Welcome to everyone who has gotten to this site via the link in Carl Bialik's Wall Street Journal "Numbers Guy" blog! For those of you who've gotten here other than through the Numbers Guy, this is what I'm referring to.
Bialik's topic was "Jacqueline Gagne, a 46-year-old Rancho Mirage, Calif., resident, [who] has hit 10 holes in one in the last four months, over a stretch of just 75 rounds of golf." In this connection, Bialik was kind enough to mention and put a link to the Hot Hand page.
The most similar thing I've ever written about is the case of Danny Leake who, right here in my home city of Lubbock, Texas last July, made a hole-in-one on the same hole on two straight days.
Bialik's blog posting on Jacqueline Gagne has generated a huge number of comments. One issue I've seen mentioned, which I would like to discuss, revolves around the fact that the kinds of statistical formulas that have been used to estimate the probability of Ms. Gagne's feat assume independence of observations (i.e., the outcome of one shot or one round does not affect the outcome of the next).
Independence characterizes such exercises as coin-tossing and dice-rolling. Because of this independence, we can, for example, calculate the probability of rolling double-sixes with two dice as 1/6 (which is the probability of a six on one die) X 1/6 (the probability of a six on the other die) = 1/36.
Whether human athletic performances -- such as shooting rounds of golf, taking shots in basketball, or getting hits in baseball -- should be discussed analogously to coin-tossing and dice-rolling is controversial. A person can vary in his or her mood, energy levels, etc., whereas a coin or die cannot. In fact, a prominent statistician was once quoted as saying, "...the thought of comparing dice with shooting baskets is silly."
Yet, studies have shown that sequences of athletic performances often match sequences generated by random processes such as coins, dice, and spinners. Interested readers are invited to peruse a write-up I did on the fifth anniversary of the Hot Hand page, in which I offered my reflections on what research on this topic has shown. In particular, please see the section where I summarized my spinner-simulation studies of Texas Tech women's basketball players' three-point shooting.
I hope those of you for whom this is your first foray into streakiness analyses have found this introduction to be thought-provoking and will be interested in coming back!
Tuesday, May 22, 2007
Tuesday, May 15, 2007
Michael Hamberger of the Washington, DC area contacted me a while back to bring to my attention an article he had co-authored on the subject of psychological momentum (PM); he was also kind enough to send me a copy, for which I thank him.
According to the cross-country page at the famous Sidwell Friends school, where he is a coach:
Mike Hamberger came to Sidwell Friends in 2004. He was a decathlete at Widener University his junior and senior years. He completed his master's degree in Kinesiology with a concentration in Sports Psychology at the University of Maryland.
As can be seen in the article reference below, Mike worked at Maryland with Professor Seppo Iso-Ahola
Hamberger, M., & Iso-Ahola, S.E. (2004). Psychological momentum and athletic performance: A critical review of research. Journal of Contemporary Athletics, 1, 207-226 [link to journal].
Most of my reading on hot-hand issues over the years has been from psychology and statistics journals, to the relative neglect of the exercise and sports science field. The review article sent to me by Hamberger is thus a nice "helper" in catching me up on the latter literature.
The article uses as a running theme the statistic of the form, When Team X scores first, it wins Y percent of the time, with Y usually being a number well above 50%. I know that I cringe every time I hear such a statistic during a game broadcast.
There are at least two problems with this type of assertion. First, especially in low-scoring sports such as soccer, hockey, and baseball, the same event -- scoring a goal/run/point -- contributes to both variables being correlated, which team scores first and which team wins the game.
Second, and relatedly, as Hamberger and Iso-Ahola quote previous authors:
...rather than attribute victory to psychological momentum gained from early success, one should consider that "athletically superior teams tend to get ahead [early] and stay there"...(p. 215).
This leads Hamberger and Iso-Ahola to probe further the idea of controlling for (or matching) the competitors' ability levels, to obtain a more rigorous test of psychological momentum. Within their "Summary and Conclusions" section, they write the following (which, to a large extent, matches my reading of the literature):
What about when two opponents are equal in skill? Evidence seems ambiguous as some studies support the PM effect... while others do not. This controversy may be due to three factors. First, some sports (e.g., tennis and racquetball) are more conducive to PM than other sports (e.g., baseball and basketball)... Second, there are methodological problems and questions about previous studies and statistical analyses reported in them... Third, PM effects may vary as a function of individual differences and duration of time. That is, certain individuals are more likely affected by PM, and PM effects may exist but may be short-lived and thus cannot be captured by crude statistical analyses (p. 221).
Given that the article appears in a relatively new journal, it may not be widely available in libraries. I would still recommend the article, if you can get your hands on it.
According to the cross-country page at the famous Sidwell Friends school, where he is a coach:
Mike Hamberger came to Sidwell Friends in 2004. He was a decathlete at Widener University his junior and senior years. He completed his master's degree in Kinesiology with a concentration in Sports Psychology at the University of Maryland.
As can be seen in the article reference below, Mike worked at Maryland with Professor Seppo Iso-Ahola
Hamberger, M., & Iso-Ahola, S.E. (2004). Psychological momentum and athletic performance: A critical review of research. Journal of Contemporary Athletics, 1, 207-226 [link to journal].
Most of my reading on hot-hand issues over the years has been from psychology and statistics journals, to the relative neglect of the exercise and sports science field. The review article sent to me by Hamberger is thus a nice "helper" in catching me up on the latter literature.
The article uses as a running theme the statistic of the form, When Team X scores first, it wins Y percent of the time, with Y usually being a number well above 50%. I know that I cringe every time I hear such a statistic during a game broadcast.
There are at least two problems with this type of assertion. First, especially in low-scoring sports such as soccer, hockey, and baseball, the same event -- scoring a goal/run/point -- contributes to both variables being correlated, which team scores first and which team wins the game.
Second, and relatedly, as Hamberger and Iso-Ahola quote previous authors:
...rather than attribute victory to psychological momentum gained from early success, one should consider that "athletically superior teams tend to get ahead [early] and stay there"...(p. 215).
This leads Hamberger and Iso-Ahola to probe further the idea of controlling for (or matching) the competitors' ability levels, to obtain a more rigorous test of psychological momentum. Within their "Summary and Conclusions" section, they write the following (which, to a large extent, matches my reading of the literature):
What about when two opponents are equal in skill? Evidence seems ambiguous as some studies support the PM effect... while others do not. This controversy may be due to three factors. First, some sports (e.g., tennis and racquetball) are more conducive to PM than other sports (e.g., baseball and basketball)... Second, there are methodological problems and questions about previous studies and statistical analyses reported in them... Third, PM effects may vary as a function of individual differences and duration of time. That is, certain individuals are more likely affected by PM, and PM effects may exist but may be short-lived and thus cannot be captured by crude statistical analyses (p. 221).
Given that the article appears in a relatively new journal, it may not be widely available in libraries. I would still recommend the article, if you can get your hands on it.
Sunday, May 13, 2007
I just finished listening to this afternoon's Oklahoma State-Texas Tech baseball game, a 10-0 run-rule-shortened seven-inning win for the Cowboys. Two lenghty streaks are still active; to borrow a line from I Love Lucy, one of these streaks is "swell" and the other is "lousy."
The "swell" streak is that of Oklahoma State's Ty Wright, who got a hit in his 27th straight game. Even though this streak is the second-longest in school history, it is highly unlikely Wright will ever approach the longest one. As noted by the OSU athletics site after Saturday's game: "Robin Ventura holds the school and NCAA record with a 58-game streak in 1987." Ventura, of course, enjoyed a long major-league career after his college days with the Cowboys.
The "lousy" streak consists of 21 straight scoreless innings by Texas Tech. I'll have to do some research to find out how long it's been since the Red Raiders put up so many zeroes, but it's probably been a long time. College baseball, in general, seems to be pretty high-scoring and, despite some recent lean years, Texas Tech has had a good program.
[UPDATE: This article on today's game from the Texas Tech athletics site notes that the last time the Red Raiders have suffered two straight shutouts was in 2004. Further research reveals that Texas Tech drew blanks twice on April 3, 2004 against the University of Texas, 4-0 and 10-0 (season archive). The Red Raiders' scoreless streak did not exceed 18 innings, however, as they scored in the ninth inning of their previous game, against Texas A&M, and then put up five runs in the first inning of their next outing, a nonconference game against Howard Payne.]
The "swell" streak is that of Oklahoma State's Ty Wright, who got a hit in his 27th straight game. Even though this streak is the second-longest in school history, it is highly unlikely Wright will ever approach the longest one. As noted by the OSU athletics site after Saturday's game: "Robin Ventura holds the school and NCAA record with a 58-game streak in 1987." Ventura, of course, enjoyed a long major-league career after his college days with the Cowboys.
The "lousy" streak consists of 21 straight scoreless innings by Texas Tech. I'll have to do some research to find out how long it's been since the Red Raiders put up so many zeroes, but it's probably been a long time. College baseball, in general, seems to be pretty high-scoring and, despite some recent lean years, Texas Tech has had a good program.
[UPDATE: This article on today's game from the Texas Tech athletics site notes that the last time the Red Raiders have suffered two straight shutouts was in 2004. Further research reveals that Texas Tech drew blanks twice on April 3, 2004 against the University of Texas, 4-0 and 10-0 (season archive). The Red Raiders' scoreless streak did not exceed 18 innings, however, as they scored in the ninth inning of their previous game, against Texas A&M, and then put up five runs in the first inning of their next outing, a nonconference game against Howard Payne.]
Friday, May 04, 2007
As I was writing last night's entry on San Antonio's Michael Finley, who hit 8-of-9 on three-pointers as the Spurs closed out Denver Wednesday night in the teams' NBA first-round play-off series (see below), I had the Dallas-Golden State game on TV in the background. Wouldn't you know it, the Warriors' Stephen Jackson went on a three-point barrage of his own, which I briefly alluded to in the midst of my Finley write-up. Now, I'd like to discuss Jackson's performance in a little more depth.
In commenting on Finley's night, I stated that his made three-pointers tended to be separated by long amounts of time, no less than about three minutes between any pair of them. Also, some of the intervals between made threes were punctuated by missed two-point attempts. This did not fit the image of a hot-handed player "knocking down a barrage of shots in rapid succession, boom-boom-boom-boom-boom."
As I'm writing this last night, I'm seeing Jackson go on a streak that did fit the above image.
As shown in this play-by-play sheet, Jackson made his only two trey attempts of the first quarter and his only trey attempt of the second quarter.
In the third quarter is where things really got interesting. From when there was 9:11 to go in the quarter to 6:41 left (a window of exactly 2 minutes and 30 seconds), Jackson made FOUR straight three-pointers. Now that's what I'm talking about!
Jackson's spurt launched a 24-3 run by Golden State against Dallas, stretching a 56-54 Warrior lead out to 80-57. Jackson had only one more three-point attempt on the evening, a fourth quarter miss, which left him at 7-of-8 from behind the arc (box score).
Whether long-term analyses would show Jackson to be a streaky three-point shooter (i.e., that his probability of a make goes up after making previous shots), I don't know. But seeing the same player hit four treys in such a short time span certainly was entertaining!
***
On a completely different matter, Ed Hartig sent in a note to the SABR-L e-mail discussion list, informing everyone that:
Cub Derrek Lee has hit a double in each of his last 8 games. I found six other stretches of players since 1957 with doubles in 7 consecutive games - but no other of 8 or more.
In commenting on Finley's night, I stated that his made three-pointers tended to be separated by long amounts of time, no less than about three minutes between any pair of them. Also, some of the intervals between made threes were punctuated by missed two-point attempts. This did not fit the image of a hot-handed player "knocking down a barrage of shots in rapid succession, boom-boom-boom-boom-boom."
As I'm writing this last night, I'm seeing Jackson go on a streak that did fit the above image.
As shown in this play-by-play sheet, Jackson made his only two trey attempts of the first quarter and his only trey attempt of the second quarter.
In the third quarter is where things really got interesting. From when there was 9:11 to go in the quarter to 6:41 left (a window of exactly 2 minutes and 30 seconds), Jackson made FOUR straight three-pointers. Now that's what I'm talking about!
Jackson's spurt launched a 24-3 run by Golden State against Dallas, stretching a 56-54 Warrior lead out to 80-57. Jackson had only one more three-point attempt on the evening, a fourth quarter miss, which left him at 7-of-8 from behind the arc (box score).
Whether long-term analyses would show Jackson to be a streaky three-point shooter (i.e., that his probability of a make goes up after making previous shots), I don't know. But seeing the same player hit four treys in such a short time span certainly was entertaining!
***
On a completely different matter, Ed Hartig sent in a note to the SABR-L e-mail discussion list, informing everyone that:
Cub Derrek Lee has hit a double in each of his last 8 games. I found six other stretches of players since 1957 with doubles in 7 consecutive games - but no other of 8 or more.
Thursday, May 03, 2007
Aided by Michael Finley's 8-of-9 performance on three-point shots, the San Antonio Spurs defeated Denver last night to close out the teams' NBA first-round play-off series in five games.
Upon closer examination of Finley's overall statistics (box score) and the game's play-by-play sheet, his shooting seemed to be anything but the prototypical "hot hand." If the latter phrase makes you think of a hoopster knocking down a barrage of shots in rapid succession, boom-boom-boom-boom-boom (just like Golden State's Stephen Jackson is doing right now against Dallas, as I write!), then Finley's sequence doesn't qualify.
First of all, Finley's overall shooting from the field was 9-of-14, meaning that he made only 1-of-5 on two-point attempts. On these two-point attempts (ignoring his launches from behind the arc), Finley (in sequence) missed from 18, 16, 16, and 9 feet, and then made a lay-up.
If you look below at the chart I made, Finley's first quarter consisted to a large degree of alternating three-point makes and mid-range two-point misses. The oft-cited phrase about the rim looking the size of a hula-hoop to a hot shooter thus probably didn't apply.
In the second half, Finley missed only one shot. However, his last four made treys were each separated by roughly three minutes. As I reflected back in January, on the occasion of the fifth anniversary of this website, the optimal conditions for streaky performance would be:
...when players could execute a short, simple motion (e.g., swing or stroke) in relation to the ball, which could be repeated often and in short succession. That way, a player could rehearse and remember how he or she executed a successful motion and apply it repeatedly.
I noted, further, that consistent with the above reasoning, evidence for hot hands had been found in such athletic endeavors as bowling, tennis, and golf-putting.
In conclusion, I guess, seeing the variety of ways in which an athlete can accomplish a substantial stretch of success (as Finley did on threes) or failure is what makes being a fan and statistician of sports so interesting!
Upon closer examination of Finley's overall statistics (box score) and the game's play-by-play sheet, his shooting seemed to be anything but the prototypical "hot hand." If the latter phrase makes you think of a hoopster knocking down a barrage of shots in rapid succession, boom-boom-boom-boom-boom (just like Golden State's Stephen Jackson is doing right now against Dallas, as I write!), then Finley's sequence doesn't qualify.
First of all, Finley's overall shooting from the field was 9-of-14, meaning that he made only 1-of-5 on two-point attempts. On these two-point attempts (ignoring his launches from behind the arc), Finley (in sequence) missed from 18, 16, 16, and 9 feet, and then made a lay-up.
If you look below at the chart I made, Finley's first quarter consisted to a large degree of alternating three-point makes and mid-range two-point misses. The oft-cited phrase about the rim looking the size of a hula-hoop to a hot shooter thus probably didn't apply.
In the second half, Finley missed only one shot. However, his last four made treys were each separated by roughly three minutes. As I reflected back in January, on the occasion of the fifth anniversary of this website, the optimal conditions for streaky performance would be:
...when players could execute a short, simple motion (e.g., swing or stroke) in relation to the ball, which could be repeated often and in short succession. That way, a player could rehearse and remember how he or she executed a successful motion and apply it repeatedly.
I noted, further, that consistent with the above reasoning, evidence for hot hands had been found in such athletic endeavors as bowling, tennis, and golf-putting.
In conclusion, I guess, seeing the variety of ways in which an athlete can accomplish a substantial stretch of success (as Finley did on threes) or failure is what makes being a fan and statistician of sports so interesting!
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