PGA, third in the '02 Master's, and second in the '02 U.S. Open), he fell into the doldrums. Over his next six majors -- with the exception of a third in the '03 Masters -- his finishes were tie for 66th, tie for 34th, tie for 55th, tie for 59th, and tie for 23rd.

We'll see this weekend if "Lefty" can get back to contending for major titles again.

In Brad Ziegler's brief major-league pitching career, he has not given up a run. Period. According to this news article:

Athletics rookie reliever Brad Ziegler stretched his scoreless-inning streak to 30 - extending the major league record to begin a career...

The prior streak of scoreless innings pitched to begin a career is 25, dating back to 1907. Heck, the Cubs have even won a World Series championship more recently than that!

The overall record for scoreless innings pitched is, of course, 59 by the Dodgers' Orel Hershiser in 1988.

Tonight's baseball game between the L.A. Dodgers and the Colorado Rockies featured the following nine-inning line score:

LA.....8 1 2...1 4 0...0 0 0 -- 16
COL...0 0 1...2 1 2...1 1 2 -- 10

According to this article, "The Dodgers began the game with five straight hits..."

Also, how often does a team score in seven straight innings and still lose???

The men's British Open golf tournament (or just "The Open" as it's sometimes called) ended today, with two of the leading final-day contenders exhibiting streaky play in various combinations of hot and cold.

Padraig Harrington ended up winning the tournament for the second straight year, but early on today, that didn't seem very likely. This chart of his day-by-day, hole-by-hole performance in this year's Open illustrates why.

Entering today's play trailing sentimental favorite Greg Norman by two strokes, Harrington shot a par on each of the first six holes, but then bogeyed hole numbers 7, 8, and 9. Granted, Norman wasn't doing too well himself at the time (discussed below), but Harrington certainly wasn't giving any sign that he was revved up for a big finish. The back nine holes would go a lot better for him, however, as he shifted from coldness to hotness.

Harrington birdied hole 13 (which he had not done in any of the initial three rounds) and 15, and eagled 17. He had no bogeys on the back nine and, in context, even some of his pars were impressive. For example, he had bogeyed hole 11 each of the first three days, but got a par today. All told, Harrington recorded a score of 69 for the final round to finish four strokes ahead of runner-up Ian Poulter.

For Norman, a lot was at stake as he unexpectedly got back in the spotlight. He had won the 1986 and 1993 British Opens (his only Grand Slam tournament titles), but he also had an extensive history of blowing leads entering the final day of major tournaments (discussed here and here). All of this set the stage for Norman's round today, as noted in this ESPN.com/AP article:

This had all the elements of a fairy tale like few others in golf. Norman, 53, married tennis great Chris Evert three weeks ago and was on the tail end of his honeymoon when he wound up with a two-shot lead going into the final round and a chance to become the oldest major champion. Instead, it ended like so many other majors when he was in his prime.

Norman got into immediate trouble, bogeying his first three holes. And unlike Harrington, Norman never turned things around, accumulating eight bogeys for the day (compared to only one birdie), and tallying a 77 to finish tied for third.

Harrington's performance earlier today may not quite rank up there with Phil Mickelson's amazing final round in the 2004 Masters, in which he birdied five of the last seven holes to claim his first victory in a Grand Slam event (discussed here). Still, considering that no golfer in this year's British Open came close to breaking par for the full tournament amidst the windy conditions and unforgiving greens, Harrington's finish should rank up there.

Picking up where my previous posting left off late-night Tuesday/early-morning Wednesday, the American League won its 11th straight Major League Baseball All-Star Game over the National League (excluding 2002's tie), thanks to a 4-3, 15-inning decision.

Last Friday, in the Wall Street Journal's "Weekend Journal," Darren Everson documented the AL's dominance over the NL -- not just in the All-Star Game, but also in recent years' World Series and interleague play -- and proffered some possible reasons for this state of affairs. These include ballparks, revenues, power hitters, and innovation.

I think we can safely say that the AL is superior and that the stretch of All-Star Games has not been like flipping a coin, with each team having a 50/50 chance of winning (the probability of a coin coming up the same way 11 straight times is .5 raised to the 11th power, or .0005; and even if we assume the AL had a .60 chance of winning each time, the probability of 11 straight would be .004).

It should also be noted that the NL had its own period of supremacy, losing only once from 1963-1982.

From one perspective, a lengthy winning streak by one league over the other is quite surprising. As Jim Albert and Jay Bennett argued in their 2005 Hot Hand web chat, baseball would seem to be much less of a "domination sport" than football or basketball. To a far greater extent than in these other sports, baseball teams are limited in how often they can deploy their top players -- starting pitchers can go only once every five days, and batters can take only one out of every nine at-bats for a team.

To the extent that baseball's rules (and the wear-and-tear on pitchers' arms) create parity between the teams, this trend would seem to be exacerbated by the traditions of All-Star play. Pitchers often throw just an inning or two, and players at the other positions might only play half the game, or so. Such shuttling in and out of players would seem to create a lot of volatility, making it harder for one league to dominate. This seems like an excellent theory, except for the fact that it completely fails to explain the data!

In what I think is a rarity, Major League Baseball's All-Star break has given us a Home Run Derby and a game that have both been exciting.

The Derby, of course, was dominated by the Texas Rangers' Josh Hamilton, who hit a single-round record 28 homers in the opening round (in what undoubtedly will become an historical footnote, Hamilton actually lost the competition to the Minnesota Twins' Justin Morneau; with totals from the earlier rounds wiped off the board for the finals and both contenders presumably with tired bats, Morneau was victorious, 5 to 3).

Years ago, I used to conduct hot-hand analyses of the Home Run Derby, but I gave it up after finding little evidence of streakiness. Hence, I was not charting Hamilton's first-round sequence of home runs and outs. However, after viewing several videos from YouTube (just search on "Josh Hamilton") and consulting some articles, I'm able to reproduce his sequence.

In particular, Jayson Stark's ESPN.com column provided some helpful descriptions of Hamilton's homering:

He hit a home run on 13 swings in a row. And 16 of 17. And 20 of 22. And 22 of 25.

Here's Hamilton's first-round sequence (shown in blocks of 10 for ease of viewing, where H = home run, and O = out).

HOHOOHHHHO
OHHOHHHHOH
HHOHHHHHHH
HHHHHHOO

Early on, Hamilton was hitting homers only a little over 50% of the time (6 homers, 5 outs), so he clearly lifted his home-run rate in the latter portion of his sequence. The problem with hot-hand analyses of the Home Run Derby, in general, is the small sample size. That probably was a factor for Hamilton, in particular, as this online runs-test calculator (with a 1 entered for each homer and a 0 for each out) showed a non-significant result.

Another factor to consider, as has been suggested by observers in the past, is "streak pitching." Indeed, the 71-year-old Clay Counsil, who used to pitch batting practice to Hamilton when the latter was a high-schooler and reprised this role on the Yankee Stadium mound Monday night, seemed particularly adept at consisently putting the ball in the same location for Hamilton. From there, Hamilton's beautiful swing did the rest...

***

As for the All-Star Game itself, it has just ended at around 1:40 a.m. Eastern, with the American League taking a 15-inning decision. Excluding the infamous 2002 tie game, the AL has now won 11 straight Mid-Summer Classics. That's a streak worthy of its own examination, but due to the lateness of the hour, I'll have to do it later!

The New York Mets won their ninth straight game tonight, shutting out the visiting Colorado Rockies, 7-0. What's more interesting, I would say, is a streak-within-the-streak. Specifically, during Games 4, 5, 6, 7, and 8 of the winning streak, Mets opponents had a hard time getting a hit, let alone runs.

According to ESPN.com's "Elias Says..." feature from the Elias Sports Bureau:

The Mets held the Rockies to one hit on Saturday, after Colorado had three hits on Friday and the Giants had three hits in each of the Mets' previous three games. It's the first time in modern (since 1900) major league history that a team has held its opponents to three or fewer hits in each of five consecutive games.

In tonight's ninth game of the winning streak, New York pitchers gave up seven hits, thus ending the three-or-fewer-hits streak. Slippage!

Phil Birnbaum's Sabermetric Research blog reports on a new study (originally from an L.A. Dodger fan site) of winning streaks in Major League Baseball and their consequences. Specifically, the new study asks whether short winning streaks raise a team's probability of winning its next game, beyond the team's established (baserate) winning percentage from large numbers of games.

Such a comparison is one of the earliest approaches to defining and testing for the existence of the "hot hand," as used by Gilovich, Vallone, and Tversky (1985, Cognitive Psychology). Gilovich and colleagues studied basketball shooting (for details, see the following PowerPoint lecture, especially slides 20-23).

The recent baseball winning-streak study -- like Gilovich and colleagues' earlier basketball-shooting study -- failed to find evidence of a hot hand. Specifically, quoting Phil, "...after winning three, four, or five consecutive games, [teams] won the subsequent game far less often than you'd expect from their record."

These findings also are similar to those for an older NHL hockey study that I discovered recently. The authors of this study concluded that, "NHL teams do indeed play better than normal after a few los[s]es and worse after a few wins."

Thus, contrary to the impressions of many athletes and sports fans, a number of studies suggest that putting together a string of successes (e.g, games won; shots made) does not appear to give performers momentum, in the sense of raising their probability of success on the next trial beyond established baselines.