In what situation should the U1 umpire check the location of R2 after a fly ball is caught?

The situation in which the U1 umpire should check the location of R2 after a fly ball is caught occurs when there is a runner on second base and less than two outs. This is important because if a fly ball is caught, the runner on second must decide whether to tag up and attempt to advance to third base or stay put. With fewer than two outs, the strategic implications of this decision can change, as the runner has to be cautious of getting doubled off if they don't successfully tag up and the defense makes a play.

Additionally, in such scenarios, the U1 is responsible for ensuring that the runner is aware of the situation and is properly adhering to the rules regarding tagging. When there is a runner on second and less than two outs, the possibility of a force play at the next base or a straightforward tag becomes relevant, making it crucial for the umpire to monitor the runner’s position closely. This attentiveness helps maintain the flow of the game and ensures that all players are following the rules.