I've always wondering whether barking and arguing with an umpire and/or getting booted out actually helps or hurts your team (or has no impact) during that game and/or the remaining games within a series.
Probably depends on the umpire. Some would say "f*ck this guy - barking in my ear about everything, he's not getting the benefit of the doubt", while others may get concerned it's become too uneven and try to balance things out? Others may be good at trying to remain impartial, not matter who's barking at them.
Interesting topic. But I'm not sure it's clear that managers should always be standing up for their team more.