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You're boiling it down to a 1 in 4 chance, all else being equal of course - that is, if we view it from a Pats perspective, what does our seeding mean for our chances?
As others have pointed out, first seed's the best odds that you can get, which of course was never argued in the OP.
However, look at what you're saying -- as an AFC 1st seed you have "only" a 1-in-4 chance of winning it all.
There are 4 teams with byes in general, and it makes sense that 1sts are in better shape than 2nds, because the only possibilities are equal or better records than the 2nds.
So your 1 in 4 chance basically works out, very roughly, to the elimination of the other 8 teams from consideration (4 are literally eliminated before the 1st seed plays.)
So although all the permutations remain possible, getting the first seed, if we are to trust the small sample, puts you into a "final four" scenario, in terms of the odds -- a week before you even get there.
This also illustrates the uselessness of the exercise, because it comes down to playing a game, winning it, playing a game, winning it, and of course, playing a game, and winning it.
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Of the 42 teams that have MADE the Super Bowl in the last 21 years, 32 of them had a first round bye. That is 76.2%.
Of the 42 teams that have MADE the Super Bowl in the last 21 yeas, 20 of them have been a #1 seed. That is 47.6%.
Of the 21 teams that have WON the Super Bowl in the last 21 years, 15 of them have had a first round bye. That is 71.4%.
Of the 21 teams that have WON the Super Bowl in the last 21 years, 9 of them have been a #1 seed. That is 42.9%.
Those are more significant stats than simple AFC vs NFC.
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If you're looking to answer the question "what is the effect of seeding," I think looking at super bowl champions by seed number is of very little relevance. The super bowl is a fixed location, fixed date game where seeding is irrelevant with respect to your opponent. Your opponent will be whichever team survived the playoffs on the other side, and whether you are a 1 seed or a 6 seed, you will get the same opponent and play in the same building.
The only advantage of a higher seed is that you might have played one less game, and thus be fresher and/or had one fewer games to sustain injuries. So, it might be mildly interesting to look at how teams that had a bye on their half of the bracket fare against teams that did not in the super bowl. But otherwise, I think asking the question whether seeding increases your chances of winning or not winning the super bowl is not a hugely productive question. (This is not to say there isn't a correlation -- seeding is often a proxy for how good you are. Probably not as good a proxy as whether you made it through your side of the bracket, but a proxy nonetheless. Thus, when a one seed plays a six seed in the super bowl, there are reasons to expect the one seed will be favored, notwithstanding the fact that the six seed has won 3 hard games in a row; but again, that's a much different question.)
So, long winded way of agreeing with other posters that the relevant question is not to look at champions by seed number, but to look at seeding's effect of a team's chances to make the super bowl, or, to put it another and more accurete way, win the half of the bracket in which there is seeding.
To ask that question, I agree with others that say you should start with a baseline. If you take away seeding and the three main advantages/disadvantages that come with it -- home field advantage, bye, and the wear and tear (or possibly, on the other side, momentum) effect of playing or not playing the extra game -- what would among evenly matched teams be of making the super bowl?
From a 1 and 2 seed's perspective, you play as though there are 4 teams in the bracket, so it should be 25 percent. From a 3-6 seed's perspective, you play as though there are 8 teams in the bracket, so it should be 12.5 percent.
Looking at the 21 years of stats, though a small sample size, you see a huge correlation between seeding and advancement to the super bowl. The 1 seed makes it 47.6 percent of the time. The two seed makes it 28.5 percent of the time. The other 4 seeds combined make it 23.8 percent of the time.
But, of course, to answer the question that I think is being asked by this thread -- what effect does seeding have on advancement, you have to account for the fact that there are two things happening here -- the higher seed has an advantage because of the seed, but also is likely a better team by virtue of its ability to earn that higher seed. How much of the deviation from the baseline is caused by the former and how much the latter?
Tough to know. One way to maybe judge would be to figure out how often the 1 seed plays the 2 seed in the conference championship and figure out stats by seed in those games. When the 1 plays the 2, most of the advantages to seed are stripped away -- both teams had a bye, both teams got to play the first game at home, and thus until that point they were equal in terms of advantage. The only remaining advantage that seeding provides is home field advantage for the one seed. There are pretty comprehensive and well-settled stats for home field advantage in the NFL, so it should be possible to normalize for that, and figure out whether these games are basically played at even (when discounting HFA) or whether there is actually typically a talent gap between 1 and 2.
My take away from the whole thing is that looking to question of how seeding affects chances to make the super bowl, it's pretty much what people alreayd expect -- Getting the bye is hugely important and it is much more likely than not that one of the bye teams will make the super bowl. There appears to be a pronounced difference between how often the 1 and 2 seeds make the super bowl, but it's a pretty small sample size and it's tough to judge very much without stats on how 1 plays 2 when they meet.