4 ms·

No, the author is not assuming that. And in fact the opposite is true. The assumption is that your performance on any given race is some combination of luck a

by btilly 8y ago

No, the author is not assuming that. And in fact the opposite is true. The assumption is that your performance on any given race is some combination of luck and ability. If you perform extremely well, it should be assumed that both were in your favor that time. The next time you'll still have whatever ability is in play, but you are unlikely to have luck. The result is that your performance is likely to be good, though not stellar. You racing one day or the next are not independent events - your ability creates a correlation. But your performance one day is also not a linear prediction of your expected performance the next. This is called regression to the mean. It comes into play in everything from stock picking to poker players.

Jtsummers 8y ago
To diagram it out: a = ability l = luck p = performance a l \ / \ / v p Each (ability and luck) has a contributing factor. Your ability is more likely to be consistent (within some stretch of time). Your luck is less consistent. So if you average a 7 minute mile, and you somehow run it in 6, unless your fundamental ability has changed it was luck (weather, mental state, wear on your shoes) that pushed you so far outside your norm, and you should anticipate returning to your average in the future.
- antidesitter 8y ago
  What is “luck” supposed to mean in your diagram?
  - Jtsummers 8y ago
    Any contributing factor outside your base ability. Weather (too hot, too cold, just right), mental state (did someone put you on edge, sleep poorly), etc. So some of those are more or less under your control. Maybe you can control your mental state better than me. Me, a particularly stressful day at work doesn't lend to the quiet mind I need for a run. Those are my 36 minute 5km days. But nicer weather, seeing the geese on the pond as they migrate, can put my mind at ease even on those stressful days and I might pull off one of my faster runs. I can't control that.
    - ZephyrP 8y ago
      so performance is ability plus the contribution of all other factors that are not ability. tough to argue with that one.
      - Jtsummers 8y ago
        I mean, we can break out luck to be all the various factors. But it can be summed up into one (for the purposes of this discussion). And each of those will still have some mean that they tend toward. The weather, outside San Diego, isn't going to be perfect year round. Your relationships (impacting mental state) won't all be rosy. Your sleep can be interrupted by a neighbor moving in at 3am. Though that last one is atypical. And if it happens, and your race time is 8 minutes instead of the average of 7, you should still expect to be closer to 7 the next race barring similar misfortune.
      - retsibsi 8y ago
        I think the main point is that performance depends on some factors that we can reasonably expect to remain constant between races ('ability'), and others that are likely to vary quasi-randomly between races ('luck'). Those names are imperfect but the underlying logic is sound: the winner of a race is relatively likely to have both high 'ability' in himself, and higher 'luck' than usual for that particular race. In the next race, his 'ability' will remain high, but he will probably have roughly average luck.
  - jimhefferon 8y ago
    Consider children of immigrants. Look at the ones who are tall, taller than their parents. Are they tall because they got good nutrition, etc.? Many people supposed that they have natural tallness genes and their parents were only shorter because of tough times in the old country. Now look at their children, the grandchildren of the immigrants. They tend back toward average. The tall kids were tall because, in part, there is a natural variation and they happened to get on one side of the bell curve. Luck, if you will.
antidesitter 8y ago
You are committing the gambler’s fallacy. There’s no reason to expect your “luck” (whatever you mean by that) to decrease rather than increase the next time you race. This is different from saying that you are likely to win again. You’re just as likely to win as you were the first time around, which may be high or low depending on ability.
- Jtsummers 8y ago
  Drop out the ability part. Let's focus on a pure luck scenario: Take 2 dice (2d6) and roll them. You get a 12. What is more probable on your next roll? Another 12 or a 7? With regard to the race, if you do really well, much better than your average, without any fundamental change to your ability that's the same as rolling a 12. It's an unlikely (though possible) event that happened to occur. Over a series of races, however, we would not anticipate a repeat of that performance (that is, it's a low probability event, and a series of such low probability events has even lower probability). The gambler's fallacy goes the other way. It's the belief that if we've had a string of bad luck [0], then we should wager on good luck being around the corner. That is, the gambler assumes a low probability event is "inevitable" after a series of high probability events. Regression to the mean: A high probability event should be anticipated after a low probability event. [0] In gambling this usually means getting close to the average, that is: the average hand is the lowest valued hand, the rarest hand is the highest valued. So a gambler making this fallacy would wager on seeing a royal flush after several hundred hands of only seeing pairs.
  - antidesitter 8y ago
    I understand what the GP was saying now (see my sibling comment). The gambler’s fallacy can apply the other way, e.g. “This die has rolled over 3 many times, so it will probably roll 3 or lower next time.” So that's not really the issue. Your dice example is not illustrating the point the GP is trying to make. It’s just comparing the probabilities of two outcomes of the same distribution (the sum-of-two-dice distribution). This has nothing to do with the selection effect the GP is talking about. That would be recording the value of the die that rolled highest (i.e. taking the maximum over dice) and then focusing on the same die next time (i.e. not taking the maximum over dice). It’s comparing the probability distribution of max {X_1, X_2, X_3, ...} with the probability distribution of any individual X_i. If A is sampled from the former and B is sampled from the latter, P(B < A) > P(B > A).

by btilly 8y ago

Jtsummers 8y ago

To diagram it out: a = ability l = luck p = performance a l \ / \ / v p Each (ability and luck) has a contributing factor. Your ability is more likely to be consistent (within some stretch of time). Your luck is less consistent. So if you average a 7 minute mile, and you somehow run it in 6, unless your fundamental ability has changed it was luck (weather, mental state, wear on your shoes) that pushed you so far outside your norm, and you should anticipate returning to your average in the future.

antidesitter 8y ago
What is “luck” supposed to mean in your diagram?
- Jtsummers 8y ago
  Any contributing factor outside your base ability. Weather (too hot, too cold, just right), mental state (did someone put you on edge, sleep poorly), etc. So some of those are more or less under your control. Maybe you can control your mental state better than me. Me, a particularly stressful day at work doesn't lend to the quiet mind I need for a run. Those are my 36 minute 5km days. But nicer weather, seeing the geese on the pond as they migrate, can put my mind at ease even on those stressful days and I might pull off one of my faster runs. I can't control that.
  - ZephyrP 8y ago
    so performance is ability plus the contribution of all other factors that are not ability. tough to argue with that one.
    - Jtsummers 8y ago
      I mean, we can break out luck to be all the various factors. But it can be summed up into one (for the purposes of this discussion). And each of those will still have some mean that they tend toward. The weather, outside San Diego, isn't going to be perfect year round. Your relationships (impacting mental state) won't all be rosy. Your sleep can be interrupted by a neighbor moving in at 3am. Though that last one is atypical. And if it happens, and your race time is 8 minutes instead of the average of 7, you should still expect to be closer to 7 the next race barring similar misfortune.
    - retsibsi 8y ago
      I think the main point is that performance depends on some factors that we can reasonably expect to remain constant between races ('ability'), and others that are likely to vary quasi-randomly between races ('luck'). Those names are imperfect but the underlying logic is sound: the winner of a race is relatively likely to have both high 'ability' in himself, and higher 'luck' than usual for that particular race. In the next race, his 'ability' will remain high, but he will probably have roughly average luck.
- jimhefferon 8y ago
  Consider children of immigrants. Look at the ones who are tall, taller than their parents. Are they tall because they got good nutrition, etc.? Many people supposed that they have natural tallness genes and their parents were only shorter because of tough times in the old country. Now look at their children, the grandchildren of the immigrants. They tend back toward average. The tall kids were tall because, in part, there is a natural variation and they happened to get on one side of the bell curve. Luck, if you will.

antidesitter 8y ago

You are committing the gambler’s fallacy. There’s no reason to expect your “luck” (whatever you mean by that) to decrease rather than increase the next time you race. This is different from saying that you are likely to win again. You’re just as likely to win as you were the first time around, which may be high or low depending on ability.

Jtsummers 8y ago
Drop out the ability part. Let's focus on a pure luck scenario: Take 2 dice (2d6) and roll them. You get a 12. What is more probable on your next roll? Another 12 or a 7? With regard to the race, if you do really well, much better than your average, without any fundamental change to your ability that's the same as rolling a 12. It's an unlikely (though possible) event that happened to occur. Over a series of races, however, we would not anticipate a repeat of that performance (that is, it's a low probability event, and a series of such low probability events has even lower probability). The gambler's fallacy goes the other way. It's the belief that if we've had a string of bad luck [0], then we should wager on good luck being around the corner. That is, the gambler assumes a low probability event is "inevitable" after a series of high probability events. Regression to the mean: A high probability event should be anticipated after a low probability event. [0] In gambling this usually means getting close to the average, that is: the average hand is the lowest valued hand, the rarest hand is the highest valued. So a gambler making this fallacy would wager on seeing a royal flush after several hundred hands of only seeing pairs.
- antidesitter 8y ago
  I understand what the GP was saying now (see my sibling comment). The gambler’s fallacy can apply the other way, e.g. “This die has rolled over 3 many times, so it will probably roll 3 or lower next time.” So that's not really the issue. Your dice example is not illustrating the point the GP is trying to make. It’s just comparing the probabilities of two outcomes of the same distribution (the sum-of-two-dice distribution). This has nothing to do with the selection effect the GP is talking about. That would be recording the value of the die that rolled highest (i.e. taking the maximum over dice) and then focusing on the same die next time (i.e. not taking the maximum over dice). It’s comparing the probability distribution of max {X_1, X_2, X_3, ...} with the probability distribution of any individual X_i. If A is sampled from the former and B is sampled from the latter, P(B < A) > P(B > A).