Punting would hand GB the ball at or around their own 20 yard line, worth 0.71 WP for CHI.
A successful conversion means a 1st and 10 at CHI's own 33, which would give CHI a Win Probability (WP) of 0.79. And a failed conversion attempt gives GB the ball at the CHI 32, worth 0.51 WP for CHI. [That's a relatively high-leverage situation--a potential swing of 0.28 WP.]
The break-even conversion probability (x) required to make it worthwhile to go for the conversion can be found by setting the value of the punt equal to the total value of the conversion attempt:
0.71 = x * 0.79 + (1-x) * 0.51
x = 71%
x = 71%
Fourth and 1 situations in that region of the field can typically be expected to be converted 74% of the time. So the total value of the go for it option was 0.72 WP, and going for it was defensible as the percentage play, but only by a hair.
The Bears went on to score a FG, killing 7 more minutes of game clock and leaving the Packers with only 50 seconds and no timeouts to try to tie the game with a desperation TD drive.
A few notes: I would always prefer to tell a coach 'Here is your break-even conversion probability...and by the way, the league average conversion rate is this,' rather than simply saying the model says go or the model says punt. This approach arms the coach with information rather than trying to replace his judgment.
The only criticism I have of Trestman is that CHI burned a timeout deciding what to do. In a one-score game at that point in the 4th quarter, timeouts can be worth a percentage point or two of WP. So by burning the timeout, CHI forfeited the slight advantage going for it offered.
Whenever possible, coaches should be prepared to make the 4th down decision before it arises. They can delegate the job to someone in the booth. For example, for each series a team has possession, someone in the booth can have a 'go for it on x or less yards to go' ready for the head coach and OC. This can be overruled of course, but it saves time and more importantly, timeouts.
One last observation--Note how muted the analysis was of the decision. Imagine the uproar if CHI failed to convert and went on to lose.