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I believe the game actually calculates it somewhat like this, which is not unlike the real world:
When a ball is hit (let's say a ground ball), the game calculates the trajectory. The player tries to field it, and the first thing that comes into play is his range. If he has a high range, he has a better change of reaching a ball that isn't right at him. If he is within range, then he attempts to field it. The fielding % is the % chance he has at successfully fielding it. So, if he has a .990 fielding percentage, he has a 99% chance of fielding it.
Once he fields it, arm strength comes into play when he throws the ball to first. I'm sure that some sort of calculation determines how quickly the runner made it to first (based on the player's speed), and how long the throw takes to get there.
So, all 3 (arm strength, range, fielding %) factor into the calculation. But, such numbers are much more important, say, for a shortstop, who is going to field many more balls in a game than a pitcher.
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