I don’t really love WAR either, but it’s convenient!
I think having a high number of inherited runners relative to the league would be counter-value.
1) you usually have multiple relievers per game, but only 1 starter. A high strand count would mean your relievers are putting a lot of runners on the bases and not striking them out.
2) a high strand rate without count doesn’t tell you much either. 100% strand rate but only 2 inherited runners isn’t useful.
WPA Win Probability Added, and Leverage stats can give you some of that flavor. But they aren’t predictive or comprehensive. The Twins Bullpen ranked 11th in MLB in 2024 by WPA. Again it’s a cumulative stat, so fewer chances, less accumulation.
edit to add: The Twins scored the 4th most runs in baseball last year, blowouts don’t accumulate WPA, late and close does.
i really like WHIP as a stat I firmly understand and it tells me how well the pitcher took care of business. Fewer base runners per inning pitched is a good thing! Twins bullpen ranked 13 in 2024.