I just finished reading the book Stumbling on Happiness by Harvard social psychologist Daniel Gilbert.

The premise of the book is that we tend not to be very good at predicting how we would react emotionally, if a given event were to occur in the future. For example, if someone were asked how he or she would feel if his or her favorite sports team were to win a championship, the person's estimated happiness would likely exceed his or her actual happiness if the team actually won a championship and you could survey the fan a while afterwards. Gilbert and his University of Virginia colleague Tim Wilson refer to this area of research as "affective forecasting."

I did not start reading the book with hot hand research in mind. However, Gilbert's chapter on “presentism” really seemed to fit what may be going on with hot hand perceptions. The meaning of presentism can be grasped via a couple of Gilbert quotes:

...when brains plug holes in their conceptualizations of yesterday and tomorrow, they tend to use a material called today...(p. 125).

...if the present lightly colors our remembered pasts, it thoroughly infuses our imagined futures... (p. 127).

To use basketball as an illustration, presentism can be applied to hot hand perceptions as follows. An observer sees a player make several shots in a row (present) and naturally expects a high likelihood of the player making his or her next several shots (future). Such expectations presumably would be what give rise to the thinking that a team should always pass the ball to a hot shooter (it actually may be beneficial to pass to a hot shooter, but only because good overall shooters are the ones most likely to go on a streak).

Jay Koehler and Caryn Conley (2003) published a study a few years ago that content analyzed TV announcer comments during NBA three-point shooting contests, held annually in conjunction with the all-star game. The main finding was that players’ shooting percentages immediately following TV announcers’ hot hand exclamations (e.g., “Legler is on fire”) were no different than their overall baseline shooting percentages, thus showing once again that the present was not predictive of the future. This paper can be obtained via Koehler's website, which is itself accessible through the links to other researchers' pages on the right-hand side of the present page.

Friday night, the Atlanta Braves suffered their third shutout in a row, falling to the Detroit Tigers, 5-0. According to this ESPN.com recap (in the box entitled, "A Closer Look"):

The Braves were shut out for the third game in a row, their scoreless streak stretching to 28 innings. It was the first time since 1988 that Atlanta has been the victim of three straight shutouts.

Atlanta finally did score a run this afternoon (in the fourth) in losing 2-1 to Detroit, but that won't affect my analyses of the probability of a three-game scoreless streak.

So, how rare is it for a team to record what might be called a "Paula Abdul" trio of games -- my reference to her 1989 song Straight Up, which includes the phrase, "Oh-Oh-Oh..."?

I present two analyses, one historical and the other statistical.

First, for the historical analysis, I inspected every team's game-by-game logs (via ESPN.com's schedule/results page for each team, which can be accessed through here) for what's been played so far in 2007 and for all of 2006.

I found no instances of a team being shut out three games in a row during this (roughly) season-and-a-half span. Several teams came close, as seen in the following examples:

The Royals had a sequence during the first half of the 2006 season that went like this: May 31 at Oakland, lose 7-0; June 2 at Seattle, lose 4-0; and June 3 at Seattle, lose 12-1.

The Twins, during an April 28-30, 2006 sequence at Detroit, lost three games by the scores of 9-0, 18-1, and 6-0.

Later in the same season (August 10-12, 2006), Minnesota had the following losing stretch while hosting Toronto: 5-0, 7-1, and 4-0.

From May 2-5, 2006, the Cubs lost four straight games while scoring a total of only one run. The opponents and scores of the Cub losses are as follows: vs. Pittsburgh, 8-0; at Arizona, 5-1 and 6-0; and at San Diego, 1-0.

Finally, the Astros, on the dates of June 27, 28, and 30, 2006, lost at Detroit by scores of 4-0 and 5-0, and then at Texas, 3-1.

For the statistical analysis, I looked at every Braves' box score for their 20 games preceding the streak of three shutout losses. For each inning, 1 through 9, of every game, I recorded in a yes/no fashion whether Atlanta had scored one-or-more runs or not.

As David W. Smith shows in the recent SABR Baseball Research Journal (Volume 35) ("Effect of Batting Order..."), average numbers of runs scored tend to be higher in some innings than in others (e.g., more tend to be scored in the first inning). Therefore, I wanted to examine the Braves' probabilities of scoring (and not scoring) on an inning-by-inning basis, even though number of runs and scoring of at least one run are different quantities.

Listed below are the numbers of times the Braves scored one-or-more runs in each inning during the 20 games I coded. Each value was then subtracted from 20 to give the number of games in which the Braves were blanked in that inning, which was then converted to a percentage (number of games blanked in that inning, divided by 20).

Inning---#Games ATL Scored---% of Games NOT Scoring

First---4 games---.80 rate of NOT scoring in this inning
Second---4 games---.80
Third---5 games---.75

Fourth---5 games---.75
Fifth---7 games---.65
Sixth---6 games---.70

Seventh---4 games---.80
Eighth---6 games---.70
Ninth---5 games---.75

Multiplying these nine component probabilities together yields .069 for the overall probability of the Braves being shut out in any one particular game. This calculation assumes independence of scoring probability from inning to inning, which may be questionable (batting orders would typically lead to the batters in one inning being better than those in the next inning). Still, the estimate seems reasonable, as the Braves were shut out only once in the 20-game sample (.05, which is close to the estimate of .069).

Because Atlanta was blanked in three straight games, we then raise .069 to the third power, yielding .0003 (or 3-in-10,000) for the probability of the Braves getting shut out every time in a three-game sequence (again assuming independence).

Given enough opportunities to get shut out three straight games -- and the Braves certain had a huge number of them, going all the way back to 1988 -- it can happen. But in the short term, even across all of Major League Baseball, it seems very rare.

Brandon Watson of the Columbus Clippers yesterday tied the 95-year-old International League record for consecutive games with at least one hit. Watson's double at Ottawa brought his hitting streak to 42 games. The IL is part of AAA minor-league baseball, the level just below the majors. The major-league affiliate, or parent organization, for Columbus is the Washington Nationals (for many years, it had been the Yankees). Two questions are: (1) how long will the streak continue?, and (2) when will the Nats bring him up to the big club?

Update: Watson's hitting streak came to an end at 43 games, but at least he surpassed the previous league record by one game.

The June issue of the academic journal Personality and Social Psychology Bulletin included an article by Keith Markman and Corey Guenther of Ohio University, entitled "Psychological Momentum: Intuitive Physics and Naive Beliefs."

The article presents a package of four brief studies, each examining college student participants' beliefs and expectations regarding psychological momentum. The studies did not examine the relation between perceived momentum and athletes' actual later performance.

In one study, participants viewed a 10-minute videotape segment of a 1998 men's basketball game between Duke University and the University of North Carolina (which participants reported having no prior familiarity with). During the segment, Duke scored 15 straight points to cut a 19-point deficit to 4. At each of 10 pause points, participants reported their perceptions of which team had the momentum and who was going to win.

Another question asked participants to identify what they felt were turning points. Out of 11 possible plays, respondents disproportionately identified two of them, suggesting the perception of momentum can be a judgment of high consensus.

Other studies, using hypothetical scenarios, examined perceivers' impressions of the impact of a win over a traditional rival on a team's likelihood of winning its next game; the anticipated carryover of momentum on one task to performance on another task; and the anticipated effects of blocking a person's momentum on a task.

A key idea guiding the study was the authors' proposed analogy between psychologial and physical momentum. As the authors discussed, the latter is calculated by multiplying an object's mass by the velocity with which it is traveling (see here for the Wikipedia page on physics momentum). At this stage, the delineation of psychological factors to correspond with mass and velocity seemed a little loose to me (e.g., a win over a longstanding rival was said to confer more mass than a win over a run-of-the-mill opponent).

Through these studies, Markman and Guenther have "gotten the ball rolling" on a potentially fruitful line of research. Whether this "ball" gathers momentum, we'll have to wait and see.

I don’t write about college softball too often, but two pitchers currently going in the NCAA Women’s College World Series warrant attention from a hot-hand perspective. Tennessee’s Monica Abbott and Washington’s Danielle Lawrie have each pitched a no-hitter thus far in the World Series.

Abbott has not allowed a run in two outings and has struck out 32 batters in 14 innings pitched (regulation length for softball is seven innings).

Lawrie has allowed only one hit in 12 innings (one of her team’s wins was in five innings, a “run-rule” shortened 9-0 victory).

Another pitcher, Arizona’s Taryne Mowatt, has not allowed an earned run in three complete-game appearances.

There will be plenty of softball action today, along with Monday, Tuesday, and perhaps Wednesday nights, on ESPN and ESPN 2, so take a look if you have a chance. Further information on the Women’s College World Series is available at my College Softball Blog.

Cleveland showed it was more than just a one-man team, with Daniel Gibson scoring 31 points as the Cavaliers closed out the Detroit Pistons, 98-82, to advance to the NBA finals. Gibson went a perfect 5-of-5 on three-point attempts (box score), including a trio of them in the first 2:18 of the fourth quarter, to break open a close game (fourth quarter play-by-play sheet). Having LeBron James on your team to draw the opponents' attention is obviously helpful, but Gibson had to make the shots himself.

The sports world is abuzz over last night's performance by Cleveland's LeBron James in his team's double-overtime win at Detroit in the NBA's Eastern Conference finals. It wasn't merely that James scored 48 points in giving his team a 3-2 series lead.

James scored the Cavaliers' final 25 points of the game, 29 of their last 30. Quoting from this game article, "He was the only Cavs player to make a field goal in the last 17:48 and the only one to score in the final 12:49."

This particular type of accomplishment is obviously a function of both James's offensive prowess and his teammates' inability to score. If we look at the game's play-by-play sheet, focusing on the final 17:48 (the last 7:48 of the fourth quarter, excluding a basket by Zydrunas Ilgauskas at the 7:48 mark that starts the clock running on our analysis, and then the two overtimes), we can see the shooting percentages for both James and the non-James Cavaliers (in the aggregate).

During the final 17:48, by my count...

James was 11 of 14 from the field, his made field goals roughly an equal blend of long-distance shots (two made three-pointers and a bunch of long two-pointers) and layups/dunks. He was also 5 of 9 from the free-throw line.

In contrast, the non-James Cavaliers were 0 for 10 from the field and 1 of 2 from the stripe.