Opening the book…
A hard threshold creates a cliff in the payoff, and all the effort concentrates at the cliff edge: barely qualifying cases get pushed over, comfortable ones get parked, and anything hopeless gets abandoned. The resulting distribution bunches suspiciously just above the number while the underlying work is unchanged. Ranges and directions spread the incentive across the whole distribution instead of piling it at one point.
Say "keep resolution time trending down, and hold the ninetieth percentile between four and eight hours" rather than "95% under four hours." Reward improvement from wherever a team starts. When you must publish a figure, publish the distribution alongside it and look for a spike at the boundary — that spike is the first evidence of threshold gaming.
Genuine cliffs deserve thresholds: a legal limit, a capacity ceiling, a safety margin where one side really is categorically different from the other. Ranges are also weaker coordination devices, so if several teams must align on a single number, pick the threshold and accept the bunching.