There is no other team even close to being near to their rate of 187 offensive plays (passes+rushes+sacks) per fumble. The league average is 105 plays/fumble. Most teams are within 21 plays of that number.
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Which in layman’s terms means that this result only being a coincidence, is like winning a raffle where you have a 0.0000616 probability to win. Which in other words, it’s very unlikely that it’s a coincidence.
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As you can see, the Patriots won their Super Bowls having a below average rate of fumbles lost given today’s average of 105 plays/game. But in 2007, something happened to propel them to a much better rate (you’ll remember, that just so happened to be the same year they went 16-0 in the regular season). But even looking at these numbers, its clear how insane the 187 number is: they are almost running 100 MORE plays without a single fumble as compared to the 2002-2006 period when they won 2 of their 3 Super Bowls.