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As a sports fan, I have a problem with this statement: '...picking the number "7" implies that number 8 got on base.' Most of the time, at least when it comes

by bjplink 16y ago

As a sports fan, I have a problem with this statement: '...picking the number "7" implies that number 8 got on base.' Most of the time, at least when it comes to sportscasting, picking the number 7 implies that's the total number of batters faced up to that point. You don't say a batter has gone 2-for-3 through 6 innings when they really went 2-for-4. When a guy is doing baseball play-by-play he doesn't say the "last 5 of 7 batters" and mean there were more than seven total and he's just choosing not to tell you about them. Look at the kid who had a hit in every college baseball game he played this season. His hit streak was 56 games long before his team was eliminated from the post-season. If his streak ends during the first game of next season, they won't go on Sportscenter the next day and say he's gotten a hit in 56 of his last 56 games and try to hide the fact that he didn't get a hit in game #57. Last night, during the Celtics-Lakers, game they mentioned that Ray Allen was 0-16 on three point attempts since his last make and that he was cold. No one would sanely argue he wasn't having a tough time shooting but I'm sure a math nerd could explain this away with a large enough sample size of shot attempts over a longer stretch of time then one playoff series. But the point of a streak is that it's based on a finite set of recent attempts. No one is saying Ray Allen is statistically a bad shooter (he's actually one of the best in the history of the game) but you can't argue that in recent games he's shooting poorly from distance. It doesn't get much worse than making 0% of your shots.

dionidium 16y ago
No one would sanely argue he wasn't having a tough time shooting but I'm sure a math nerd could explain this away with a large enough sample size That's exactly what I would argue. I think the math nerd is right. Given consistent shot mechanics, we'd expect occasional "streaks". Unless you're proposing that circumstances may change the shooter's mechanics, I don't get what you're saying. You don't say a batter has gone 2-for-3 through 6 innings when they really went 2-for-4 You're right that they don't do that sort of thing about a single game, but they say stuff like "last 5 of 7 batters" to refer to streaks across games all the time, which makes the example I quoted a straw man.
- bjplink 16y ago
  The math nerd would be right Ray Allen is a good shooter. You can look over the course of his career and verify that. But that's not the issue with streaks in sports. The issue is that Ray Allen isn't a good shooter right now. The idea that you "expect" something doesn't diminish its importance; especially when the Celtics need Ray Allen to hit threes to improve their chances of winning. They don't care that he's hit them in the past because previous scores don't count in current games.
  - dionidium 16y ago
    I think you're missing my point. The question is about why he is missing so many shots in this game. Is it because he's cold or is it for the same reason that flipping a coin sometimes results in a series of heads? When heads comes up ten times in a row, you don't say that the coin isn't a 50/50 coin right now.
- philwelch 16y ago
  "Unless you're proposing that circumstances may change the shooter's mechanics, I don't get what you're saying." You think circumstances don't change the shooter's mechanics? Consider that if a basketball player had perfectly consistent shot mechanics, and always shot from the same point on the court, he would always score. Shooting a basketball is a fairly deterministic ballistics problem--no wind since it's indoors, large target, large projectile. Thankfully, basketball gives us exactly that situation: free throws. The very best free throw shooters in the game only make 90% of free throws: http://www.basketball-reference.com/leaders/ft_pct_career.html http://www.basketball-reference.com/leaders/ft_pct_career.ht... A basketball player who makes 45% of three point shots isn't some sort of machine which has a 45% probability of sinking any given three-pointer, he's a human being who varies in terms of age, physical condition, fatigue, and even psychology. When betting on black loses at the roulette wheel 16 times in a row that's pure math--when a human being misses 16 straight three point shots, it's more likely he's mentally and physically tired and his mechanics are shot.
btilly 16y ago
I'll be that math nerd. His lifetime field goal percentage is 0.45. That means that in a string of 16 attempts, one time out of 14,000 or so he'll have 16 misses in a row. He's played over 1000 games, and in a typical game how many attempts does he have at a field goal? A bad run as long as the one you are citing is not that surprising. To settle the question, you have to collect more data and carefully analyze statistics. And when you do that, the data doesn't support the existence of streaks. But you don't believe those statistics. How to convince you? Well under your theory that there are streaks, you should expect to see record streaks out there that are longer than statistics would suggest possible. For instance if there are 500 players across time who've had a .45 field goal percentage, who've averaged 20,000 shots each, statistics says that the record streak of consecutive field goals made should be somewhere in the range 18-23 or so. If those people have even a slight tendency towards streaks on top of those percentages, you'd expect the length of the top streaks to get higher. If, during a streak, they shoot about .55, then under the same assumptions the top streak should be 25-30 or so. So we have a test. Look at the longest streaks and see if they are longer than expected. Not even a lot longer, just slightly longer will do. Lots of sports keep track of lots of player stats, and streaks. In a fascinating essay many years ago Stephen J. Gould pointed out that, across all sports tracked and all types of streaks records are kept for, all but one are within a statistically plausible range given the number of players, games, and their playing averages. The lone exception is Joe DiMaggio's 56 game hitting streak in 1941. That one is truly exceptional, a repeat is unlikely in the next thousand years. However when you look at the second, third, etc performances, they are in line with what statistics suggests is likely. Now what about this college kid that you were talking about? The answer there is interesting. College is played at a more varied level than the professional leagues. Therefore there is more variation in player performance. Exceptional performances become much more likely if you add even a small number of players who are hitting somewhat more reliably. So his streak is not as impressive as it may seem. Incidentally this applies to DiMaggio. When he played, pro baseball wasn't as consistent as it is today, so he was able to sustain stats that were above what you find in today's players. In fact http://online.wsj.com/article/SB10001424052970204556804574261942466979118.html http://online.wsj.com/article/SB1000142405297020455680457426... reports on a Monte Carlo simulation of baseball that used every historical player and season with their actual hitting percentages. Fully 42% of the simulated histories had a streak as long as DiMaggio's or longer. Therefore even a slight tendency towards streaks should show up clearly in the record books. But nowhere in the record books is there any streak that shows strong evidence of streakiness.

by bjplink 16y ago

dionidium 16y ago

No one would sanely argue he wasn't having a tough time shooting but I'm sure a math nerd could explain this away with a large enough sample size That's exactly what I would argue. I think the math nerd is right. Given consistent shot mechanics, we'd expect occasional "streaks". Unless you're proposing that circumstances may change the shooter's mechanics, I don't get what you're saying. You don't say a batter has gone 2-for-3 through 6 innings when they really went 2-for-4 You're right that they don't do that sort of thing about a single game, but they say stuff like "last 5 of 7 batters" to refer to streaks across games all the time, which makes the example I quoted a straw man.

bjplink 16y ago
The math nerd would be right Ray Allen is a good shooter. You can look over the course of his career and verify that. But that's not the issue with streaks in sports. The issue is that Ray Allen isn't a good shooter right now. The idea that you "expect" something doesn't diminish its importance; especially when the Celtics need Ray Allen to hit threes to improve their chances of winning. They don't care that he's hit them in the past because previous scores don't count in current games.
- dionidium 16y ago
  I think you're missing my point. The question is about why he is missing so many shots in this game. Is it because he's cold or is it for the same reason that flipping a coin sometimes results in a series of heads? When heads comes up ten times in a row, you don't say that the coin isn't a 50/50 coin right now.
philwelch 16y ago
"Unless you're proposing that circumstances may change the shooter's mechanics, I don't get what you're saying." You think circumstances don't change the shooter's mechanics? Consider that if a basketball player had perfectly consistent shot mechanics, and always shot from the same point on the court, he would always score. Shooting a basketball is a fairly deterministic ballistics problem--no wind since it's indoors, large target, large projectile. Thankfully, basketball gives us exactly that situation: free throws. The very best free throw shooters in the game only make 90% of free throws: http://www.basketball-reference.com/leaders/ft_pct_career.html http://www.basketball-reference.com/leaders/ft_pct_career.ht... A basketball player who makes 45% of three point shots isn't some sort of machine which has a 45% probability of sinking any given three-pointer, he's a human being who varies in terms of age, physical condition, fatigue, and even psychology. When betting on black loses at the roulette wheel 16 times in a row that's pure math--when a human being misses 16 straight three point shots, it's more likely he's mentally and physically tired and his mechanics are shot.

btilly 16y ago

I'll be that math nerd. His lifetime field goal percentage is 0.45. That means that in a string of 16 attempts, one time out of 14,000 or so he'll have 16 misses in a row. He's played over 1000 games, and in a typical game how many attempts does he have at a field goal? A bad run as long as the one you are citing is not that surprising. To settle the question, you have to collect more data and carefully analyze statistics. And when you do that, the data doesn't support the existence of streaks. But you don't believe those statistics. How to convince you? Well under your theory that there are streaks, you should expect to see record streaks out there that are longer than statistics would suggest possible. For instance if there are 500 players across time who've had a .45 field goal percentage, who've averaged 20,000 shots each, statistics says that the record streak of consecutive field goals made should be somewhere in the range 18-23 or so. If those people have even a slight tendency towards streaks on top of those percentages, you'd expect the length of the top streaks to get higher. If, during a streak, they shoot about .55, then under the same assumptions the top streak should be 25-30 or so. So we have a test. Look at the longest streaks and see if they are longer than expected. Not even a lot longer, just slightly longer will do. Lots of sports keep track of lots of player stats, and streaks. In a fascinating essay many years ago Stephen J. Gould pointed out that, across all sports tracked and all types of streaks records are kept for, all but one are within a statistically plausible range given the number of players, games, and their playing averages. The lone exception is Joe DiMaggio's 56 game hitting streak in 1941. That one is truly exceptional, a repeat is unlikely in the next thousand years. However when you look at the second, third, etc performances, they are in line with what statistics suggests is likely. Now what about this college kid that you were talking about? The answer there is interesting. College is played at a more varied level than the professional leagues. Therefore there is more variation in player performance. Exceptional performances become much more likely if you add even a small number of players who are hitting somewhat more reliably. So his streak is not as impressive as it may seem. Incidentally this applies to DiMaggio. When he played, pro baseball wasn't as consistent as it is today, so he was able to sustain stats that were above what you find in today's players. In fact http://online.wsj.com/article/SB10001424052970204556804574261942466979118.html http://online.wsj.com/article/SB1000142405297020455680457426... reports on a Monte Carlo simulation of baseball that used every historical player and season with their actual hitting percentages. Fully 42% of the simulated histories had a streak as long as DiMaggio's or longer. Therefore even a slight tendency towards streaks should show up clearly in the record books. But nowhere in the record books is there any streak that shows strong evidence of streakiness.