A lot of the probabilities I give, especially in the most competitive races, are pretty easy to understand. Rep. Bruce Braley's odds of beating Joni Ernst in the Senate election in Iowa (48%) are no better than a coin toss. Secretary of State Alison Lundergan Grimes's chances of unseating Sen. Mitch McConnell in Kentucky (12%) are about the same as the odds of flipping a coin three times and getting three heads. But some of them are a bit tougher to grasp, especially in the safest seats. If we say, for example, that Shenna Bellows has less than a 1% chance of defeating Sen. Susan Collins in Maine, you should be getting two things from that statement:
- Because the page is only so wide, we can't include all of the decimal places needed before we start seeing numbers that aren't zero. That's how low her chances are.
- Her chances, however, are not zero. There is always the outside chance that she can win; very little in the world is 100% certain. The only candidate who is 100% assured of victory this year is Sen. Jeff Sessions, who is unopposed by any candidate. Even if he drops dead in the time between when I finish typing this sentence and when I click "publish", Alabama voters don't have the option to vote for anyone else. (Someone would be appointed to fill his place and then a special election would take place, probably next year, but the now-late Sen. Sessions would still be elected.)
But again, it's hard to get a real-life grasp on how low those chances are. FiveThirtyEight gets around this by using sports analogies in its "A Probabilist Equivalent From The Sports World" segment, where Messrs. Silver and Enten use a (presumably familiar) sporting statistic, such as "The GOP’s current chances of taking the Senate, 57.6 percent, are the same exact chances the New England Patriots had of winning Super Bowl XLVI against the New York Giants with eight seconds left in the first half."
I have two problems with this, though. Problem #1 is that I'm not a sports guy, so I understand what he's saying even less than I did before he gave the analogy (although that's more a personal problem). Problem #2 is that the probability is near-meaningless unless it's A) greater than the arbitrary 95% confidence threshold statisticians and social scientists agreed on somewhere down the line or B) reporting a statistic that can be reproduced in repeated experiments. That sports analogy is neither; presumably that example means that in situations resembling whatever it is he just said, the team in the Patriots' position won 58% of the time. It can't be repeated, and even if some games come close to it the sample size isn't large enough to make that kind of probabilistic statement down to the decimal point.
I do, however, love myself some poker, so I find it easier to express these probabilities in terms of poker hands. This has some nice side effects, the first of which is that poker hands, being drawn from a fixed deck of cards, have expected probabilities predicted purely by math; we know that the probability of drawing any particular poker hand is 1 in 2,598,960. Second, poker as a game can be simulated and has in effect been simulated over the millions and billions of hands that have been played in its history. Not only can you calculate probabilities mathematically, you could also theoretically observe them, given the patience.
For your amusement, here are some results I picked out:
I have two problems with this, though. Problem #1 is that I'm not a sports guy, so I understand what he's saying even less than I did before he gave the analogy (although that's more a personal problem). Problem #2 is that the probability is near-meaningless unless it's A) greater than the arbitrary 95% confidence threshold statisticians and social scientists agreed on somewhere down the line or B) reporting a statistic that can be reproduced in repeated experiments. That sports analogy is neither; presumably that example means that in situations resembling whatever it is he just said, the team in the Patriots' position won 58% of the time. It can't be repeated, and even if some games come close to it the sample size isn't large enough to make that kind of probabilistic statement down to the decimal point.
I do, however, love myself some poker, so I find it easier to express these probabilities in terms of poker hands. This has some nice side effects, the first of which is that poker hands, being drawn from a fixed deck of cards, have expected probabilities predicted purely by math; we know that the probability of drawing any particular poker hand is 1 in 2,598,960. Second, poker as a game can be simulated and has in effect been simulated over the millions and billions of hands that have been played in its history. Not only can you calculate probabilities mathematically, you could also theoretically observe them, given the patience.
For your amusement, here are some results I picked out:
