Quote:
Originally Posted by Ace Gunner
it's fourteen season of data -- why is that not a large enough sample size? also, this is an abstract comparison, but to say the number of games is going to change the final conclusion is nuts, imo.
14 x 16 = 224 games, that's a good sample size. when all teams are included, the size increases to 224 x 16 = 3,584 games which is more than enough sample data imo.
if you reduced the numbers in each sport to 3,584 games, I don't think these charts will change much, really. in fact, it may make football even more varied, by comparison.
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The limiting sample size is 16 games per season. A team's record in a given year is a random variable that is some function of the underlying True Strength of the team. People that don't think statistically tend to equate the team record and the True Strength.
Think of it this way: if Tiger Woods hit two golf balls twice in a row under exactly the same conditions, they might land somewhat close to one another but not exactly in the same exact spot. There is some randomness that factors into his golf swing. In an NFL game there are probably millions of these golf-ball sized random variations. So if the Chiefs were able to replay all of their games this season, they would not finish 9-0 every time. There are enough random variations in any given game to allow the outcome to change if it were to be "replayed". If we would represent the Chiefs on the graph they would be 9-0. However if we replayed their season 100 times I suspect that on average we would be about 7-2. This is my guess of our True Strength. So if the season were now over, and we were to play another 9 game season in a year we would not necessarily expect the Chiefs to win 9 games again even if the rosters all remained in tact and the schedules were exactly the same. We'd expect some random variation. If next year the Chiefs went 5-4 with the same exact conditions, it wouldn't be that surprising. To a large degree we just don't know how good the Chiefs really are.
On the other hand if the Chiefs and played 160 games so far this season and had won 155 of them, we would know the Chiefs are really, really good. We would be shocked if a year from now they kept the same roster, every other team kept the same roster and we played the same schedule and went 90-70. Over a 160 game season the record will be a much better indicator of a team's True Strength than a 16 game season.
That is why the variance of MLB will have a smaller variance than the NFL, and why sample size matters.