Is Coach Mack too cautious with foul trouble?

Your friend and mine Ken Pomeroy is filling his time in the non-basketball portion of the calendar by looking at foul trouble data from recent NCAA seasons. Today he's quantifying how coaches respond to foul trouble. I'll let him explain his methodology:

To make this as simple as possible, for each head coach I'm going to determine how often a starter with two fouls is on the floor in the first half... To make this happen, I'm using the last seven seasons of play-by-play data. I've sampled every game at each minute of the first half. For example, with exactly 19:00 left, I'm checking if there is a starter with two fouls and whether that starter is on the floor, then repeating this for 18:00 and each minute thereafter all the way to the end of the half.

Basically a lower ranking means the coach is more protective of his starters with two fouls, while the 1st ranked coach is just letting his guys hang in there and hoping for the best.

Coach Mack, somewhat surprisingly to me, falls right in the middle of the pack. Of the 2,065 first-half minutes where a Xavier starter had 2 fouls, Mack left the player with 2 fouls out there for 352 minutes. That equals about 17% of the time, good for 172nd of the 321 active coaches for whom data was available.

Mack seems really conservative to me, especially considering that Xavier plays the majority of its games at home. Officials are going to be loathe to stick a home starter with his third before the interval; Coach Mack could do to keep his starters out there a bit more, or at least not be letting foul trouble influence his subs as much.

The caveat here is Jalen Reynolds, who officials would gladly foul out before the first media timeout if given the opportunity. Protecting Jalen probably skewed the data a bit for Coach Mack.

Here's the data on the entire Big East:

Other than Dave Leitao, who has been around a long time in his own right, you can basically sort it by experience and get the same results. Coaches who have been around a while tend to protect their starters more. You're also seeing some really good coaches congregate near the bottom here.

I've long felt like a coach could gain an advantage by being more aggressive with his best players when they're in foul trouble. On the other hand, the data from the Big East seems to indicate the guys who really know what they're doing disagree with me. What do you think?