Can you help me identify the right test for my data?

I’m trying to identify the right statistical method to use. Here’s a case analogous to mine:

Let’s say I’m interested in whether basketball team A or team B is better at shooting free throws. I get 7 players from team A, and 8 from team B. I get them each to shoot a bunch of free throws (~200-600 each) and note how many each one attempts and makes.

I want to allow for a random ‘player effect’ while testing for a ‘team effect’. I also want to include another variable, let’s say the number of tattoos that each player has (which happens to be 0, 1, or 2 for the players in question).

What would be the simplest way to model this scenario and test whether ‘team’ has a significant effect on free throw shooting?

Thank you.
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