(Submitted by blog reader John Hordyk)
What are the chances the two teams (from states) that legalized pot, both made it to the Super Bowl?
I came up with on in 509,600 to 1.
Fifty states could have legalized pot, if you assume two would, you have a 2450 to 1 chance it would be those two.
Twenty-two states that have football teams, so a chance that it would be those two, this will take a little longer to figure out.
Two hundred eight to one chances it would be these teams, so.
509,600 to one chance the two teams that legalized pot would be in the Super Bowl?
Is that right?
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Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 230. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own sarcastic and hilarious commentary. Also, visit Barbara’s blog.
I think this is an interesting question, but I got a different answer from the author.
According to my calculations, there are 1225 ways to pick 2 from 50, so the chance of any two specific states legalizing pot (assuming that two would, which is a big assumption, but one we have to make) is 1 in 1225.If the Super Bowl teams were chosen at random (rather than performance), there are 231 ways to pick 2 from 22.We can then calculate the odds that both events will happen by multiplying them: .00082 x .00432 = .0000035.Pretty small! BUT… football teams making the Super Bowl and the passing of legislation like the legalization of pot are not random events. There are probably all kinds of factors which make these two things correlated, even if that correlation is extremely small. Even the smallest correlation can have a dramatic effect on the likelihood of the event.
Hey, drive-by posting cause I just heard this segment on the podcast. There are some other factors that affect the odds bit here, but I’m no statistician …
But it sounds like you calculated based on a pool of potential match ups — state-by-state, rather than team-by-team.
This makes a difference!
First, there may be twenty-two *states* with football teams but since only two teams out of the league’s 32 represent states where non-medical marijuana use has been legalized, a matchup between Denver and ANY other team, or Seattle and ANY other team, would not be “interesting” in the sense we’re looking at here.
It shouldn’t make a difference if some of the non-“interesting” teams share a state. After all, the numerical odds of a Denver/Seattle Super Bowl would still be the same even if ALL the other 30 teams were based in Wisconsin, or something. It’s a match of 2 pot-state teams out of 32 total teams.
Except it isn’t quite, because of the second part: The Super Bowl is a tournament, and the league is split into two conferences. No matter what happens in the regular season or in the playoffs, any team that wins the AFC championship can only face one of the 16 possible NFC champions in the final game, and vice versa.
So there were only *16* potential teams Seattle could have faced in the final — not 31 (the whole rest of the league), and not 21 (calculating by state) — all of which except Denver would have made the matchup “uninteresting”. The same figure applies to Denver’s potential matchups.
In light of the above … uh … I’m not sure how to work out the calculation. My best guess is just to say (16 possible AFC champs) * (16 possible NFC champs) = 256 potential Super Bowl pairings. Of which only one would be between teams from states with legalized marijuana.
Which isn’t that far off Barbara’s applying the “handshake formula” to 22 states and getting 231.
But still.