They do better in High Leverage Situations. Here is what their hitters do in all three cases in OPS
Now what the pitchers allow
So you can tell their differential is much better in High cases. But it is not like the bullpen is doing great. They allow an OPS of .796 while the starters allow .752. The bullpen also allows a higher SLG, .453 vs. .421.
They allow a .727 OPS in close and late cases while their hitters have .731. So no big deal there. Neither the hitters nor the pitchers do much different with runners on versus none on. But somehow they ramp things up in High cases.
The Rangers have grounded into 72 DPs while their opponents have 114. That gives them a good edge and maybe some of those are in key situations. On stealing and reaching on errors, there is not much difference between the Rangers and their opponents.
The Rangers have turned 50 DPs in High leverage cases. That leads MLB while the next highest has 42. The Rangers have grounded into 37 DPs in these cases. So they have a net of 13 here. That probably helps, but only a little.
Rangers also take the extra base running 45% of the time while the average in the AL is 40%
Sam Dyson, who has the most saves on the Rangers, has a save% of 90.9%. That is good, but it is only 7th in the AL for guys with 20+ saves (Dyson has 20). He has a 2.53 ERA and has allowed a .657 OPS. Those are good numbers but not great.