To me it's a perfect logical premise that confidence and comfort levels in clutch situations have *some* variance from one player to another.
I think you have admitted to the existence of other psychological factors:
1) The biggest job of the manager is off the field, keeping his players loose and ready to play. All psychological.
2) Some hitters tend to be more comfortable in certain spots in the batting order, and it's not a good idea to mess with their heads. All psychological.
3) Some pitchers are more comfortable working with some catchers than others. Some of which may relate to actual skill factors, but much of it is psychological.
And yet you totally reject the premise that some players handle pressure moments better than others.
What data supports the first two propositions above?