Thank you for your hard work.
About the conversation - I'd take it as meaning "since we patrol faster, every part of the city is unwatched in shorter periods, meaning altercations don't always have time to escalate into fights before the guards arrive and can begin defusing the situation" and "since we have more endurance, the patrols ain't very tiresome, so we have more energy left to actually pay attention to our surroundings and notice things that are beginning to go awry"
(All of which is also shown, not only told, through the example of a beginning bar brawl being stopped before the first fist flies)