Exactly. No matter what outcome is observed, the probability of that specific outcome is going to be extremely low. The ignorant observer can grab any 6 year stretch, look at the results, and say "holy smokes! The odds of those exact results coming up are ridiculously low, so it must be rigged!" That is why statistical techniques exist to try and determine how far away the observed events are relative to the expected outcome.
In this case, it is worth noting that 3 WC's winning in a 7 year span is unusual. But it hardly rises to the level of statistical proof of anything. (The all-6-seeds-in-6-years thing is virtually meaningless)
The #1 thing working against our ignorant friend is the low sample size. When n=7, it's pretty tough to prove anything. 3 WC's winning in 7 years means nothing. But 30 WC's winning in 70 years would definitely get my attention.
No it's
not exactly that. Because ordering isn't even an issue in this case, but the mix itself. It wouldn't matter if its 123456, or 653421.
And the wild cards is not only unusual, its improbable and yet still more probable than all 6 seeds winning in the shortest possible time span, which again, actually has meaning.
For example the chances of a group of 1 and 2 following each other, in any order, is roughly 21%, depending on what exactly you want to use for homefield advantage. Or roughly once every 5 years. And sure enough, despite the small sample, it's happened at roughly that rate.
The chances of 1,2,3 following each other, in any order, in a 3 year span is roughly 3.4 percent, or once every 30 years. And sure enough it happened once in 30 years.
Even the chances of 6 #1 seeds
in a row, is actually not that improbable, since one would expect it to happen roughly once every 76 years, and in fact it already happened from 1982-1987. In fact the chances of 6 #1 seeds winning in a row is even more probable than seeing 5 #1 seeds and specifically 1 #2 seed, if you wanted to search for that, included in that same timespan. But less probable than 5 #1 seeds and any
other seed.
But after that, when you start mixing in lower seeds, and specifically all 6 seeds, things start dropping off dramatically. Again, if you look at the history, it should be pretty obvious where things stayed consistent with expectations and where things went haywire, without even doing any math.
And once again sample size, has nothing to do with the specifically rare probability of ever seen all 6 seeds winning the tournament in a 6 year time span. Which once again,
has meaning, and that meaning is basically perfect seed parity among Superbowl winners. If it happened twice, or three times or 4 times, and you wanted to see if it was in line with expectations you would need a very large sample. But that's not the argument here. The argument is that its very presence over
such a small sample size is incredibly, incredibly rare. It would be something someone would expect to see happen at a time interval of hundreds if not thousands of years. And yet it's already happened pretty soon after division reshuffles. This would be a small sample size, if we were trying to look for it, and
DIDN'T find it. But we're not searching for it. It's there. The question was what are the freaking odds?
Let alone, all the other unusual circumstances.
This is something the tournament is basically designed to PREVENT. And I didn't even include this year's results, #4 vs #3 which once again outcasted the #1 seed out of even appearing in a Superbowl, so it's continuing this bizzare deviation as well as the incredible run of underdog seeds which is now close to 90% in Superbowls over the past 13 years. This "perfect mix" of seeds that are taking place, is something someone would expect to notice if there was no bye week, no team strength and no homefield advantage. Or even something that came out of a round robin tournament, where seeding has little meaning in comparison to team strength.
But in this tournament, when it comes to making and winning the Superbowl, seeding is incredibly important. It's extremely important.
Or....it should be. Until something inexplicably changed and the lower seeds have dominated 86% of the matches over the past 13 years along with all of these other highly suspect patterns. Pretty crappy odds to keep fighting for that #1 and #2 seed.
PS: I also enjoyed watching a statistician pump his chest out and blow out nothing but ignorance while waving a diploma(it's kind of like strippers with an MBA) by assuming he's the smartest guy in the room or that he would intimidate a physics and math major. It's always cute. It's like a lightweight pumping his muscles. Then you have to do what every statistician does when comes time to show proof. Ask a mathematician. Or ignore, tuck your tail between your legs and run off. In your case, both.
