4 ms·

I don't really understand the disagreement. The main disagreement seems to be that others say it increases the win probability by 12% assuming you score the nee

I don't really understand the disagreement. The main disagreement seems to be that others say it increases the win probability by 12% assuming you score the needed touchdown afterwards, and the author says that it's not really 12% because there's a 90% chance you won't score the touchdown? On its face, I tend to agree with the others that that's irrelevant. In the linked blog post with the actual statistics in it, she argues that it only increases your chance from 11.2% to 12.9%, so it only really increases your chances by 1.7%. But that just seems to be dishonestly reframing the numbers so people think a 1.7% absolute increase is nothing. But that really is a 15% increase in win chance. It sounds like the data says the 2 points is even better than its proponents claim? His only other argument is that failing the conversion psychs a team out, which I respect, but that's still just a bare assertion. I don't know why you'd get so mad at statistics for ignoring your feelings. People are complex and absent data otherwise, I would think it just as plausible that the added pressure and imminentness increases performance.

fluoridation 3y ago
>But that really is a 15% increase in win chance. No, that's dishonest. Probabilities are already ratios between magnitudes (desirable vs. undesirable outcomes), so when comparing them you should be subtracting them, not dividing them. A relative increase in probability of 15% doesn't tell you anything if you don't already know the base probability. Also, why go for the 15%? You could also say that the loss probability is reduced by 2%. But I guess you don't get a nice juicy number that way.
- peeters 3y ago
  If you are given the option of taking one lottery ticket or two lottery tickets, is it dishonest to say that taking two lottery tickets would increase your odds of winning by 100% over taking just one? Do you need to know the odds of a single ticket winning to make that claim? I think you're using a restrictive and non-standard interpretation of percentages. They can be used to convey overall probability, but also a change in probability. Only allowing one usage is just a communication deficit.
  - fluoridation 3y ago
    > If you are given the option of taking one lottery ticket or two lottery tickets, is it dishonest to say that taking two lottery tickets would increase your odds of winning by 100% over taking just one? Not in that particular case, because no one would believe in an increase of 100% (although it would still be preferable to say that it doubles your chances of winning). But if you're at a slot machine and you can put in an extra dollar for a 10% extra chance to win the jackpot, and in fact you chances increase from 0.001% to 0.0011%, would you think that's honest or scummy? >They can be used to convey overall probability, but also a change in probability. They can be. They shouldn't be used this way because it lends itself to miscommunication.
    - peeters 3y ago
      > But if you're at a slot machine and you can put in an extra dollar for a 10% extra chance to win the jackpot, and in fact you chances increase from 0.001% to 0.0011%, would you think that's honest or scummy Casinos in general are scummy, but I can't fault with the phrasing. What's the threshold at which the world is allowed to use percentages in the way they're meant to be used, without having to be accused of being dishonest?
      - fluoridation 3y ago
        IMO they should never be used this way period, or at least not without also indicating the values with and without the change. You'll be accused of being dishonest if you use a number that is convenient to your argument (e.g. "buying this is good value!") but which a significant number of people will interpret incorrectly.
    - datadrivenangel 3y ago
      You're right that in situations where you're still rounding to zero, talking about a 100% increased chance of winning is still basically zero. It's important to distinguish the scummy behavior from the actual statistical practices, as data literacy helps people see through numerical slight of hand.
    - 3y ago
- aidenn0 3y ago
  Win probabilities are not ratios between magnitudes of desirable and undesirable outcomes. They are the fraction of total possible outcomes that are desirable. Otherwise a 1/3 win probability would be 1/2 and a 9/10 win probability would be 9. One number never fully captures the reality. If I have a net worth of 1 penny and I earn a second penny, it is 100% true to say I've doubled my net worth. It also doesn't tell the full story. If a coach can take an action that would move the win probability from 0.01% to 1%, it would be malpractice to not do so, and correct to say they've increased their win chances by a factor of 100. It's also correct to say they're probably going to lose.
eitally 3y ago
I agree with you. She may be technically correct (the best kind!) but only in post hoc analysis of completed games. That should have 0 bearing on a coach's decision making during a game, since from the in-progress perspective it's still a 12.5% increase in win probability. So from a coach's POV, what's the worst that can happen: not getting the conversion and still losing by 1 (assuming :00 on the clock and no additional opponent possession). What's the best that can happen: tying and having an opportunity to play for the win in ensuing possessions.

fluoridation 3y ago

>But that really is a 15% increase in win chance. No, that's dishonest. Probabilities are already ratios between magnitudes (desirable vs. undesirable outcomes), so when comparing them you should be subtracting them, not dividing them. A relative increase in probability of 15% doesn't tell you anything if you don't already know the base probability. Also, why go for the 15%? You could also say that the loss probability is reduced by 2%. But I guess you don't get a nice juicy number that way.

peeters 3y ago
If you are given the option of taking one lottery ticket or two lottery tickets, is it dishonest to say that taking two lottery tickets would increase your odds of winning by 100% over taking just one? Do you need to know the odds of a single ticket winning to make that claim? I think you're using a restrictive and non-standard interpretation of percentages. They can be used to convey overall probability, but also a change in probability. Only allowing one usage is just a communication deficit.
- fluoridation 3y ago
  > If you are given the option of taking one lottery ticket or two lottery tickets, is it dishonest to say that taking two lottery tickets would increase your odds of winning by 100% over taking just one? Not in that particular case, because no one would believe in an increase of 100% (although it would still be preferable to say that it doubles your chances of winning). But if you're at a slot machine and you can put in an extra dollar for a 10% extra chance to win the jackpot, and in fact you chances increase from 0.001% to 0.0011%, would you think that's honest or scummy? >They can be used to convey overall probability, but also a change in probability. They can be. They shouldn't be used this way because it lends itself to miscommunication.
  - peeters 3y ago
    > But if you're at a slot machine and you can put in an extra dollar for a 10% extra chance to win the jackpot, and in fact you chances increase from 0.001% to 0.0011%, would you think that's honest or scummy Casinos in general are scummy, but I can't fault with the phrasing. What's the threshold at which the world is allowed to use percentages in the way they're meant to be used, without having to be accused of being dishonest?
    - fluoridation 3y ago
      IMO they should never be used this way period, or at least not without also indicating the values with and without the change. You'll be accused of being dishonest if you use a number that is convenient to your argument (e.g. "buying this is good value!") but which a significant number of people will interpret incorrectly.
  - datadrivenangel 3y ago
    You're right that in situations where you're still rounding to zero, talking about a 100% increased chance of winning is still basically zero. It's important to distinguish the scummy behavior from the actual statistical practices, as data literacy helps people see through numerical slight of hand.
  - 3y ago
aidenn0 3y ago
Win probabilities are not ratios between magnitudes of desirable and undesirable outcomes. They are the fraction of total possible outcomes that are desirable. Otherwise a 1/3 win probability would be 1/2 and a 9/10 win probability would be 9. One number never fully captures the reality. If I have a net worth of 1 penny and I earn a second penny, it is 100% true to say I've doubled my net worth. It also doesn't tell the full story. If a coach can take an action that would move the win probability from 0.01% to 1%, it would be malpractice to not do so, and correct to say they've increased their win chances by a factor of 100. It's also correct to say they're probably going to lose.

eitally 3y ago

I agree with you. She may be technically correct (the best kind!) but only in post hoc analysis of completed games. That should have 0 bearing on a coach's decision making during a game, since from the in-progress perspective it's still a 12.5% increase in win probability. So from a coach's POV, what's the worst that can happen: not getting the conversion and still losing by 1 (assuming :00 on the clock and no additional opponent possession). What's the best that can happen: tying and having an opportunity to play for the win in ensuing possessions.