There's a lot of garbage statistics going around the internet regarding the Patriots, but I was just curious what the well-versed in statistics have to say about this.
The main question is - in what cases would distribution of season fumbles (y) by NFL team (x) be a normal distribution? In what cases would it not?
My thoughts are simply -- it would be a normal distribution if the fumble rate for each team per game/ season is equal (which is a big assumption).
It would appear less and less normal the more of an influence that non-random, independent factors --- such as player skill, play-calling, coaching, incentives, home field qualities, potential cheating, or whatever else -- had on fumble rates.
Is my thought process correct or not?
I've also heard a lot of people commenting that the distribution of fumbles per season by NFL team is actually a Poisson distribution.
I've dealt with Poisson distributions before, and this seems preposterous and completely off-base, though I could be wrong. Isn't a Poisson distribution usually uses in entirely different cases? I thought it was used for modeling when a call might come in within the next hour, or when a dice might come up 6 after N tosses. I can see this modeling fumble distribution of N plays, but comparing the NFL teams season fumbles?
Any ideas appreciated --- I'm not super into this media issue --- I'm barely into football -- I was more interested in the numbers. I don't even think the data in question here (that the Patriots fumble rate is an outlier) was even gathered or appropriated managed to answer the right question in any case.