They've done it! The Detroit Lions have completed a "perfect" 0-16 season in the National Football League. This is the first time a team has lost all of its games since the league switched from a 14- to a 16-game schedule in 1978. An historical list of awful NFL teams compiled by ESPN.com (which looks to be at least a few years old, as it excludes, for example, the 2007 Miami Dolphins' 1-15 season) is available here.

In today's Ohio State men's basketball game against West Virginia, the 'eyes didn't have it. With the Buckeyes trailing 49-40, the Mountaineers went on a 27-4 run to increase their lead to a monstrous 76-44 en route to an easy victory (second half play-by-play). Ohio State's collapse is all the more surprising, considering that the Buckeyes came in nationally ranked (No. 13) whereas West Virginia was unranked, and the Buckeyes were playing at home.

Penn State last night won the NCAA women's volleyball championship, defeating Stanford three games to none. The Nittany Lions' title run was built upon multiple layers of streaks:

*Penn State won all of its matches this season, compiling a 38-0 record.

*This is the second straight year the Nittany Lions have won the NCAA championship; they won their final 26 matches of 2007, bringing their aggregate winning streak to 64 matches.

*Heading into last Thursday's semifinal match against Nebraska, Penn State had won all of its 2008 matches (36 matches at that point) via 3-0 sweeps. In other words, the Nittany Lions had not lost a game (also known as a "set") all season, taking all 108 they had played. Penn State then won the first two games against Nebraska, only to drop the next two, setting up a dramatic fifth-game victory for the Lions.

Though Penn State didn't quite achieve a season free of any lost games -- which would have been unprecedented in NCAA women's play -- it did set a record by winning 111 straight games (in addition to the 110 straight in the 2008 season, the Nittany Lions won the fifth and final game of the 2007 championship match, after losing Game 4).

This is probably one of the more unique streaks I've written about! Chris Paul of the NBA's New Orleans Hornets just set a new league record with a steal in 106 straight games.

The Lakers and Pacers played a wild and streak-laden NBA game Tuesday night, with a last-second tip-in giving host Indiana a 118-117 victory. Quoting from this ESPN.com/AP article:

...when [Los Angeles] closed the third quarter with a 17-0 run to take a 101-86 lead, it seemed as if the Lakers were destined for yet another rout...

[But] when Los Angeles put together its big run at the end of the third, [Danny] Granger and [Troy] Murphy returned the favor by igniting a 10-0 spurt early in the fourth to get the Pacers within seven.

Also, Indiana made 20 of 21 free throws.

LATE-NIGHT UPDATE: The University of Dayton -- though ultimately winning its game against Auburn, 60-59 -- went 0-for-24 on three-pointers. As a result, the following entry from the NCAA basketball record book must now be erased:

THREE-POINT FIELD-GOAL ATTEMPTS WITHOUT MAKING ONE
22—Canisius vs. St. Bonaventure, Jan. 21, 1995

[Update: I later learned of an 0-for-24 game by South Carolina State in 2004.]

Dayton entered tonight's game hitting from behind the arc at a .395 clip (for purposes of the calculations to come, the same figure can be expressed as a .605 failure rate, i.e., one minus the success rate).

To estimate the probability of a team with the Flyers' previous success rate going 0-for-24 on three-point attempts, we simply raise .605 to the 24th power, yielding .000006 or 6-in-1 million.

This analysis assumes independence of observations, that the outcome of one Dayton shot has no bearing on the next, like coin flips. Though reasons can be generated for why basketball shots should not be independent -- such as confidence, momentum, or fatigue -- sports performances have tended to be consistent with an independence model.

One reason a team might have such a disastrous night is that it fell way behind and jacked up a lot of desperation three attempts. This does not appear to be true of the Dayton situation, however, as the Auburn game appears to have been close throughout; the Flyers led 26-21 at the half and won in overtime.

Another line of inquiry is whether the lion's share of Dayton's trey attempts somehow were taken disproportionately by the team's weakest shooters from long distance, thus rendering the aforementioned .395 baseline inappropriate. Looking once again at the Flyers' pre-Auburn stats, Dayton's top three-point shooters coming in were Marcus Johnson, .500 (7-14); Mickey Perry, .455 (5-11); Chris Johnson, .417 (5-12); and Luke Fabrizius, .412 (7-17). According to the box score of the Dayton-Auburn contest, this quartet took 13 of the team's 24 shots, so at first glance, the Flyers' best long-distance shooters appear to have been reasonably well represented.

---

Trailing 65-57 to Georgetown with 9:15 remaining in a battle of nationally ranked teams earlier today, Tennessee went on a 23-6 run to take an 80-71 lead right around the two-minute mark. Then, with the Hoyas starting to foul in desperation in the final minute, the Vols went 7-of-8 from the free-throw line to take a 90-78 victory. The second-half play-by-play sheet from ESPN.com can be viewed here.

Though Oklahoma and Texas Tech both came into their game last night with records of offensive explosiveness, only the Sooners kept the scoreboard operators busy, shellacking the visiting Red Raiders, 65-21. As the following brief excerpts from this morning's Lubbock Avalanche-Journal detail, Texas Tech was outplayed in all facets of the game:

Every element that the Raiders had deployed on the way to a 10-0 start – pass protection, the run game, Graham Harrell-to-Mike Crabtree and timely defense – fell flat on senior night at Owen Field/Memorial Stadium...

Tech had allowed only one 100-yard rusher all season, but OU had two. Tech had allowed only five sacks all season but, against OU, gave up four. The Raiders’ usually prolific offense was 1-for-13 on third down.

The latter bit of faltering, in particular, is highly amenable to statistical analysis; it will thus be the focus of the rest of this entry. Prior to last night, Texas Tech had a .64 (48/75) third-down conversion rate (i.e., success at getting first downs) in Big 12 conference play.

Using this online calculator for binomial probabilities (i.e., events that can have two outcomes, such as success and failure), one can ask what the probability is of a team with a prior .64 success rate achieving at a level of 1-for-13 (or worse) on third-down opportunities. Because any one specific occurrence, such as 1-for-13, is likely to be rare, statisticians add in the "or worse" element (or in other scenarios, "or better").

The answer is .00004, or 4-in-100,000. This fraction can be simplified further, allowing us to say that the Red Raiders' third-down performance last night would occur around once in 25,000 games!. Allowing for the fact that Oklahoma's defense (last night, at least) is better than that of Tech's other Big 12 opponents, the odds would be somewhat less astronomical. Still, the Raiders' dismal third-down conversion rate was pretty surprising.

This calculation can be broken down into different components. To estimate the probability of Texas Tech going 0-for-13 on third down, we simply raise .36 (the team's prior failure rate on third down) to the 13th power, yielding .000002.

For the probability of exactly 1 success and 12 failures in 13 opportunities, we take .36 to the 12th power, times .64 to the first power. This yields .000003. However, there are 13 different ways a team can go 1-for-13, namely getting its single first down on either its first, second, third,..., twelfth, or thirteenth opportunity. We thus multiple the previous .000003 by 13, yielding .00004. We would also add in the aforementioned probability of a 0-for-13 performance (.000002), but the solution would still round to .00004.

There would seem to be two major factors that determine success on third-down opportunities: whether a team finds itself with long distances to go to earn a first down; and how well the team moves the ball, even on short-yardage situations.

According to the OU-TTU play-by-play sheet, the distances to go on the Red Raiders' third downs were: 9, 10, 22, 3, 4, 2, 18, 10*, 11, 7, 21**, 6, and 1 (the single asterisk denotes the one successful conversion, which actually resulted in a touchdown, whereas the double asterisk indicates where an Oklahoma personal foul gave Texas Tech a first down, which apparently is not credited as an "earned" first down).

As can be seen, both of the above suggested factors appeared to be operative. The Red Raiders were left with several long third-down situations (7 with 9-or-more yards to go), but they also failed on several short opportunities.

This Saturday night, two of the most explosive offensive teams in college football -- Texas Tech and Oklahoma -- will meet in a game that has possible national championship implications. For starters, I thought I'd simply graph the two teams' offensive sequences (i.e., whether they resulted in touchdowns, field goals, or no score) against their five common Big 12 conference opponents (this information is available via ESPN.com's collection of college football team pages, by going to a given team's page, looking up particular games, and finding the Drive Charts). You can click on the following graph to enlarge it.


There are formal statistical tests one can do, such as the "runs test," which examines whether like events (such as touchdowns) are more commonly clustered together than would be expected by chance. Such statistical tests require large sample sizes, however, and the only way they could be obtained in the present situation is through the questionable practice of combining games into a long chain (i.e., have the final drive of one game be grafted onto the first drive of the next game).

Therefore, it's probably best to view the above chart only in a descriptive manner. As can be seen, both the Red Raiders and Sooners have put together several streaks of at least three consecutive touchdown-scoring drives. Though Oklahoma has recorded more such streaks than has Texas Tech, the Red Raiders seem to have more of a tendency to keep their streaks carrying over from one quarter to the next (and even over the halftime break).

In the games examined, Oklahoma has only one fourth-quarter touchdown, total. In many of games, however, the Sooners may have been trying not to run up the score.

One can also break down these streaks into smaller units than the scoring drive, such as pass completions. In Texas Tech's fast start against Kansas, for example, Red Raider quarterback Graham Harrell hit on 22 of his first 24 passing attempts. Oklahoma QB Sam Bradford once completed 18 straight passes in a game.

As a final note, amazing spurts are certainly not limited to Texas Tech and Oklahoma. Trailing Troy 31-3 in the third quarter last Saturday, LSU scored 37 unanswered points to win going away, 40-31.

Fittingly for Halloween night, the goaltenders for the Vancouver Canucks and Anaheim (Mighty) Ducks had to keep their masks on longer than usual.

Tied 6-6 after regulation, the teams played a five-minute overtime period, but there was no scoring. The game then went to a shootout, a sequence of one-on-one shooter-goalie encounters with the teams alternating roles. Vancouver won the shootout, 2 goals to 1, resulting in an official 7-6 final score (i.e., the shootout win counted as 1 goal in the final score). This was far from a normal shootout, however!

As per the rules, each team fields three shooters to go up against the other team's goalie, analogous to a three-inning baseball game. If the two teams are tied after the initial three rounds -- which was the case between Vancouver and Anaheim -- then an "extra-innings" system is used. As soon as one team scores in a round and the other team doesn't, the game is over.

After the Canucks and Ducks completed the main three-round shootout tied at a goal apiece, one extra round after another kept passing by with neither team able to score. Here is a line score I created from a narrative summary in the above-linked game article.


That's right, the shootout lasted for 13 rounds! Both goalies -- Vancouver's Roberto Luongo and Anaheim's Jonas Hiller -- sparkled in the shootout. Luongo was beaten only once by the Ducks in the shootout, whereas Hiller stopped 11 straight Canuck shots before giving up the game-winner.

(Unsuccessful attempts can be divided into saves, shots that would have gone in but for the presence of the goalie, and misses, shots that were off-target wide or high. I would argue that goalies still deserve some credit for misses, as good goaltending likely induces shooters to take risky shots, such as aiming for corners of the net.)

The question I decided to pursue was as follows: Given these goalies' prior success rates, what was the probability of each netminder doing as well as he did in last night's shootout?

In conducting this analysis, I was aided greatly by the amazing website NHLShootouts.com, which provides extensive, up-to-date data on shootouts.

Hiller did not have a lot of experience in shootouts; other than last night's, he participated in three shootouts last season, giving up 5 goals in 12 shots overall. The NHL Shootouts website gives Hiller a save percentage of .583 (evidently not distinguishing saves from misses). I next went to the Vassar College online binomial calculator and asked how likely it was that a goalie with a prior .583 success rate could stop 11 (or more) shots out of 13. The answer comes to a probability of approximately .05, a level social scientists would traditionally consider "statistically significant."

A similar analysis was conducted for the more experienced Luongo. Over the three seasons preceding the current one, Luongo had participated in 30 shootouts, compiling a cumulative success rate of .714. For a goalie with such a percentage to rebuff 12 (or more) shots out of 13 yields a probability of .08. Another way to look at this finding is that Luongo is a better shootout (if not overall) goalie than Hiller (albeit based on small sample sizes), so Luongo's stellar shootout performance would be less surprising.

For the record, last night's Canuck-Duck marathon was not the longest shootout since the NHL started using it as an ultimate tie-breaker in the 2005-06 season. The record is at least 15 rounds, from a November 2005 contest (the score was 4-3 within the shootout).

By finishing off the Tampa Bay Rays in Wednesday night's rain-delayed World Series finale, Philadelphia Phillies' closer Brad Lidge achieved relief-pitcher perfection on the "Save" statistic.

Combining regular-season (41 games) and post-season (7 games) play, every time Lidge had the opportunity to protect a Phillies' lead at the end, he succeeded. He thus ended up a perfect 48-for-48 on save opportunities.

A few years ago as a member of the Houston Astros, the 6-foot-5 right-hander was so powerful at the end of games that the team's middle/set-up relievers knew that their job was to provide a "Bridge to Lidge." As noted in this article:

With Houston in 2004, [Lidge] averaged 15 strikeouts per nine innings. In the seven-game National League Championship Series loss to St. Louis, he held the Cardinals to one hit in his eight innings...

The Astros and Cardinals met again in the next year's NLCS, and when Houston was one out from the World Series, Lidge gave up a game-deciding homer to Albert Pujols. Houston won the pennant in the next game, but somehow, Lidge seemed to become better known for that Pujols homer than for all his good work.

For now, at least, it looks like the "Heartbreak Lidge" moniker he obtained in Houston will likely be a thing of the past.

One week from tonight, two of college football's hottest teams (both undefeated) and most hot-handed quarterbacks will do battle when the University of Texas plays at Texas Tech.

The Red Raiders' Graham Harrell hit on 22 of his first 24 passes today, as Tech routed Kansas 63-21. The game was once tied 14-14 before the Red Raiders scored 49 straight points. The Jayhawks, fans will recall, won the Orange Bowl and finished as the No. 7-ranked team in the nation last season. Although clearly not as good this year, KU came into the game ranked 19th in the nation, thus serving as a quality opponent for Texas Tech.

The Longhorns' Colt McCoy has been similarly scintillating. As this ESPN.com article notes:

Through Texas' first six possessions Saturday [in a 28-24 win over previously unbeaten Oklahoma State], McCoy was ridiculously good. He led the Horns to four touchdowns and completed 30 of 33 passes including a school-record 18 straight at one point. Go back to last week's dissection of Missouri and McCoy was 59 of 65 (91 percent accuracy) across a span of 15 possessions, with a couple of drops and batted balls in there. On those drives Texas scored 77 points.

Inspired, presumably, by Boston's amazing comeback from a 7-0 deficit to win Game 5 of the American League Championship Series against Tampa Bay (although ultimately not the series), Tom Tango has just written a piece at Hardball Times probing the historical record of similar comebacks. Does evidence exist for comeback wins inspired by what the article calls "in-game momentum"?

Specifically, Tango identified games in which a team rallied from five or more runs down to tie a game, but not take the lead before the end of the inning. The idea is that the game would now have been back to square one -- dead even -- but one team would have had the momentum. Tango then investigated how often the latter team went on to win the game by scoring in a later inning, which might be seen as a sign of momentum on the part of the team that tied the game (or demoralization on the part of the team that squandered the lead).

Tango finds evidence that teams coming back from five or more runs have won games with a slightly greater frequency than that of teams coming back from smaller deficits (and thus with lesser momentum). However, he urges caution as follows:

...don't forget that we're talking extreme momentum here; in-game momentum in which the team scored five runs in an inning to tie the game. One must believe that the effect of momentum must be even less day-to-day.

Boston's postseason dominance over the California/Anaheim/Los Angeles Angels continued last night, with a 3-2 Red Sox victory to capture the first-round series, three games to one. According to a sidebar note with the above-linked article:

The Red Sox improved to 4-0 all-time against the Angels in postseason series, having beaten them in 1986, 2004, 2007, and 2008. Boston has also won 12 of the last 13 playoff games against Los Angeles.

The story begins, of course, with the 1986 American League Championship Series, in which the Red Sox, trailing three games to one, staged an unlikely comeback to take three straight and win the series, 4-3.

Boston then recorded 3-0 series sweeps against the Halos in 2004 and 2007, before winning 3-1 this year.

As I like to point out from time to time, streaks can arise from some combination of (a) sharp ability differences between the two competitors; (b) momentum and other psychological factors (though most statisticians are skeptical of this); and (c) random chance.

The idea that the Red Sox were substantially superior talentwise over the Angels -- for this year at least -- can be safely ruled out, as the Angels won eight out of the nine regular-season meetings between the teams.

Statistical research tends to show that athletes who have experienced consecutive successes (e.g., made baskets, hits in baseball) do not raise their probability of success on the next attempt, relative to their long-term baserates. For example, a long-term .50 basketball shooter will not be any more likely than .50 to make his or her next shot after making, say, three straight hoops. This runs contrary to the popular belief that the athlete is "hot" and therefore at an elevated rate of success. Another way of conveying the lack of a true "hot hand" is that athletes' instances of several successes in a row tend not to occur any more frequently than runs of several heads in a row (or tails in a row) from large numbers of coin tosses.

Despite most studies' lack of evidence for hot-handed performances beyond chance, however, I have never disputed that athletes may feel something special is going on during their runs of success. One type of perception, until recently (I thought) only in the realm of the anecdotal, is that relevant athletic stimuli (e.g., a basketball hoop, the baseball on the way from the pitcher) look larger or clearer than when the athlete is not in the midst of a streak.

An item from July on the "Nudge" blog, which I did not see until recently, cites evidence that successful athletes really do seem to see their targets as bigger.

The research in question is by Jessica Witt of Purdue University and colleagues, and is entitled "Putting to a bigger hole: Golf performance relates to perceived size" (published in Psychonomic Bulletin & Review, June 2008). The above-linked Nudge posting provides a concise description of the study's details.

In looking up Dr. Witt's faculty website, I noticed that she had published a similar study (with Dennis Proffitt) with recreational softball players ("See the ball, hit the ball: Apparent ball size is correlated with batting average," Psychological Science, December 2005).

The story does not end there, however. In their softball article, Witt and Proffitt cite a study by Wesp et al. (2004, Perception & Psychophysics) that "demonstrated that dart-throwing ability affects perceived size of the target. Participants who hit the target with fewer attempts selected larger circles as matching the size of the target than participants who were not as successful" (p. 938).

My apologies for not noticing these studies earlier, but better late than never!

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.

LPGA golfer Paula Creamer had an amazing opening round Thursday in the Jamie Farr Classic near Toledo, Ohio. In shooting a 60, Creamer "birdied nine of the last 11 holes," according to this ESPN.com article. The LPGA single-round record is 59, held by Annika Sorenstam; one must take into account differences in courses' difficulty before putting too much stock in overall tour records, in my view.

Today, Creamer "cooled off" to a 65.

Cincinnati's batters were hot, "red hot" if you will, as the team outslugged the Cubs in Chicago, 12-7. In doing so, the Reds homered in six straight innings, the second through seventh; they added another in the ninth, as well.

Here at the Hot Hand page, we try to get an idea of how unlikely something is, through either a statistical or historical lens. In this instance, an historical reference point is readily available. According to this MLB.com article:

More breathing room came as [catcher David] Ross led off the seventh with his second homer of the game -- this time a shot to left field. It gave the Reds a home run in six straight innings, marking the first time they'd done so since Sept. 4, 1999, when they slugged homers over seven consecutive innings at Philadelphia.

OK, so we have an answer. For the Reds, at least, nearly nine years had elapsed since the last time this happened.

This ESPN.com article has an accompanying chart of all the scoring plays in the Reds-Cubs game.

This Baseball Almanac page lists a number of different kinds of home-run records, including each franchise's record for most homers in a single game. Several teams have hit eight (or more) homers in a game. Visual inspection of box scores would be needed, of course, to see over how many consecutive innings a team's homers were hit, in a particular game. The more homers hit within a single inning, the fewer innings would be needed to accumulate a bunch of dingers.

I recently finished reading Leonard Mlodinow's book The Drunkard's Walk: How Randomness Rules Our Lives, which I'd like to discuss. In the name of full disclosure, in case this may have colored my reaction to the book, I want to note that Dr. Mlodinow contacted me, offering a free review copy of the book, and I accepted.

Perhaps the foremost task of hot-hand analysts is trying to determine whether streaky sports performances simply reflect random variation on established generating processes (i.e., like a tossed coin coming up heads several times in a row due to chance) or something beyond chance. The relevance of The Drunkard's Walk is thus clear, and in fact, the book cites hot-hand research (pp. 178-179).

I actually found The Drunkard's Walk to be like two books, the first reviewing the subleties of probability calculation and the second, discussing how people can be mislead by random processes, consistent with the book's title.

The first major part of the book, on probability calculation, matches closely with how I teach probability in my introductory graduate statistics course. I have boiled probability down into one simple question: "How many possible ways can something turn out?" and Mlodinow presents the subject matter in much the same way (Chapter 3).

Then, after shifting to the second major topic, how randomness can mislead, the book finishes strongly, in my opinion. Concepts covered during this latter part of the book include hindsight bias, the arbitrariness of starting and ending points when measuring someone's success, and the distinction between a specific, named person experiencing some type of coincidence or unusual accomplishment and someone, somewhere doing the same (here's an additional example of the latter, beyond what's in the book).

On a somewhat negative note, the central message of The Drunkard's Walk is not exactly new. The book Fooled by Randomness, written several years ago by Nassim Nicholas Taleb and which I reviewed in the Journal of Behavioral Decision Making, plowed similar ground, and many of the ideas in that book had some history.(Parenthetically, Taleb has a follow-up book in the stores, entitled The Black Swan.)

There was only one assertion by Mlodinow that raised questions of accuracy in my mind. Specifically, on page 138, he stated that the "normal" (bell-shaped) curve is "the most widespread manner in which data have been found to be distributed." I am not prepared to say that this statement is flat-out wrong, but it does contradict the evidence of which I'm aware. The textbook I use in my introductory statistics class (King & Minium, 2008, Statistical Reasoning in the Behavioral Sciences, 5th ed.) cites a 1989 Psychological Bulletin article by Theodore Micceri, who:

“…examined the distributions of 440 measures of achievement and psychological traits… Nearly 70% included samples of 1,000 or more. Only 19 of the 440 distributions were found to approximate the normal curve” (p. 101).

Mlodinow has a lively writing style. If, like me, you've enjoyed the recent genre of relatively non-technical books on mathematics and statistics for a general, educated audience, the The Drunkard's Walk is for you; however, if you haven't yet read either of Taleb's books, that might be a better place to start.

Today's Wimbledon tennis men's singles final between Rafael Nadal and Roger Federer -- one that former champion John McEnroe has been quoted as calling the "greatest match I've ever seen" -- also had plenty to offer on the streakiness front (ESPN.com article). With Nadal's 6-4, 6-4, 6-7, 6-7, 9-7 victory, here's what the men's tennis landscape now looks like.

*Federer had his streak of five consecutive Wimbledon men's singles titles snapped, keeping him in a tie with Bjorn Borg for the modern record. William Renshaw won six straight between 1881-1986.

*Federer had also won 65 straight matches overall on grass surfaces.

*Nadal became the first male player since Borg in 1980 to win both the French Open and Wimbledon titles in the same year (these, along with the Australian and U.S. Open tournaments, comprise the "Grand Slam" of tennis). Nadal, in fact, has won the last four French Open titles, the last three by beating Federer in the finals.

*According to the statistics of the final match (which can be accessed via this scoreboard), Nadal won every game except one on his own serve, with Federer going only 1-for-13 on break-point opportunities (Nadal was 4-for-13).

*Had Federer been able to successfully complete his Houdini-type comeback attempt, what would have stood out as a turning point is the eighth game of the third set, with Federer trailing two sets to none and 3-4 in games. As described in this "Minute-by-Minute" journal from the UK's Guardian newspaper:

Big points win matches, and at the key moments of this final Federer has been found wanting... But this game could change everything. Nadal opens with a brilliant improvised backhand pass and quickly races to a 0-40 lead. But Federer - effectively staring defeat in the face - gets himself out of trouble with some big serving, reeling off five points in a row to hold. Courageous stuff...

Recently in Mansfield, Texas, another golfing hole-in-one oddity occurred. As reported in this article from the Fort Worth Star-Telegram, two men aced the same hole, one day apart from each other. The Star-Telegram writer was kind enough to consult with me and cite an analysis I did two years ago about a similar incident in Lubbock that involved the same golfer acing the same hole on back-to-back days.

Happy Fourth of July everyone, and enjoy the fireworks!

One of the key issues in hot-hand research is whether, when a team (or individual) exhibits a stretch of strong performance, the result is due to random variation on the team's ordinary performance level or, instead, represents a substantive rise in the term's underlying playing ability. Stated differently, an inherently .500 team might play at a .700 clip due to random fluctuation, like a coin coming up heads several times in a row due to chance. Or, the team might really have improved its true ability level to one characteristic of a .700 team (see Albert and Bennett's 2001 book Curve Ball for further discussion).

Although I don't have any definitive analysis at the moment, Fresno State's rise from being the No. 89-ranked college baseball team entering the post-season (as per the RPI) to winning the NCAA national championship in last night's decisive victory over Georgia, just seems to be too momentous to attribute to random variation.

According to this Baseball America column in the immediate aftermatch of the College World Series, "Statistically, Fresno's the biggest upset winner in CWS history, perhaps all of college sports history."

To dramatize the point, a report on ESPN this morning noted that another underdog that had captured the nation's imagination, George Mason University's 2006 men's final four basketball team, had an RPI all the way up at 26 (also confirmed here).

After finishing the regular season with a 33-27 record (21-11 in the Western Athletic Conference), Fresno State proceeded to go 4-0 in the WAC tournament, 3-1 in an NCAA regional hosted by highly regarded Long Beach State, 2-1 at highly ranked Arizona State in the super-regionals, and 5-2 in the College World Series; one CWS loss occurred in pool play, and the other in the two-out-of-three title round (game-by-game log). All told, playing against many of the nation's top teams, Fresno State went 14-4 in the post-season.

In addition to some top-shelf pitching, Fresno State showed robust offensive production, scoring a CWS record-tying 62 runs.

In conclusion, based on a first glance, Fresno State appears to be a team that lifted its underlying level of ability, perhaps moreso than any other team in recent sports history!

The NBA finals are over, and the Boston Celtics have defeated the L.A. Lakers four games to two. If nothing else, this past postseason has shown us that both of these teams were capable of going on -- or giving up -- huge scoring runs. Below is a list of scoring runs achieved and allowed by the Celtics and Lakers (that I was aware of) during the various rounds of this year's playoffs...

Celtics vs. Lakers (NBA finals)

Game 6: Boston closes out second quarter on 26-6 run

Game 5: L.A. goes up 17 after first quarter, but only leads by three at halftime

Game 4: Boston overcomes 24-point deficit to win

Game 2: L.A. cuts late 24-point deficit to two

Celtics vs. Pistons (Eastern Conference finals)

Game 6: Boston uses 19-4 spurt to oust Detroit

Celtics vs. Cavaliers (Eastern Conference semi-finals)

Game 6: Cleveland's 24-2 run helps force Game 7

Game 3: Cleveland wins, helped by 27-4 run

Lakers vs. Spurs (Eastern Conference semi-finals)

Game 5: Comeback from 17 down powers L.A. to series win

Game 1: L.A. overcomes 20-point deficit to win

In Game 2 of the NBA finals, the L.A. Lakers almost erased a 24-point deficit against the Celtics, but fell short and lost to Boston (see a few entries down on this blog).

Tonight, with the Lakers trying to even the series at two games all in Game 4, the Celtics did them one better. Boston successfully overcame a 24-point deficit and won the game, 97-91, to take a 3-1 series lead (article). The lion's share of the comeback stemmed from a 21-3 run by the Celtics to close out the third quarter (play-by-play sheet).

With the NBA finals, pro and college baseball, and yet another failed bid for a horse racing Triple Crown capturing my attention in recent days, I've been remiss in acknowledging Rafael Nadal's dominance of clay-court tennis, in general, and his blow-out win over Roger Federer in the French Open final, in particular.

Usually, a 24-point lead with 7:54 remaining in a basketball game would be a comfortable margin as the clock counted down to an easy win. In fact, if any team were to come back from that size deficit to put the outcome into doubt, it would probably be a college team, given the short three-point line.

But no, this all took place last night in the NBA finals, as the Boston Celtics saw their 95-71 advantage get cut by the L.A. Lakers all the way down to 104-102 with 38 seconds remaining (fourth-quarter play-by-play sheet). The Celts ultimately prevailed, 108-102, to go up 2-0 in the series (article). But the game left a lot of things to marvel at, from a hot-hand perspective:

*By scoring 31 points in roughly the last eight minutes of the game, the Lakers would have been on a pace to score over 180 points for the contest, if (hypothetically) they could maintain such a scoring clip.

*Boston had a 15-2 run to end the third quarter, and a 10-0 spurt to open the second.

*The Lakers were a perfect 10-for-10 from the free-throw line for the game, although what attracted most observers' attention was the disparity in number of attempts (Boston had 38, making 27).

*Even though three-pointers played a big part in the Lakers' comeback (they were 5-of-7 from long distance during a stretch in which they cut the deficit from 24 points to 6), the Celtics actually fared a lot better from behind the arc, 64.3% (9-of-14) to 47.6% (10-of-21) for the men in purple (box score).

A couple of quick baseball notes:

The Yankees' Johnny Damon went 6-for-6 yesterday. According to the linked article, "His six hits matched a Yankees record, and tied the American League mark for a nine-inning game."

At the college level, LSU had its 23-game winning streak snapped, in a loss to UC Irvine. The loss occurred in the first game of a two-out-of-three Super Regional series (the round to determine who goes to the College World Series), so the Tigers can still get back into national championship contention.

Later today, the racehorse Big Brown will run in the Belmont Stakes, seeking to become the first Triple Crown winner since 1978. Enthusiasm for horse racing has been dampened in the hearts and minds of many observers because of the life-ending injuries suffered by Eight Belles this year and Barbaro in 2006, and for other reasons.

Still, however reluctantly, the sports world will recognize the achievement of Big Brown, if he wins the Triple Crown. Therefore, in recognition of this potentially historic day, I'm going back into the "vaults" of the old version of my Hot Hand page to share this 2004 statistical analysis, from when Smarty Jones narrowly missed winning the Triple Crown. That 2004 write-up also attracted an unusual number of commentaries, which are shown here.

POST-RACE UPDATE

Once again, it's "wait till next year..." (article on the race).

In falling to the Boston Celtics 98-88 in last night's opening game of the NBA finals, the L.A. Lakers closed the game by going 1-for-13 from the field for roughly the last seven minutes. Some of the later shots, of course, were long-distance desperation attempts to get back into the game. But still, after making a hoop with 6:52 remaining in the fourth, to make only one more basket the rest of the way is pretty poor.

The Boston Celtics used a late 19-4 run to beat the Detroit Pistons and close out the teams' Eastern Conference final series. An NBA final series between the league's two historic glamour franchises, the Celtics and L.A. Lakers, is up next.

The San Antonio Spurs and L.A. Lakers traded major runs, all within the span of a single period of their NBA playoff game tonight. According to this ESPN.com article:

The Spurs outscored the Lakers 14-2 to start the third quarter for a 65-45 lead, drawing groans from the crowd of 18,997 at Staples Center, where the Lakers haven't lost since March 28.

Suddenly, the Lakers came together, scoring 14 straight points in a span of 3:05 to draw within six. [Kobe] Bryant had seven points and two assists during the run.

The Lakers ultimately prevailed, 89-85. The article also includes a chart of big playoff comebacks of the past decade.

Lance Berkman of the Houston Astros has a 17-game hitting streak going. The record for consecutive games with at least one hit is, of course, 56 by Joe DiMaggio. Berkman thus has quite a ways to go and, in fact, I typically don't even mention an ongoing hitting streak until it reaches 30 games.

What makes Berkman's streak noteworthy, however, even at this early stage, is the "surplus" offensive production he's showing. According to this article on today's Astro game vs. the Texas Rangers:

Lance Berkman was 2-of-5 to keep his average at .399. Berkman is on a 17-game hitting streak in which he is 36-of-66 with eight home runs and 21 RBIs.

Not only is his batting average during the streak an amazing .545, via the 36 hits in 66 official at-bats. With 36 hits in the 17 games, he's averaging more than two hits per game (2.12). And there's more!

As can be seen in the following screen capture from Berkman's player page at ESPN.com (which I've done only because the statistics will change on a daily basis), his slugging percentage in his past seven games exceeds his career figure by nearly .400. (You can click on the image to enlarge it.)


It's a short-term trend, to be sure. However, Berkman really seems to have taken his hitting to a rarefied level.

***

Though not quite to the same level as Berkman, the Cubs' Alfonso Soriano and the Braves' Chipper Jones have also been hitting the ball well.

Streaky outbursts were abundant in last night's two NBA playoff games...

Trailing 25-31, the Cleveland Cavaliers reeled off a 24-2 run to take a 49-33 lead over Boston. Shortly thereafter, the Celtics answered with a 13-0 run to get back in the game. Ultimately, the Cavs prevailed 74-69, to force a seventh game in the series (game article; play-by-play sheet).

Out west, the Utah Jazz trailed the L.A. Lakers by double-digits for most of the game, including a 99-88 deficit as the clock went under 3:00 (play-by-play sheet). But then, in roughly the last 2:30, the Jazz hit five three-pointers while the Lakers were -- for the most part -- making free throws. The Jazz even had two good looks from behind the arc in the closing seconds in an attempt to send the game to overtime, but neither shot went in. The Lakers survived 108-105, to take the series in six games.

My brother Steve in Los Angeles has requested a "Cold Hand" analysis of veteran outfielder Andruw Jones, who moved from Atlanta to the Dodgers via free agency this past winter at a price of $36 million over two years. Jones's strong suit has always been defense, but for that kind of cash, Dodger fans also have a right to expect some offensive punch.

A Google search of the terms "Andruw Jones" "slump" brings up quite a bit:

*A June 20, 2007 article in USA Today noting that, "Jones was hitless in 18 straight at-bats coming into the game against the Boston Red Sox, dropping his average to .202."

*An "honor" from early in the 2008 season by Sports Illustrated, placing Jones on the "All-Slump Team." The award proclamation reads, in part, "Jones, who hit 51 home runs just three years ago, has hit just one dinger in his first 27 games and is hitting .159."

*An April 22, 2008 New York Times piece entitled "Dodgers’ Jones Plumbs Depths of Hitting Slump." This article goes into some statistical depth, at least over the past four seasons. Now in his 13th major-league season (although only 31 years old), Jones could simply be experiencing natural career decline. However, he has also shown considerable offensive volatility in recent years. According to the Times article:

In 2005, Jones hit .185 through 18 games and finished with 51 home runs. He was the runner-up for the National League Most Valuable Player award. In 2006, he hit .262 with 41 homers.

Still, according to a report entitled "The Effects of Age on Hitting," most offensive abilities appear to peak when players are in their mid-20s.

No one likes a good sports streak any more than your friendly Hot Hand blogger. Sometimes, though, one or more qualifiers have to be appended to a streak to maximize its length. A case in point is today's headline on Cleveland's 4-2 baseball win over the Oakland A's, "Starter scoreless streak ends at 44 1/3 innings but Indians still sweep."

As can be seen in this game-by-game log, the results of Cleveland's last five games before today were as follows:

Cleveland 12, Toronto 0
Cleveland 3, Toronto 0
Toronto 3, Cleveland 0 (10 innings)
Cleveland 4, Oakland 0
Cleveland 2, Oakland 0

Don't get me wrong -- Cleveland's pitching has been superb. Yet, given Toronto's three runs in the third game listed, it's hard at first glance to discern a long scoreless streak by Cleveland's pitchers. Ah, what happened in that game was that Cleveland starter Cliff Lee pitched nine scoreless innings, only to have his reliever give up the three runs.

Hence, the headline's reference to "Starter scoreless streak ends..."

Detroit's Richard (Rip) Hamilton went a perfect 16-of-16 from the free-throw line tonight, as the Pistons eliminated the Orlando Magic from the playoffs.

From what I can find on the web, the NBA playoff record for most made free throws in a game without a miss is 21, held by Boston's Paul Pierce in a 2003 contest against Indiana. The NBA regular-season record for a perfect free-throw night is 23 made, by Dominique Wilkins.

During the 2004-05 regular season, Hamilton recorded a 20-for-20 free-throw game.

Some streakiness-related items from yesterday...

In doing research for another of my blogs, on college softball, I was alerted that the team from my school, Texas Tech, was doing something unusual offensively in its opening Big 12 tournament game against Missouri. Indeed, as I confirmed in the partial screen capture below from a CSTV Gametracker (and elsewhere), the Red Raiders had hit seven straight singles (you can click on the graphic to enlarge it).


The Red Raiders' special media kit for the Big 12 tournament provides a treasure trove of information. For one thing, Texas Tech entered the conference tourney with a .251 batting average (overall season), the second-lowest in the league. Also, in fewer than half of their Big 12 contests (7-of-18) did the Raiders amass at least 7 hits for an entire game!

A crude estimation of Texas Tech's probability of getting seven hits in a row (putting aside the fact that they were all singles) would be .251 raised to the seventh power, which yields .00006 (6-in-100,000). Taking into account that the Red Raiders would have several opportunities within the game -- let alone an entire season -- to record such a streak, the odds would not be quite so astronomical. Still, it's a pretty unusual feat.

***

Staying with the bat and ball, but this time in Major League Baseball, the Texas Ranger pitching staff had its shut-out inning streak snapped at 33 innings. According to the linked ESPN.com article, "Texas pitchers had posted three shutouts in a row and the scoreless streak was the second-longest in franchise history."

***

Finally, in NBA playoff action, the Cleveland Cavaliers unleashed an early burst en route to taking Game 3 of their series from the Boston Celtics. As seen in this play-by-play sheet, Boston opened the game with a 4-0 lead. Next thing everybody knew, Cleveland was ahead 27-8 -- the result of a 27-4 Cavalier run!

Last night in NBA playoff action, the Orlando Magic hit seven straight three-pointers in the third quarter of its game at Detroit. The Pistons ultimately won, however, 100-93. Jameer Nelson made three of the treys, Rashard Lewis made a pair, and Hedo Turkoglu and Maurice Evans each contributed one. All four of these players were roughly .400 shooters from behind the arc in the regular season, ranging from Nelson's .416 to Evans's .396.

The probability that, of the seven three-point attempts the Magic put up in the third quarter, all of them would go in, is calculated as (.400) raised to the 7th power. This roughly equals .002 or 1-in-500.

Overall, Orlando went 11-of-26 on three-pointers in the game. Using a more subtle approach, which takes into account the multiple opportunities for the Magic to have experienced a streak of seven straight made threes, yields a different probability for what Orlando did.

First, of the 26 three-point attempts, 19 were outside the scope of the streak of seven straight made ones. Of those 19, approximately 11 of them would be expected to be missed, given our assumed baserate of .400 success and .600 failure. Adding in the 1 from the formula linked above, we then multiple our previous probability estimate of .002 by 12, yielding .024. In other words, after each miss (as well as at the start of the game), there would have been a new opportunity to start a streak of seven made threes. Still rare, but not that rare (a conceptually similar analysis of mine from many years ago is available here).

Here in Lubbock, Texas, the prominent collegiate athletic program belongs to Texas Tech University, where I'm on the faculty. With their (mostly) glitzy sports facilities, Red Raider squads compete in the prestigious Big 12 conference.

Texas Tech is not the only university in town, however. There's a smaller school called Lubbock Christian University, which competes at the NAIA level in sports.

Texas Tech's baseball program, a major player on the national scene several years ago, has been struggling in recent years. LCU, in contrast, has remained strong in its own sphere of play and, in fact, had risen to No. 1 in the national NAIA rankings with a dominant stretch of play.

Last night, though, LCU had its 38-game winning streak snapped, against Wayland Baptist.

Compared to the situation in basketball or football, the most talented teams in baseball tend to be less dominant. As Jim Albert and Jay Bennett hypothesized during an online chat on my old Hot Hand page, the rules and physical demands of baseball limit, respectively, how often a team's top hitter can bat or top pitcher can take the mound. In contrast, a great football quarterback or basketball shooter can be involved in a vast majority of his or her team's plays.

Thus, regardless of league affiliation or competition level, winning 38 straight baseball games isn't easy, and LCU deserves great congratulations on the streak.

Lorena Ochoa won her fourth straight tournament on the LPGA tour earlier today, which is also her fifth win in her last six events. In winning four straight LPGA tourneys, she joined rarefied company, as the feat has only been accomplished five times; Annika Sorenstam did so in 2001 and it happened three times from 1962-1969. In anticipation of the final round of this weekend's tournament, the New York Times ran a feature article on Ochoa this morning.

On the college baseball scene, the University of Missouri's Jacob Priday has been swinging a hot bat, including a four-homer game last Friday against perennial power Texas. Accordingly, Priday was named Big 12 offensive Player of the Week.

With the Major League Baseball season upon us, I wanted to mention an article in the initial 2008 issue of the Journal of Quantitative Analysis in Sports by Jim Albert, entitled "Streaky Hitting in Baseball" (articles are generally limited to paid subscribers, but limited guest-viewer privileges are available).

Albert, a longtime friend of the Hot Hand website, uses data from the 2005 MLB season to investigate various streakiness-related questions. One of the major conclusions in his abstract is that, "[An] exchangeable model that assumes that all players are consistent with constant probabilities of success appears to explain much of the observed streaky behavior."

Another of Albert's conclusions is that, "...a player who appears unusually streaky in hits doesn't generally appear streaky in strikeouts and home runs" (p. 28).

***

News has just come over the wire services that 91-year-old Tommy Holmes, who held one of the longest consecutive-game hitting streaks in National League history, has died.

A reporter from the New York Times contacted me a few days ago on a hockey-related matter. He asked if I could do some statistical analyses of NHL teams, over the years, that have the put together the top win-loss record in the regular season (for which they receive the President's Trophy) and how likely these teams would have been (in retrospect) to win the Stanley Cup championship in the playoffs. The reporter's thought was that, among other things, teams that compile the top record in the regular season may have done so by keeping their top players on the ice a lot, thus tiring them out for the playoffs. Here's the article from today's Sunday Times.

***

Last night's two national semifinal games of the men's college basketball Final Four featured a number of streak-relevant phenomena. Most dramatic were the stretches of dominance exchanged by Kansas and North Carolina in the nightcap (play-by-play sheet).

After a UNC hoop cut an early KU lead to 15-10, the Jayhawks took off on an incomprehensible 25-2 spurt that made the score 40-12 with 6:49 left in the first half. The Tar Heels scored the next 10 points to make it 40-22, and the teams played at parity for the final minutes of the half, leaving the score 44-27 at the intermission.

With Kansas leading 54-36 a few minutes into the second half, North Carolina scored 14 straight to close to within 54-50 with 11:16 remaining. For roughly the next six minutes, the two teams held their ground, with the Jayhawks leading 67-61. At this point, it was KU that had the last offensive flurry to unleash, outscoring UNC 17-5 the rest of the way, to win 84-66.

In the opening game, a 78-63 Memphis win over UCLA, what stood out most to me was both teams' loss of their early three point-shooting touch, whether due to stepped-up defense, fatigue, pressure, or something else (box score and play-by-play sheet).

For the first 7:02 of the game, the Tigers and Bruins were shooting a combined 5-for-7 from behind the arc (UCLA 3-of-4, Memphis 2-of-3). The teams then went a combined 3-for-18 the rest of the way, to end up a combined 8-for-25 (UCLA 4-13, Memphis 4-12).

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.

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 ESPN.com 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!

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.