Sample size is completely irrelevant.
You misunderstand the problem here. People aren't using sample size as a measure of champion health. People are using sample size as a way to say that the winrate stats aren't accurate, and they're absolutely correct.
A very basic rule of statistics is that whenever you take a very small sample of a population, you are opening up your results to a huge amount of random variance. If I'm only looking at 37 games, it's impossible to know if the results are due to champion strength, or just luck. It's very likely that in a large percentage of Irelia's 37 games, there just happened to be a feeder playing, while Akali's games didn't have any. If they had 1,000 games played, I couldn't make that claim because it would so improbable as to be redicious, but over 37 games, I absolutely can claim that this, or any other random factor, produced the results.
When you have more samples, random luck stops being such a large factor, because the probability of luck being a definitive factor in the results gets closer and closer to 0 as you increase the size of the sample.
Hell, if we were so inclined, we could mathematically show you how unreliable these results are.