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> For instance, say you’re in a race at school. You do surprisingly well and beat most of your classmates. All things being equal, the next time around, you’re

> For instance, say you’re in a race at school. You do surprisingly well and beat most of your classmates. All things being equal, the next time around, you’re actually not likely to do as well, relative to the other runners. If the events are independent (as I believe the author is assuming at this point), then your performance in the first race has no effect on your performance in the next race, right? Maybe it's just a poor choice of wording, but it comes dangerously close to reinforcing a common misconception about probability (Gambler's fallacy).

CamTin 8y ago
If you have a competition where everyone flips coins, and you are eliminated as soon as you flip a tail, and you win, it's likely that you will also win the next time. This is not because the events are not independent, but because you are always unlikely to win. Likewise, if you get a royal flush in a hand of poker, you probably won't get as good a hand next time. Again, this is not because the deals aren't independent events, but because it is always unlikely to get a royal flush.
- astroalex 8y ago
  Good points. > Likewise, if you get a royal flush in a hand of poker, you probably won't get as good a hand next time. I understand what you mean, but I think that most people who haven't taken a probability class would misinterpret this. A sentence of the form "if [this] then [that]" is usually meant to express dependence. Don't you think that most people would interpret your sentence as: "Because I got a royal flush this time, I probably won't get one next time."? I think the average pop-sci article reader will get confused by this.
  - leetcrew 8y ago
    it's really hard to map subtle statements about probability to natural English sentences. pretty much any non-awkward formulation of that sentence is going to admit misinterpretations.
- antidesitter 8y ago
  > it's likely that you will also win the next time. This is... because you are always unlikely to win. Did you mean to write “it’s not likely that you will also win next time”?
  - CamTin 8y ago
    I did. Unfortunately the editing window is closed. Thank you.
buddhistan 8y ago
I don't think it's phrased to correlate the second outcome dependent on the first. That part of the article was referring to the racer regressing to their mean. With the assumption that they overperform in their first race based on the phrasing "surprisingly well", then the conclusion is still correct because the likelihood of them performing to their average performance level (whatever that may be) is still more likely than overperforming.
Someone 8y ago
I don’t see why you think that. Let’s say each of your classmates has a number of dice representing their innate ability, and rolls all of them. You have 5 dice, do surprisingly wel and roll four sixes and a four for a total of 28, beating some classmates who have 6, 7, or even 8 dice. If you repeat this, it’s unlikely you will do similarly well.
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.
nimonian 8y ago
I was surprised at this passage, too. It begins by quoting the Oxford dictionary, which always raises alarm bells that the author's ideas on the topic are inchoate, but the wording of the 'racing' example is an unforgivable blunder. The 'mean' referred to in 'regression to the mean' is the mean of the individual, not of the pack.

CamTin 8y ago

If you have a competition where everyone flips coins, and you are eliminated as soon as you flip a tail, and you win, it's likely that you will also win the next time. This is not because the events are not independent, but because you are always unlikely to win. Likewise, if you get a royal flush in a hand of poker, you probably won't get as good a hand next time. Again, this is not because the deals aren't independent events, but because it is always unlikely to get a royal flush.

astroalex 8y ago
Good points. > Likewise, if you get a royal flush in a hand of poker, you probably won't get as good a hand next time. I understand what you mean, but I think that most people who haven't taken a probability class would misinterpret this. A sentence of the form "if [this] then [that]" is usually meant to express dependence. Don't you think that most people would interpret your sentence as: "Because I got a royal flush this time, I probably won't get one next time."? I think the average pop-sci article reader will get confused by this.
- leetcrew 8y ago
  it's really hard to map subtle statements about probability to natural English sentences. pretty much any non-awkward formulation of that sentence is going to admit misinterpretations.
antidesitter 8y ago
> it's likely that you will also win the next time. This is... because you are always unlikely to win. Did you mean to write “it’s not likely that you will also win next time”?
- CamTin 8y ago
  I did. Unfortunately the editing window is closed. Thank you.

buddhistan 8y ago

I don't think it's phrased to correlate the second outcome dependent on the first. That part of the article was referring to the racer regressing to their mean. With the assumption that they overperform in their first race based on the phrasing "surprisingly well", then the conclusion is still correct because the likelihood of them performing to their average performance level (whatever that may be) is still more likely than overperforming.

Someone 8y ago

I don’t see why you think that. Let’s say each of your classmates has a number of dice representing their innate ability, and rolls all of them. You have 5 dice, do surprisingly wel and roll four sixes and a four for a total of 28, beating some classmates who have 6, 7, or even 8 dice. If you repeat this, it’s unlikely you will do similarly well.

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.

nimonian 8y ago

I was surprised at this passage, too. It begins by quoting the Oxford dictionary, which always raises alarm bells that the author's ideas on the topic are inchoate, but the wording of the 'racing' example is an unforgivable blunder. The 'mean' referred to in 'regression to the mean' is the mean of the individual, not of the pack.