Saturday, September 29, 2012

Baseball Streaks in Regular Season's Final Days

With only five days left (including today) in Major League Baseball's regular season, a number of hot and cold streaky performances are adding to the excitement down the stretch.

The Detroit Tigers' Miguel Cabrera is threatening to become the first Triple Crown winner in either league since 1967. As of Saturday morning, he leads the American League in batting average (.327, to .322 for his nearest competitor) and runs batted in (133, with his closest rival at 125). Cabrera's 42 home runs put him one behind the leader, Texas's Josh Hamilton. However, Toronto's Edwin Encarnacion also has 42 homers and there are players with 41 and 40. Thus, a homer outburst by any of Cabrera's rivals could sink his Triple Crown hopes. Here's a link to's baseball statistics page, for monitoring the situation. As can be seen on this page of Cabrera's personal statistics, he has raised his performance in some categories from before the All-Star break (taken as a rough marker of the season's halfway point) to after. Before the break, he had 18 homers in 343 at-bats; after the break, he's hit 24 round-trippers in only 262 AB. His batting average is also somewhat higher post- than pre-All Star break (.332 to .324). However, in the past seven days, he has hit only .226 and homered only once. He had a recent 0-for-8 slump that he ended on Thursday. Stay tuned!

The Pittsburgh Pirates, whose bid to end their streak of 19 straight seasons with a losing (sub-.500) record we've been following, are now 76-81. The best they can do is finish 81-81. It wouldn't be a winning record, but it would be a non-losing mark. Honestly, though, it seems highly unlikely the Pirates can win out the rest of the way, so their streak of losing seasons is almost certain to reach 20.

Last night's opener of a series between the Tampa Bay Rays and the Chicago White Sox featured teams going in the opposite direction. The White Sox had lost 8 of their last 9 to fall behind Detroit in the AL Central standings (with virtually no hope for a wild-card path to the playoffs), whereas the Rays had won 8 straight to keep their playoff hopes alive. The Sox won last night's game, however, by a 3-1 score. The win keeps Chicago in contention for the division title, 1 game behind the Tigers.

The Los Angeles Angels of Anaheim are keeping the pressure on the Baltimore Orioles and Oakland A's, the teams currently positioned for the AL's two wild-card slots. The Angels, having won 25 of their last 35, are only 2 games behind the O's and A's in the wild-card standings. The Angels' talent -- free-agent superstar acquisition Albert Pujols, top youngsters Mark Trumbo and Mike Trout, and stellar pitchers Jered Weaver and Zack Greinke (a late-season acquisition) -- make them a team no one wants (potentially) to face in the playoffs.

The Chicago Cubs are ending a dismal season in a dismal way, dropping 10 of their last 11 games. One small measure of glory for the Cubs was the immaculate fielding of second-baseman Darwin Barney, who had a major streak going for consecutive error-free games. However, after tying the record for his position at 141 straight games without an error, he made one last night!

Friday, September 21, 2012

Orioles' 15-Game Winning Streak in Extra-Inning Contests

With Wednesday's 11-inning victory at Seattle, the Baltimore Orioles have won their last 15 extra-inning games, the longest such streak since 1949. One might hypothesize that an extra-inning game is like a coin-flip, with each team having close to a 50/50 chance to win.

Once a game goes beyond nine innings, it can be decided by as little as one extra frame, where one swing of the bat can be decisive. Perhaps the home team is at a little bit of an advantage, but baseball in general has one of the smallest home-field advantages among popular team sports.

If one flipped a coin in series of some defined length (e.g., sets of 10 or 15 flips) and then plotted a histogram of how frequently different breakdowns of heads and tails occurred (e.g., 50% heads/50% tails; 20% heads/80% tails), the most common occurrence in the long run would be 50/50. Other divisions close to 50/50, such as 49/51, 51/49, 48/52, and 52/48 would also be fairly common, though progressively less so the further one moved away from 50/50. As long as the number of tosses in each series was not too small, extreme breakdowns such as 0% heads/100% tails and vice versa would be very rare. This pattern of outcomes yields the familiar "normal" or "bell-shaped" curve

To see if the outcomes of extra-inning baseball games are like coin flips, therefore, we can examine teams' winning percentages in extra-inning games and see if the frequencies of different winning percentages resemble the bell-shaped distribution of coin-flips.

Using's "expanded standings" from 2012 (as of last night), 2011, and 2010, I generated 90 team-year winning percentages in extra-inning games (see column with the heading "XTRA"). In other words, the 2012 Orioles, 2011 Orioles, and 2010 Orioles would be three separate data points, as would the 2012 Yankees, 2011 Yankees, and 2010 Yankees, and so forth.

For the 2012 season to date, Baltimore's extra-inning record is 15-2 (.882), as shown in the far right-hand side of the following graph (which you can click to enlarge). As the graph shows, .500 is the most common extra-inning record in the past three seasons, which occurred 15 times among the 90 team-specific data points. This result is consistent with extra-inning games being like coin-tosses, as is the general tapering off of the curve in both directions from 50/50.

Under a prior assumption of a 50/50 success rate in extra-inning games, the probability of a team (in this case, the Orioles) winning 15 or more out of 17 is about 1 or 2 in 1,000, according to this online binomial calculator from Vassar College. Such an occurrence would thus be rare, but would be expected to happen every several decades.

Keeping in mind that Major League Baseball expanded to 26 teams in 1977, 28 in 1993, and finally 30 in 1998 (history of MLB expansions), one would have to go back 36 years to compile roughly 1,000 team-years. Interestingly, as noted above, one must go back 63 years, to 1949, to find an extra-inning winning streak at least as long as the 2012 Orioles' 15 games. Back in 1949, the Cleveland Indians won 17 straight.  

At the low end of the above distribution stands the 2012 Houston (Dis)Astros. The probability of a team winning 1 or fewer out of 12, given the 50/50 assumption, is around 4 in 1,000.

Further supporting the idea of extra-inning games as coin flips is the finding of non-significant skew (tilt to the right or left) and kurtosis (exaggerated peak) in the plot of teams' extra-inning winning percentages.

UPDATE: On Saturday afternoon, September 22, the Orioles extended their streak to 16 straight wins in extra-inning games, with a 9-6 win over Boston in 12.

Wednesday, September 19, 2012

"Hot Hand" Book to Be in Texas Tech Faculty Exhibit

Hot Hand, the book, will be part of the Texas Tech University library's annual faculty authors exhibit, beginning Wednesday, October 17. I am shown in the upper-right corner of the Brady Bunch-like promotional video, trying my hand at different sports and games. Take a look by clicking here; it's very cute!

Sunday, September 16, 2012

Hot and Cold Streaks Shape NL Wild-Card Race

At the conclusion of today's play, the race for the second wild-card spot in the National League baseball playoffs is very much up for grabs. This is the first year that each league will have two wild-card teams, who will face each other in a one-game playoff (within each league) to begin the postseason. Barring a major collapse, the Atlanta Braves should capture a wild-card slot without much problem (although the Braves did fall apart in a similar situation a year ago).

As shown in the following table, some of the other wild-card contenders have experienced recent streaks that have either strengthened or weakened their playoff prospects.

Team Record Recent Streak?
Atlanta 84-63
St. Louis 77-70 Lost 8 of 10 (Sept. 5-15)
L.A. Dodgers 76-71 Lost 8 of last 11
Milwaukee 74-72 Won 20 of last 26
Pittsburgh 73-72 Lost 25 of last 35
Philadelphia 73-74 Won 15 of 19 (Aug. 23-Sept. 12),
but lost 3 of 4 in Houston this wkd
Arizona 72-74

Of the teams listed above, the one threatening to make the most dramatic comeback is (or perhaps "was") Philadelphia. The Phillies occupied last place in the NL East until mid-August and were "sellers" at the trading deadline (i.e., trying to build for the future rather than win now), trading away outfielders Shane Victorino and Hunter Pence. However, any team whose pitching staff includes Roy Halladay, Cliff Lee, and Cole Hamels can win games, and that's exactly what Philadelphia did. Losing 3 of 4 to lowly Houston this weekend has put a serious dent in the Phillies' playoff hopes, though.

Over in the right-hand column,you can vote in a poll regarding who you think will grab the second NL wild-card slot (assuming Atlanta wins the first one). You can examine the contending teams' remaining schedules here.

Thursday, September 06, 2012

Does a Defensive "Big Play" in U.S. Football Carry Over to the Offense?

With college and professional football swinging into action, now is a good time to look at a study of whether "psychological momentum" carries over from the same team's defense to its offense. For example, if the Chicago Bears' defense thwarts a Green Bay Packers' attempt to go for it on fourth down, does this development spur the Bears' offense to greater immediate success than it would have achieved absent the big defensive play? Presented by Aaron W. Johnson, Alexander J. Stimpson, and Torin K. Clark at last spring's MIT Sloan Sports Analytics Conference, the paper is entitled "Turning the Tide: Big Plays and Psychological Momentum in the NFL." A copy of the paper can be found here.

Johnson and colleagues looked at archival records of nearly one-half million plays from almost 3,000 NFL games between 2000-2010. The way defenses ended their opponents' drives were classified into "big plays" (e.g., fourth-down stops, turnovers due to interception or fumble) or routine stops (forcing the opponent to punt). The authors then asked: Do offenses that take the field as a result of a big play by their defensive teammates do better than offenses who take over after a routine defensive stop?

Three criteria of immediate offensive success were used: number of yards gained on the first play of the drive, whether the offense gained a first down (or touchdown) on the drive, and the number of points scored on the drive.

As I understand the authors' approach, they would find in their vast database, one pair at a time, an offensive drive that began immediately following a big defensive play and another offensive drive that followed a routine defensive stop. The authors made sure, within each contrasting pair, that both drives began from roughly the same yard line, to hold constant field position. Ultimately, a huge number of pairs were analyzed.

What the authors found, contrary to the idea of momentum carryover from defense to offense, is that offensive units that took the field after their defensive teammates had made a big play did not produce significantly more yards, first downs, or points than their counterparts who took the field after a routine stop by their defense.

One question, I feel, that would be interesting to address in future research is whether a big defensive play leads to a team's decision to have the offense go for its own big play upon taking possession (e.g., by throwing a long pass or running a double-reverse). Such a play could come to naught, but if the other team's defense comes onto the field with its heads hanging, the offense could catch the defense off guard.