New England Patriots and Super Bowl luck

It looks like a good super bowl this year. I was hoping for Baltimore in the AFC championship game and they made it.

There's been some talk over the years about Tom Brady and Bill Belichick after losing their last two appearances. That makes them 3-2 in the big game. I think a lot of that talk is ill informed. Let's look at the modern Pats SB results

Year	Result
2001	beat St. Louis 20-17
2003	beat Carolina 32-29
2004	beat Philadelphia 24-21
2007	lost New York Giants 17-14
2011	lost New York Giants 21-17

Well the first thing you notice is how close the games were. Looking at the final scores they could all pretty much be described as toss ups. Now going 3-2 in "coin flips" is a pretty standard result. This table is the coin flips results.

Result	Likelihood Percent
0-5	3
1-4	16
2-3	31
3-2	31
4-1	16
5-0	3

hmmm so 3-2 is just about right. that might also help explain the Tom Landry Cowboys going 2-3 in the Super Bowl.

Another way to look at it is in terms of expectation. To do this we have to estimate the chance going into the game that the Patriots would win. In 2001 against the greatest show on turf Rams team they were an underdog. In 2007 coming in 18-0 they were a strong team and the favorite. Now there's some subjective guesswork in estimating their chances going into each game but here goes

Year	Pregame Chance of Winning
2001	30%
2003	60%
2004	55%
2007	75%
2011	60%

add them together and it comes to 2.80 expected wins. so again 3-2 is just about right