Monday, January 26, 2009
Sunday, January 25, 2009
Saturday, January 24, 2009
The Hot Hand page would like to pay tribute to North Carolina State women's basketball coach Kay Yow, who died today at age 66 following a 20-year-plus battle with cancer. Over the years, the cancer kept coming back, but each time Yow fought back even harder. Further, Yow's determination could, at times, fuel her team to heightened levels of performance. As noted in this article on Yow's passing:
Yow's fight was never more public than when she took a 16-game leave to focus on her treatments during the 2006-07 season. After her return, her inspired Wolfpack won 12 of its final 15 games with wins against highly ranked rivals Duke and North Carolina in a run that attracted plenty of fans wearing pink -- the color of breast-cancer awareness.
Yow's fight was never more public than when she took a 16-game leave to focus on her treatments during the 2006-07 season. After her return, her inspired Wolfpack won 12 of its final 15 games with wins against highly ranked rivals Duke and North Carolina in a run that attracted plenty of fans wearing pink -- the color of breast-cancer awareness.
Friday, January 23, 2009
With Friday night's NBA win over Chicago on the books, Toronto point guard Jose Calderon now "has made 83 straight free throws dating to last season, the second-longest streak in NBA history. Michael Williams holds the record, making 97 in a row for Minnesota in 1993" (article).
In addition to making all four of his free-throw attempts to keep the streak going, Calderon shot 9-of-10 from the floor against the Bulls. Remarkably, Calderon's sharp-shooting performance came after a long stretch of inactivity due to a hamstring injury!
The next few games for the Raptors, during which Calderon conceivably could approach -- or even surpass -- the record, are as follows:
Sun, Jan 25 Sacramento
Wed, Jan 28 at New Jersey
Fri, Jan 30 Milwaukee
(Click here for the team's full schedule.)
As seen in Calderon's career statistics, this is his fourth season in the league and his annual free-throw percentage has never been below .818.
Check back for updates!
In addition to making all four of his free-throw attempts to keep the streak going, Calderon shot 9-of-10 from the floor against the Bulls. Remarkably, Calderon's sharp-shooting performance came after a long stretch of inactivity due to a hamstring injury!
The next few games for the Raptors, during which Calderon conceivably could approach -- or even surpass -- the record, are as follows:
Sun, Jan 25 Sacramento
Wed, Jan 28 at New Jersey
Fri, Jan 30 Milwaukee
(Click here for the team's full schedule.)
As seen in Calderon's career statistics, this is his fourth season in the league and his annual free-throw percentage has never been below .818.
Check back for updates!
Thursday, January 22, 2009
New Jersey Institute of Technology ended its 51-game losing streak in men's college basketball last night.
Long losing streaks would appear to stem from one (or both) of two factors: either a team is repeatedly overmatched physically, or it plays opponents of a comparable ability level but keeps losing due to a "momentum" of failure. The latter, which could include a randomness component, would consist of missed shots in the clutch, a loss of confidence, etc. The "overmatched" explanation would presumably yield a long streak of blow-out losses, whereas the "negative momentum" explanation would seem to call for a number of the losses to be by relatively small margins.
(Long winning streaks would represent the opposite patterns -- a team either being physically superior to its opponents or taking advantage of some combination of luck, clutch play, and confidence).
Which factor played a bigger role in NJIT's losing streak? Given that the team is currently making the transition from Division II to Division I play, one might be tempted to argue that inferiority of physical ability and talent is the culprit. Indeed, NJIT has played against many schools with well-established basketball (or general athletic) programs, such as Penn State, St. John's, and Rutgers.
However, if one looks at NJIT's page on Ken Pomeroy's statistical ranking website, one finds that a large share of the team's games appear to have been against comparably weak opposition.
NJIT is ranked No. 344 -- and last -- among Division I teams and several of its losses have come to teams ranked 250th or worse in the nation (Yale, 250; Towson, 268; Hartford, 274; Columbia, 294; St. Peter's, 296; Wagner, 299; Monmouth, 303; and Maryland-Eastern Shore, 334). Bryant University, whom NJIT defeated to end the streak, was ranked No. 329.
Admittedly, some of the games don't fit into my dichotomous scheme. NJIT lost to Yale by 29 points and to Columbia by 23 -- in other words, blow-out losses to teams with comparable rankings to NJIT. Go figure!
Long losing streaks would appear to stem from one (or both) of two factors: either a team is repeatedly overmatched physically, or it plays opponents of a comparable ability level but keeps losing due to a "momentum" of failure. The latter, which could include a randomness component, would consist of missed shots in the clutch, a loss of confidence, etc. The "overmatched" explanation would presumably yield a long streak of blow-out losses, whereas the "negative momentum" explanation would seem to call for a number of the losses to be by relatively small margins.
(Long winning streaks would represent the opposite patterns -- a team either being physically superior to its opponents or taking advantage of some combination of luck, clutch play, and confidence).
Which factor played a bigger role in NJIT's losing streak? Given that the team is currently making the transition from Division II to Division I play, one might be tempted to argue that inferiority of physical ability and talent is the culprit. Indeed, NJIT has played against many schools with well-established basketball (or general athletic) programs, such as Penn State, St. John's, and Rutgers.
However, if one looks at NJIT's page on Ken Pomeroy's statistical ranking website, one finds that a large share of the team's games appear to have been against comparably weak opposition.
NJIT is ranked No. 344 -- and last -- among Division I teams and several of its losses have come to teams ranked 250th or worse in the nation (Yale, 250; Towson, 268; Hartford, 274; Columbia, 294; St. Peter's, 296; Wagner, 299; Monmouth, 303; and Maryland-Eastern Shore, 334). Bryant University, whom NJIT defeated to end the streak, was ranked No. 329.
Admittedly, some of the games don't fit into my dichotomous scheme. NJIT lost to Yale by 29 points and to Columbia by 23 -- in other words, blow-out losses to teams with comparable rankings to NJIT. Go figure!
Sunday, January 18, 2009
In losing yesterday to Arizona State, the UCLA men's basketball team appears to have borrowed a page from Notre Dame's protracted dry spell down the stretch against Louisville a few nights ago.
Wednesday, January 14, 2009
In men's college basketball last night, Kentucky's Jodie Meeks scored 54 points. He was a perfect 14-for-14 from the free-throw line, and hit on 10 out of 15 three-point attempts (article).
Tuesday, January 13, 2009
So much for momentum! One would have thought Notre Dame was on a clear path to victory against Louisville last night in Big East men's basketball action, when Luke Harangody made two free throws with 5:35 remaining to cap a 14-3 Irish run and give Notre Dame a 71-67 lead.
However, the Irish went on to score no more points in regulation (with Louisville only scoring four) and only two in overtime. The result: An 87-73 Cardinal win (play-by-play sheet).
However, the Irish went on to score no more points in regulation (with Louisville only scoring four) and only two in overtime. The result: An 87-73 Cardinal win (play-by-play sheet).
Sunday, January 11, 2009
I recently received the 2008 annual Baseball Research Journal (volume 37) from SABR (the Society for American Baseball Research). In it, Trent McCotter has published an article entitled "Hitting Streaks Don't Obey Your Rules: Evidence That Hitting Streaks Aren't Just By-Products of Random Variation."
McCotter, a recent Phi Beta Kappa inductee at the University of North Carolina-Chapel Hill who has written extensively on baseball hitting streaks, once again presents an interesting take on the statistical aspect of streak hitting in his latest effort.
McCotter and his faculty collaborator Peter Mucha started by creating a huge database of year-specific game-by-game hitting data for all players active from 1957-2006. Someone who played 10 years would thus have 10 different lines of data. Each line (hypothetically) would look something like the following, where H = getting at least one hit in a game, and N = no hits in the game; in reality, however, there would be up to 162 entries for a player, depending on how many games he appeared in:
HHNNN NHNHN...
For each player-year, McCotter and Mucha then re-sorted the sequences of H's and N's into some random alternative, such as the following (the number of H's and N's would, of course, be constant between the player's actual sequence and the random re-sorting):
NHNNH NHNNH...
In fact, each player-season was randomly re-sorted 10,000 times!
McCotter's reasoning was that, if lengthy hitting streaks were simply a result of random variation on a player's underlying hitting ability, the random simulations should produce as many streaks of a given length as actually occurred in a player's real-life hitting portfolio.
The initial results (summarized in Table 2 of the article) showed the actual frequency of lengthy hitting streaks to be greater than the frequency obtained in the random simulations. For example, 274 actual hitting streaks of 20 or more games occurred in real life, whereas the average of all the excess simulated hitting logs generated 192.43 streaks of that length. For streaks of 25 or more games, 62 actually occurred whereas 35.74 were generated randomly. Similar trends occurred for 30+ and 35+ hitting streaks, although the numbers started to get very small (i.e., 5 streaks of 35 or more games actually occurred in real life, whereas 1.48 were generated randomly).
The greater number of actual, real-life hitting streaks of a given length, relative to the random simulations, is consistent with the idea of a "hot hand" (i.e., a player systematically raising his underlying hitting ability when in the midst of a hot streak), but does not prove the existence of one. As McCotter acknowledges, there could be other reasons for a greater number of lengthy hitting streaks existing than would be expected by chance.
For example, a player could be highly aware of his hitting streak and take special action to perpetuate it, such as an aggressive pull-hitter "going with what he's given" and slapping an outside pitch to the opposite field for a single. Also, a hitter may benefit from a generous ruling of "hit" (vs. "error") by the official scorer. (As an aside, a theory of Joe DiMaggio achieving his record 56-game hitting streak in part through such generosity has been making the rounds.)
Further, McCotter noted that his original random simulations included games in which the batter had not started, which could downwardly affect the numbers of streaks in the simulated sequences (i.e., a non-hit game owing to when the batter only appeared once as a pinch-hitter, could insert itself between hit games in the random sequences, thus holding down the length of hitting streaks).
A second series of simulations was run, this time excluding non-start games. Indeed, much of the difference between the actual and simulated numbers of streaks disappeared. McCotter describes the following finding, as one example:
...in real life for 1957-2006, there were 274 streaks of 20 or more games; the first permutation (including non-starts) had an average of a mere 192 such streaks; and the second permutation (leaving out non-starts) had an average of 259 such streaks. The difference between 259 and 274 may not sound like much, but it is still very significant when viewed over 10,000 permutations, especially since we still aren't quite comparing apples to apples (p. 68).
McCotter concludes his article on the following note:
This study shows that sometimes batters really may have a hot hand, or at least that they adapt their approach to try to keep a long hitting streak going -- and baseball players are nothing if not adapters (p. 69).
To the extent McCotter is claiming evidence for a relatively modest-sized hot-hand effect, subject to other possible interpretations, I would concur with him.
McCotter, a recent Phi Beta Kappa inductee at the University of North Carolina-Chapel Hill who has written extensively on baseball hitting streaks, once again presents an interesting take on the statistical aspect of streak hitting in his latest effort.
McCotter and his faculty collaborator Peter Mucha started by creating a huge database of year-specific game-by-game hitting data for all players active from 1957-2006. Someone who played 10 years would thus have 10 different lines of data. Each line (hypothetically) would look something like the following, where H = getting at least one hit in a game, and N = no hits in the game; in reality, however, there would be up to 162 entries for a player, depending on how many games he appeared in:
HHNNN NHNHN...
For each player-year, McCotter and Mucha then re-sorted the sequences of H's and N's into some random alternative, such as the following (the number of H's and N's would, of course, be constant between the player's actual sequence and the random re-sorting):
NHNNH NHNNH...
In fact, each player-season was randomly re-sorted 10,000 times!
McCotter's reasoning was that, if lengthy hitting streaks were simply a result of random variation on a player's underlying hitting ability, the random simulations should produce as many streaks of a given length as actually occurred in a player's real-life hitting portfolio.
The initial results (summarized in Table 2 of the article) showed the actual frequency of lengthy hitting streaks to be greater than the frequency obtained in the random simulations. For example, 274 actual hitting streaks of 20 or more games occurred in real life, whereas the average of all the excess simulated hitting logs generated 192.43 streaks of that length. For streaks of 25 or more games, 62 actually occurred whereas 35.74 were generated randomly. Similar trends occurred for 30+ and 35+ hitting streaks, although the numbers started to get very small (i.e., 5 streaks of 35 or more games actually occurred in real life, whereas 1.48 were generated randomly).
The greater number of actual, real-life hitting streaks of a given length, relative to the random simulations, is consistent with the idea of a "hot hand" (i.e., a player systematically raising his underlying hitting ability when in the midst of a hot streak), but does not prove the existence of one. As McCotter acknowledges, there could be other reasons for a greater number of lengthy hitting streaks existing than would be expected by chance.
For example, a player could be highly aware of his hitting streak and take special action to perpetuate it, such as an aggressive pull-hitter "going with what he's given" and slapping an outside pitch to the opposite field for a single. Also, a hitter may benefit from a generous ruling of "hit" (vs. "error") by the official scorer. (As an aside, a theory of Joe DiMaggio achieving his record 56-game hitting streak in part through such generosity has been making the rounds.)
Further, McCotter noted that his original random simulations included games in which the batter had not started, which could downwardly affect the numbers of streaks in the simulated sequences (i.e., a non-hit game owing to when the batter only appeared once as a pinch-hitter, could insert itself between hit games in the random sequences, thus holding down the length of hitting streaks).
A second series of simulations was run, this time excluding non-start games. Indeed, much of the difference between the actual and simulated numbers of streaks disappeared. McCotter describes the following finding, as one example:
...in real life for 1957-2006, there were 274 streaks of 20 or more games; the first permutation (including non-starts) had an average of a mere 192 such streaks; and the second permutation (leaving out non-starts) had an average of 259 such streaks. The difference between 259 and 274 may not sound like much, but it is still very significant when viewed over 10,000 permutations, especially since we still aren't quite comparing apples to apples (p. 68).
McCotter concludes his article on the following note:
This study shows that sometimes batters really may have a hot hand, or at least that they adapt their approach to try to keep a long hitting streak going -- and baseball players are nothing if not adapters (p. 69).
To the extent McCotter is claiming evidence for a relatively modest-sized hot-hand effect, subject to other possible interpretations, I would concur with him.
Saturday, January 10, 2009
The other night, the Arizona State men's basketball team exploded for a 20-0 run en route to routing Oregon State, 69-38 (play-by-play sheet).
After the Beavers' Lathen Wallace made a layup to narrow an early ASU lead to 19-15 with 5:29 to go in the first half, the Sun Devils ran their advantage up to 39-15, until Wallace scored again with 14:23 left in the second half, to break the streak. In fact, for almost exactly a 20-minute stretch (from 9:49 remaining in the first half to 9:32 remaining in the second half) Wallace was the only Beaver to score!
As many readers will be aware, Oregon State has a new coach this year, Craig Robinson, who is the brother of Michelle Obama. The ASU debacle notwithstanding, Robinson is showing some early signs of giving Beaver fans "change they can believe in." OSU was 0-18 in Pacific-10 play last year, and this year has already beaten USC.
After the Beavers' Lathen Wallace made a layup to narrow an early ASU lead to 19-15 with 5:29 to go in the first half, the Sun Devils ran their advantage up to 39-15, until Wallace scored again with 14:23 left in the second half, to break the streak. In fact, for almost exactly a 20-minute stretch (from 9:49 remaining in the first half to 9:32 remaining in the second half) Wallace was the only Beaver to score!
As many readers will be aware, Oregon State has a new coach this year, Craig Robinson, who is the brother of Michelle Obama. The ASU debacle notwithstanding, Robinson is showing some early signs of giving Beaver fans "change they can believe in." OSU was 0-18 in Pacific-10 play last year, and this year has already beaten USC.
Tuesday, January 06, 2009
Happy New Year to everyone! Please pardon my lack of timeliness, but back on Christmas Day, Shaquille O'Neal recorded the dubious career milestone of missing 5,000 free throws. Wilt Chamberlain is the only other member of this club.
Though O'Neal has carried a well-deserved reputation throughout his career as a disaster at the stripe (detailed here), strange things can happen when one plays as many games as he has (somewhat over 1,000, coming into this season).
As stated on O'Neal's official NBA biography page, he "was a perfect 13-13 from the foul line against Denver on Apr. 17, establishing a career high for most free throws made in a game without a miss" in the 2000-01 season (this is the only perfect free-throw shooting game by O'Neal, with a large number of attempts, I'm aware of, but I can't rule out the existence of others; he also once had a 16-of-18 game ).
For his career, O'Neal has been around a 52% free-throw shooter. His probability of pulling off a perfect 13-for-13 free-throw performance purely by chance (i.e., under an independence model) can therefore be estimated by raising .52 to the 13th power, which yields .0002. This probability is somewhat smaller than O'Neal's (apparent) actual rate of flawless nights from the line -- once in roughly 1,000 games -- but not all that different. Phil Maymin comes up with some similar calculations here.
Maymin's article makes an important point regarding the symmetry of extreme tails on the normal, bell-shaped curve: "If Shaq takes, for simplicity, about ten free throw attempts per game, then it would take one thousand games before he either made or missed all ten" (my emphasis added). In fact, O'Neal once had an 0-for-11 free-throw game (again, I can't be sure that he hasn't had additional all-miss games from the stripe).
I hope readers will forgive me for not looking up box scores from all 1,000-plus O'Neal games and creating a frequency distribution of game-specific free-throw percentages to compare to the normal curve. Based on this cursory review, however, Shaq's free-throw shooting appears consistent with coin-tossing.
Though O'Neal has carried a well-deserved reputation throughout his career as a disaster at the stripe (detailed here), strange things can happen when one plays as many games as he has (somewhat over 1,000, coming into this season).
As stated on O'Neal's official NBA biography page, he "was a perfect 13-13 from the foul line against Denver on Apr. 17, establishing a career high for most free throws made in a game without a miss" in the 2000-01 season (this is the only perfect free-throw shooting game by O'Neal, with a large number of attempts, I'm aware of, but I can't rule out the existence of others; he also once had a 16-of-18 game ).
For his career, O'Neal has been around a 52% free-throw shooter. His probability of pulling off a perfect 13-for-13 free-throw performance purely by chance (i.e., under an independence model) can therefore be estimated by raising .52 to the 13th power, which yields .0002. This probability is somewhat smaller than O'Neal's (apparent) actual rate of flawless nights from the line -- once in roughly 1,000 games -- but not all that different. Phil Maymin comes up with some similar calculations here.
Maymin's article makes an important point regarding the symmetry of extreme tails on the normal, bell-shaped curve: "If Shaq takes, for simplicity, about ten free throw attempts per game, then it would take one thousand games before he either made or missed all ten" (my emphasis added). In fact, O'Neal once had an 0-for-11 free-throw game (again, I can't be sure that he hasn't had additional all-miss games from the stripe).
I hope readers will forgive me for not looking up box scores from all 1,000-plus O'Neal games and creating a frequency distribution of game-specific free-throw percentages to compare to the normal curve. Based on this cursory review, however, Shaq's free-throw shooting appears consistent with coin-tossing.
Sunday, December 28, 2008
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.
Saturday, December 27, 2008
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.
Sunday, December 21, 2008
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).
*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).
Thursday, December 18, 2008
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.
Tuesday, December 02, 2008
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.
...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.
Friday, November 28, 2008
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.
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.
Sunday, November 23, 2008
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.
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.
Tuesday, November 18, 2008
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.
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.
Saturday, November 01, 2008
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).
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).
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