Statistical Food for Thought

Let's say, purely theoretically, that there is a bad officiating crew. This crew is so bad that that they make 4 egregious calls per game. There are two teams involved, which means that one teams wins each call and one team gets burned on each call.

We're next going to proceed with the apparently outlandish assumption that this officiating crew is merely bad and not potentially employed by the possibly racist family of the theoretically fictional Corleone family and their possible/likely alien connections.

The odds that your team will get the short end of the stick on any given egregious call is 50%.

The probability for each set of outcomes for the 4 calls are below:

The basic argument for conspiracy theorists is usually that the probability of the event in question happening completely by chance is so astronomical that there is another, more likely (and nefarious) explanation. They rely on the fact that humans are generally bad at judging risk associated with rare events, which has some interesting outcomes. Often, it is difficult to truly disprove the conspiracy theories because it's difficult to give accurate estimates of probability when the events are so incredibly rare.

This is not one of those cases. An event happening 6.25% of the time means it will happen in 1 in 16 times. College football teams play 12-13 games per year. If you think all officiating crews make egregious calls at a rate of 4 per game, then your team will have all of the bad calls go against them roughly once a year. If you think it's half the crews, then about once every 2 years. If you think it's just 2 of the 10 Big 12 officiating crews that do this, then it will happen roughly once in five years.

These are all estimates. It's entirely possible that you make it through a full year without one of these rare, bad luck events happening to you. Who knows, you may even be incredibly fortunate in the setting of other institutional advantages and not have one of these rare, bad luck games happen to you for years or decades.

That would seem rather fortunate indeed. But who knows, this is just a little fun theoretical exercise...