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It depends on the context. Hillary Clinton had a >70% of winning the US presidential election according to the most responsible analyses (see 538: https://proj

It depends on the context. Hillary Clinton had a >70% of winning the US presidential election according to the most responsible analyses (see 538: https://projects.fivethirtyeight.com/2016-election-forecast/ https://projects.fivethirtyeight.com/2016-election-forecast/). Most folks took 70% to mean that she would certainly win and were bitterly disappointed the morning after. On the other hand no sane person would (willingly) play Russian roulette with a 70% or even 5 of 6 chance of "winning". In everyday life, one conflates probability with severity of outcome. This is normal and is part of how people assess and act on risk in a qualitative way.

lifeisstillgood 8y ago
That's probably the first time I have mapped Russian Roulette odds to percentages - and 83% chance used to look pretty good. Now I understand Robert Downey Jrs maths skills in Kiss Kiss Bang Bang.
- sp332 8y ago
  Pascals' Wager: multiply the odds by the cost or benefit of each outcome. The higher the potential cost, the less good your odds look even if the percentage is the same.
  - oculusthrift 8y ago
    Not sure what that has to do with Pascal’s wager? This is just basic “expected value” in probability terms.
    - lifeisstillgood 8y ago
      The cost of "believing" in God, near zero, the expected value if correct - huge :-) Plus wasn't it pascal who invented expected value?
      - sp332 8y ago
        And the negative side: eternal damnation in hell (which he valued at -infinity) times a very very small chance, still means it's worth putting in whatever work to be righteous. And yes he was the inventor.
        krapp 8y ago
        Pascal's Wager assumes the only God that can possibly exist is the Judeo-Christian one, and that the Bible is correct in its description of what that God wants, and of what awaits those who fail Him. But logically, if any one God can exist, then so might any God or set of Gods from any pantheon, including sets never even conceived of by human beings. Since the evidence of any one God over another is the same (zero, it's entirely a matter of faith,) the benefit of belief in any one God over another is also zero, since the set of all possible Gods is infinite.
        sp332 8y ago
        Yeah there's a real difference between a very small but still finite chance, and an infinitesimally small chance. If you're trying to multiply negative infinity by reciprocal infinity, you have to be specific about how big each infinity is. :)
smallnamespace 8y ago
> In everyday life, one conflates probability with severity of outcome Probability * (new status - old status) = Expected Payoff
DINKDINK 8y ago
>Hillary Clinton had a >70% of winning the US presidential election Probabilities without confidence intervals[1] are by-and-large meaningless (She has a 90% chance of of winning with a confidence interval of +11% -100%). No amount of d3.js on 538's blog will change this. https://en.wikipedia.org/wiki/Confidence_interval https://en.wikipedia.org/wiki/Confidence_interval
- OscarCunningham 8y ago
  From a Bayesian perspective, or from a betting one, it doesn't make sense to put probabilities in a confidence interval. You might be uncertain about the world, but you can be certain about how much uncertainty you have, since it's a property of your own mind.
  - fragsworth 8y ago
    How do we quantify the difference between coin tosses, which we are very certain is 50% likely to end up heads, from political elections, where we only have a few examples to go off of?
    - edbaskerville 8y ago
      In terms of predicting what's going to happen next, it really isn't that different if your model's any good. Looking backwards, if the 2016 election had been determined by two coin tosses both coming up heads, would we be surprised? And yet 538's polling model indicated that the probability was even better than two coins coming up heads. They probably should have just written that right there: "71%, better odds than two coins coming up heads." But: in order to understand if the model is any good, you need to try to build a good model, describe your model, and describe what you know about the underlying processes. With words, visuals, and math. Which is pretty much what 538 does better than most.
    - OscarCunningham 8y ago
      Good question. The difference is how the probability changes in response to new information. Learning more about the coin won't change the probability of heads from 50%, but doing more exhaustive polls would have likely improved our prediction about the election. However I don't think there's as much of a difference as you think. If we learnt more about how the coin was going to be flipped then that would certainly improve our estimate of the outcome. If we found out the exact way it would be flipped we could calculate the outcome exactly. So we can't really compare the two situations quantitatively, since there's no way to match up like-for-like the information we could receive. But we can say, for each possible piece of information we could receive, how much we expect it to change our probability.
moolcool 8y ago
The analysis after the elections was interesting-- think pieces asking things like "How could the stats have been so wrong?!". A fair dice has a roughly 83% chance of landing on a number between 1 and 5, but if you roll a 6 you don't ask yourself the same question.
- albertgoeswoof 8y ago
  People are mixing up % of vote with likelihood of victory. If she was polling at 70% that would be an almost 100% chance of winning because a 20% swing is unlikely. However a 70% chance of victory is much much closer.
  - Izkata 8y ago
    Exactly right, and you can see the polling percentage on the linked page; scroll down to "How the forecast has changed" and click the almost-looks-like-a-button "popular vote"; it was bouncing around 46-48% Clinton and 40-44% Trump (and 5-8% Johnson).
  - moolcool 8y ago
    I'm talking about the fivethirtyeight 'percentage of winning'
denzil_correa 8y ago
> In everyday life, one conflates probability with severity of outcome In other terms, "Expected Value" can help in this case where you factor in the magnitude along with the frequency of occurrence.
evandijk70 8y ago
Most people, bookmakers and statisticians thought Hillary Clinton had more than 90% chance to win the electronisch - Nate Silver was aan outlier
- OscarCunningham 8y ago
  I think the betting odds were also around 70:30 on the day before the election. The newspapers were almost all way off though.
arendtio 8y ago
> In everyday life, one conflates probability with severity of outcome. My everyday example for that is the weather forecast and the question 'will it rain' often answered with a precipitation probability? - Probability: How likely is it that I will be hit by at least one rain drop - Severity: How many rain drops will hit me It sounds a little abstract, but whenever I see some everyday weather forecast I wonder what they are trying to tell me. At least 0% seems unambiguous to me :-)
- Infernal 8y ago
  From http://www.wesh.com/article/what-does-a-chance-of-rain-really-mean/4440726 http://www.wesh.com/article/what-does-a-chance-of-rain-reall... The "Probability of Precipitation" (PoP) describes the chance of precipitation occurring at any point you select in the area. How do forecasters arrive at this value? Mathematically, PoP is defined as follows: PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measurable precipitation, if it occurs at all. So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur (confidence is 100%), he/she is expressing how much of the area will receive measurable rain. (PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%) But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )
- caf 8y ago
  Some forecasts show both the "chance of any rain" as well as various percentiles of the expected rainfall amount, eg this one: http://www.bom.gov.au/places/vic/melbourne/forecast/detailed/ http://www.bom.gov.au/places/vic/melbourne/forecast/detailed...
- dionidium 8y ago
  If you ask Alexa, "will it rain today?" she'll respond, "it probably won't rain today" for any probability below 50%. I always thought this was an interesting and illustrative example. If there's a 40% chance of rain, I wouldn't in casual conversation say that, "it probably won't rain today."
gnicholas 8y ago
> no sane person would (willingly) play Russian roulette with a 70% or even 5 of 6 chance of "winning". That’s because there’s no upside to Russian roulette. Put some money on it, and people would be more likely to take the wager. In its standard form (as I understand it), the only benefit to winning is the rush from having played.
hanoz 8y ago
> Most folks took 70% to mean that she would certainly win and were bitterly disappointed the morning after. Surely, given the outcome, more of those folks were pleasantly surprised at the outcome than "bitterly disappointed".
- asfasgasg 8y ago
  Given that Clinton won the popular vote, and by a substantial margin, it is probable that more people were disappointed.
  - fjsolwmv 8y ago
    The margin was not "substantial". She didn't even get a majority of the vote.
- crispyambulance 8y ago
  Yeah, certainly "A LOT" of people were actually pleasantly surprised. From my point of view in Philadelphia, however, virtually everyone was disappointed modulo a few crazies or people who had been hiding under a rock or some closeted college republicans. This just goes to show how bifurcated America has become, people on opposite sides view the other side as incomprehensibly batshit-crazy and/or evil.
Reedx 8y ago
> according to the most responsible analyses (see 538: https://projects.fivethirtyeight.com/2016-election-forecast/ https://projects.fivethirtyeight.com/2016-election-forecast/) Yeah, it was amazing to see the storm of hate that poured down on Nate Silver as a result. Thousands of people calling him a fraud (and worse), saying they would never trust him again, etc. Even if he had said there was a 99% chance, that still leaves 1%!
- c3534l 8y ago
  What's worse is before the election, 538 was getting massive heat for over-estimating the likelihood of Trump winning. People see what they want to see and rewrite the history accordingly.

lifeisstillgood 8y ago

That's probably the first time I have mapped Russian Roulette odds to percentages - and 83% chance used to look pretty good. Now I understand Robert Downey Jrs maths skills in Kiss Kiss Bang Bang.

sp332 8y ago
Pascals' Wager: multiply the odds by the cost or benefit of each outcome. The higher the potential cost, the less good your odds look even if the percentage is the same.
- oculusthrift 8y ago
  Not sure what that has to do with Pascal’s wager? This is just basic “expected value” in probability terms.
  - lifeisstillgood 8y ago
    The cost of "believing" in God, near zero, the expected value if correct - huge :-) Plus wasn't it pascal who invented expected value?
    - sp332 8y ago
      And the negative side: eternal damnation in hell (which he valued at -infinity) times a very very small chance, still means it's worth putting in whatever work to be righteous. And yes he was the inventor.
      - krapp 8y ago
        Pascal's Wager assumes the only God that can possibly exist is the Judeo-Christian one, and that the Bible is correct in its description of what that God wants, and of what awaits those who fail Him. But logically, if any one God can exist, then so might any God or set of Gods from any pantheon, including sets never even conceived of by human beings. Since the evidence of any one God over another is the same (zero, it's entirely a matter of faith,) the benefit of belief in any one God over another is also zero, since the set of all possible Gods is infinite.
        sp332 8y ago
        Yeah there's a real difference between a very small but still finite chance, and an infinitesimally small chance. If you're trying to multiply negative infinity by reciprocal infinity, you have to be specific about how big each infinity is. :)

smallnamespace 8y ago

> In everyday life, one conflates probability with severity of outcome Probability * (new status - old status) = Expected Payoff

DINKDINK 8y ago

>Hillary Clinton had a >70% of winning the US presidential election Probabilities without confidence intervals[1] are by-and-large meaningless (She has a 90% chance of of winning with a confidence interval of +11% -100%). No amount of d3.js on 538's blog will change this. https://en.wikipedia.org/wiki/Confidence_interval https://en.wikipedia.org/wiki/Confidence_interval

OscarCunningham 8y ago
From a Bayesian perspective, or from a betting one, it doesn't make sense to put probabilities in a confidence interval. You might be uncertain about the world, but you can be certain about how much uncertainty you have, since it's a property of your own mind.
- fragsworth 8y ago
  How do we quantify the difference between coin tosses, which we are very certain is 50% likely to end up heads, from political elections, where we only have a few examples to go off of?
  - edbaskerville 8y ago
    In terms of predicting what's going to happen next, it really isn't that different if your model's any good. Looking backwards, if the 2016 election had been determined by two coin tosses both coming up heads, would we be surprised? And yet 538's polling model indicated that the probability was even better than two coins coming up heads. They probably should have just written that right there: "71%, better odds than two coins coming up heads." But: in order to understand if the model is any good, you need to try to build a good model, describe your model, and describe what you know about the underlying processes. With words, visuals, and math. Which is pretty much what 538 does better than most.
  - OscarCunningham 8y ago
    Good question. The difference is how the probability changes in response to new information. Learning more about the coin won't change the probability of heads from 50%, but doing more exhaustive polls would have likely improved our prediction about the election. However I don't think there's as much of a difference as you think. If we learnt more about how the coin was going to be flipped then that would certainly improve our estimate of the outcome. If we found out the exact way it would be flipped we could calculate the outcome exactly. So we can't really compare the two situations quantitatively, since there's no way to match up like-for-like the information we could receive. But we can say, for each possible piece of information we could receive, how much we expect it to change our probability.

moolcool 8y ago

The analysis after the elections was interesting-- think pieces asking things like "How could the stats have been so wrong?!". A fair dice has a roughly 83% chance of landing on a number between 1 and 5, but if you roll a 6 you don't ask yourself the same question.

albertgoeswoof 8y ago
People are mixing up % of vote with likelihood of victory. If she was polling at 70% that would be an almost 100% chance of winning because a 20% swing is unlikely. However a 70% chance of victory is much much closer.
- Izkata 8y ago
  Exactly right, and you can see the polling percentage on the linked page; scroll down to "How the forecast has changed" and click the almost-looks-like-a-button "popular vote"; it was bouncing around 46-48% Clinton and 40-44% Trump (and 5-8% Johnson).
- moolcool 8y ago
  I'm talking about the fivethirtyeight 'percentage of winning'

denzil_correa 8y ago

> In everyday life, one conflates probability with severity of outcome In other terms, "Expected Value" can help in this case where you factor in the magnitude along with the frequency of occurrence.

evandijk70 8y ago

Most people, bookmakers and statisticians thought Hillary Clinton had more than 90% chance to win the electronisch - Nate Silver was aan outlier

OscarCunningham 8y ago
I think the betting odds were also around 70:30 on the day before the election. The newspapers were almost all way off though.

arendtio 8y ago

> In everyday life, one conflates probability with severity of outcome. My everyday example for that is the weather forecast and the question 'will it rain' often answered with a precipitation probability? - Probability: How likely is it that I will be hit by at least one rain drop - Severity: How many rain drops will hit me It sounds a little abstract, but whenever I see some everyday weather forecast I wonder what they are trying to tell me. At least 0% seems unambiguous to me :-)

Infernal 8y ago
From http://www.wesh.com/article/what-does-a-chance-of-rain-really-mean/4440726 http://www.wesh.com/article/what-does-a-chance-of-rain-reall... The "Probability of Precipitation" (PoP) describes the chance of precipitation occurring at any point you select in the area. How do forecasters arrive at this value? Mathematically, PoP is defined as follows: PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measurable precipitation, if it occurs at all. So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur (confidence is 100%), he/she is expressing how much of the area will receive measurable rain. (PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%) But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )
caf 8y ago
Some forecasts show both the "chance of any rain" as well as various percentiles of the expected rainfall amount, eg this one: http://www.bom.gov.au/places/vic/melbourne/forecast/detailed/ http://www.bom.gov.au/places/vic/melbourne/forecast/detailed...
dionidium 8y ago
If you ask Alexa, "will it rain today?" she'll respond, "it probably won't rain today" for any probability below 50%. I always thought this was an interesting and illustrative example. If there's a 40% chance of rain, I wouldn't in casual conversation say that, "it probably won't rain today."

gnicholas 8y ago

> no sane person would (willingly) play Russian roulette with a 70% or even 5 of 6 chance of "winning". That’s because there’s no upside to Russian roulette. Put some money on it, and people would be more likely to take the wager. In its standard form (as I understand it), the only benefit to winning is the rush from having played.

hanoz 8y ago

> Most folks took 70% to mean that she would certainly win and were bitterly disappointed the morning after. Surely, given the outcome, more of those folks were pleasantly surprised at the outcome than "bitterly disappointed".

asfasgasg 8y ago
Given that Clinton won the popular vote, and by a substantial margin, it is probable that more people were disappointed.
- fjsolwmv 8y ago
  The margin was not "substantial". She didn't even get a majority of the vote.
crispyambulance 8y ago
Yeah, certainly "A LOT" of people were actually pleasantly surprised. From my point of view in Philadelphia, however, virtually everyone was disappointed modulo a few crazies or people who had been hiding under a rock or some closeted college republicans. This just goes to show how bifurcated America has become, people on opposite sides view the other side as incomprehensibly batshit-crazy and/or evil.

Reedx 8y ago

> according to the most responsible analyses (see 538: https://projects.fivethirtyeight.com/2016-election-forecast/ https://projects.fivethirtyeight.com/2016-election-forecast/) Yeah, it was amazing to see the storm of hate that poured down on Nate Silver as a result. Thousands of people calling him a fraud (and worse), saying they would never trust him again, etc. Even if he had said there was a 99% chance, that still leaves 1%!

c3534l 8y ago
What's worse is before the election, 538 was getting massive heat for over-estimating the likelihood of Trump winning. People see what they want to see and rewrite the history accordingly.