I've been hearing the term "arbitrary endpoint fallacy" for years with regards to sports statistics, but google doesn't seem to think it's a thing outside of various sports message board posts. Hmm. You don't see any sort of potential logical problem with going back into the past, lopping off at an endpoint that makes the player look better than average, coming up with an explanation based on that endpoint, and going from there? If someone had asked you "What sample size would be the best way to judge how Felix Pie is doing right now," without looking, you would have never chosen "since May 1." So why choose it, other than to conveniently wedge the data into fitting the hypothesis? Anyways, you aren't sure what I'm arguing against? It's everything that sabermetrics has been about debunking: making assumptions based on poorly chosen samples, assuming that random variations must have some sort of explanation, and coming up with an individualized hypothesis that can't be examined for a larger body of players. It's certainly possible, but I'm not sure why we would project it based on the data at hand. If he has a hot streak, he ends up okay. If he has a cold one, he ends up looking awful again. There's definitely not enough real data to project a "trend" one way or the other. (And not relevant to the immediate point, but he's also being given a major platoon boost with his usage, making him look better than he is).