[Bongle]

Just having the percentages isn't really enough, you need to show that there is a statistically significant improvement over picking teams at random. That is, if I picked 18 teams at random, what is the variability of that group's retention rate?

Come to think of it, that's a pretty easy stats problem that I could do if it hadn't been 2 years since my last stats course.

So basically, you are choosing 20 teams at random, each of which has a 55% chance of succeeding. We are asking "what are the chances of 14 or more of them being retained?". So we have 20 independant trials, and want to know the chances that we will have 14 or more successes.

Probability(14 or more successes) = prob(14 successes) + prob(15 successes) + prob(16 successes) + prob(17) + ... + prob(20)

The binomial distribution can tell us the probability of a given number of successes:
prob(k successes out of n) = (n choose k)*(Probability of success)^k*(Probability of Failure)^(n-k)
Example: prob(14 of 20) = (38760)*(0.55)¹⁴*(0.45)⁶ = around 0.07.

Repeat that for 15,16,17,18,19 and 20, then sum to find the answer.

Answer: The probability that a randomly chosen set of 20 teams has 14 or more of them still in the competition is 12.9%. So this really isn't THAT unlikely. There are many numerical patterns (in fact, 12.9% of ALL patterns) you could pick that would have a similar retention rate. To show that your hypothesis of "Teams with patterned numbers retain longer" is more likely, pick more numerical patterns and see if the average retention rate is still high. If you can specify a picking pattern that results in a 70% retention rate after 50 or 100 teams, then the probability of something odd going on with those teams rather than random luck gets much higher.