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.
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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.
Friday, November 28, 2008
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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