I went to a statistical physics talk about sports today

but I would say this about the model that I am talking about. It does not care about final scores and historically football actually had a lower rate of upsets as defined by the team with the poorer win % beating the team with the higher winning % so the idea that football inherently has better parity due to the nature of the number of scoring possessions made is not supported by the data. Interestingly enough Soccer and Baseball had the greatest parity of the five leagues analyzed, which might support your theory better with football being the outlier.

In general, the mean of a random variable can be any (real) number. See: http://en.wikipedia.org/wiki/Random_variable.

If we view the outcome of NBA games as a random variable, it’s a bernoulli random variable, with mean bounded between 0 and 1. See: http://en.wikipedia.org/wiki/Bernoulli_distribution. Because the outcome of games is always Bernoulli, the amount of variance in the outcomes is also quite limited.

I would define an upset in the following way: If X* is the underlying “strength” of team 1 and Y* is the underlying “strength” of team 2, an upset occurs if X>Y and team 2 beats team 1 (or if X and team 1 bests team 2). The proprotion of upsets comes from how the combination of X* and Y* map onto the outcome of the game.

I’d view both X* and Y* as random variables (since on some days some humans perform better than on other days). So, suppose X>Y, both are normally distributed with equal variance (sigma2)... you could use different distributions, but it doesn’t really matter.

The are three many factors that will determine the number of upsets, given these defenitions.

1) How close X* and Y* are to each other. Ceteris paribus, the closer X* is to Y* the more upsets (so long as they are not equal). This is simply the idea of teams with roughly equivalent skills are likely to be evenly matched; it’s probably what most people have in mind when they talk about parity. There are more upsets in the NFL than in college football because teams are

2) The size of the variance (sigma2). The larger the variance, the more upsets, ceteris paribus. Is basketball a game where your performance depends a lot on your mood? What you ate for breakfast? Whatever? I do not know. This is something I would need to think about. If you compare soccer to basketball, I’d think that the variance is greater because the process that generates points in soccer has more variation in than the process that generates points in basketball.

3) How many times the two teams play. It should be obvious that outcome of a playoff series is also a bernoulli variable, but there will be fewer upsets, ceteris paribus, in the playoffs than in any single game. This is the main reason that there are more upsets in the NCAA tournament than in the NBA playffoffs.

4) How many possessions in the game. As Engineering problem pointed out, the more possessions in a game, the higher the liklihood that the better team will prevail, ceteris paribus. The underlying principle is the same as in point three, but it’s probably not noticed as frequently… One of the major reasons that there a fewer upsets in the NBA than in the NFL is that there are far, far more possesions in NBA game than in NFL football. If an NBA game was 12 possessions, there were be far more upsets than we see today.

Changing the mean of a Gaussian distribution does not change the mean. If you have a decent random number generator you should be getting Gaussian distribution for large samples as that is the limit of Lorentzian distributions.