When is hypothesis testing necessary? (Or trying to figure out if the data I've been given comes from a population or a sample)
I've recently been getting into baseball statistics, and I'm trying to use what I know about stats to answer the question "how do we know if a player's hitting has fundamentally improved/gotten worse, or if they're just on a hot/cold streak?" from looking at their batting average (BA). I know it's reductive to equate "higher batting average" to "better hitting", since there's other stuff like SLG to quantify how impactful those hits are, but I wanted to start small with just one factor. For example, Samuel Basallo is currently hitting at 0.248 this season, while he finished last season hitting at 0.165. [https://www.baseball-reference.com/players/b/basalsa01.shtml](https://www.baseball-reference.com/players/b/basalsa01.shtml) Obviously 0.248 > 0.165, so it's true that his BA is higher this season. The thorny part is whether I can interpret this as the player being "better" than they were last season just from these numbers. The concern that I have is that it's possible that both of these BAs could come from the same underlying true batting average, but Basallo got really unlucky last season compared to this one. What I'm wondering is whether this concern is legitimate. If it is, then I'd use a hypothesis test. If it isn't, then I'd just say "this number is bigger than that one" and be done.
Essentially, is a players' BA in a previous full season a parameter or a statistic? If the populations being looked at are the ABs for a season, then it would suggest the season BA is a parameter, since it is found using every AB for that season. However, a theoretically infinite number of baseball games could be played, leading to a theoretically infinite number of ABs. So, if the population is all possible ABs for a player, then the ABs for a season would be a sample of this infinite population.
From the stats classes I took in school, it was always clear-cut when what I was looking at was a smaller portion of some whole. Polling was the go-to example for proportions since it's impractical to get the opinions of everyone in a country with hundreds of millions of people. For means, the go-to was quality control tests, where some batch of product appears outside a given specification, and you use the stats test to see if the machine's broken or not. You use inference tests there because it might not be economical to test every product that comes off the line.
However, with baseball, you're given information about every game played. Again, it comes down to not being sure whether "every at-bat for a player in a season" describes a population or a sample. It also doesn't help that I'm trying to use these descriptive statistics to make a (possibly non-descriptive) claim about a player's performance mid-way through a season. For a more concrete example, Ben Rice's BA was 0.255 in 2025 and it's currently 0.279 for the 2026 season. [https://www.baseball-reference.com/players/r/ricebe01.shtml](https://www.baseball-reference.com/players/r/ricebe01.shtml) Again, it's obvious that 0.279 > 0.255, so his batting average for this season right now is higher than it was for the entirety of the 2025 season. But does this mean he's gotten better at hitting the ball since last season, or has he just gotten lucky?
It seems silly to ask questions about whether using ABs from every game played in a season is specifically a simple random sample, or if the varying factors between games and seasons even make BAs across seasons reasonably comparable using something like a two-sample z-test for proportions, when I'm not even sure if I should even be using a hypothesis test in the first place.
Any answers or clarifications would be appreciated.