Percentage chance Edit
I'm aware the conditional is GetRandomPercent < 7.5, which sure looks like a 7.5% chance at first-glance, but that's not how GetRandomPercent works. In Fallout 4, as in all past Bethesda games, GetRandomPercent returns a random integer (so fractions aren't even possible) from 0 to 99 (not from 1 to 100). So, there are 8 integers out of the 100 possible (0, 1, 2, 3, 4, 5, 6, and 7) that can be returned that are less than 7.5. Thus, this is actually an 8% chance. The higher ranks adding 2% each time work the same way, ending up with a 14% chance, not the intended 13.5%.
I'm not good with math, so I can't calculate it directly, but this seems a questionable investment. Luck determines how many hit it takes to fill the critical bar, and at 9, the minimum to learn this skill, it's only 6 hits. So with a 14% chance per hit to fill the bar all the way, that's going to reduce the number of hits necessary by an average of, what, 2, and not reliably? Meanwhile, bumping your luck to 10 would reduce the total number of hits required to 5, resulting in a guaranteed improvement for 1 perk point versus spending 4. Of course, you can do both, but then the average decrease in hits necessary is even less. The first level gives an 8% chance, which may be worth it, but it seems mathematically unwise to invest more unless you seriously have nothing else to put your points into.