Probability, Rap Sheets, and Police Brutality

Consider this thought experiment: In the city of Metropolis, the police force makes a secret pact to randomly beat senseless 1 out of every 100 people they arrest. Aside from this, they are a model police force. What sort of people would mostly get beat up?

Most of them would be frequent criminals with lots of prior arrests. Why? Because people who get arrested frequently get arrested frequently, and thus would have a higher chance of getting one of the 1% of arrests that included a senseless beating. Someone who's never been arrested would have zero change of a beating. Someone arrested once would have a 1% change. Someone arrested ten times a 10% chance.

If all you looked at was whether the person who got beaten was frequently in trouble with the law, and assumed that if the person was frequently arrested, then probably the beating was somehow justified, the random beatings would mostly look justified, and the beatings of people without prior criminal records would look very rare.

This isn't to claim that police brutality is in fact random, or that the police are never justified when using grave or even deadly force on someone. It's the nature of the job of the police to deal with situations which often require the use of force, and sometimes make it very difficult to know what's really going on. Mistakes that may look bad to outsiders may seem fairly reasonable to an officer at the time -- though with training and experience police departments try to reduce that as much as possible.

However, if even a completely arbitrary use of excessive force by police would end up being primarily used against people with frequent arrest records, one clearly can't simply take the existence of a long arrest record as proof that force was justified in some given situation.