Actually no, the projectiles hitting the target and the damage they do is what counts. If we look at an individual event, in this case a timed burst of fire e.g. one second, the important factors are probability of a strike, which is the probability of a strike per projectile calculated with the number of projectiles fired, and probability of damage given a strike, in this case the 20mm being three times more effective than the .50 cal
Here is a repeat of my post on another thread comparing the F-86 to the F9F in firepower, reformatted.
I did run a few simple probability calculations on probability of number of strikes given the probability of a strike for 47 r/sec (F9F) vs.125 r/sec (F-86). This is for a one second burst. Two 20mm rounds are used as a reference.
For 2% probability of a strike per projectile:
Out of 47 attempts, the F9F has a 24% probability of 2 or more 20 mm rounds hitting.
Out of 125 attempts, the F-86 will have 4 or more 50 cal rounds hitting (24%).
For 5% probability of a strike per projectile:
Out of 47 attempts the F9F has a 69% probability of 2 or more rounds hitting.
Out of 125 attempts, For slightly better probability, the F-86 will have 5 or more rounds hitting (75%).
For 10% probability of a strike per projectile:
Out of 47 attempts the F9F has a 96% probability of 2 or more rounds hitting.
Out of 125 attempts, the F-86 will have 7 rounds hitting (97%).
Obviously, the more round fired the higher the probability of hits. As shown here, for increasing probability of hits, the F-86 will deliver more hits, from 2x at 2% probability of a hit to 3.5x at 10%. As the planes get closer, or the pilot more accurate, or the aircraft more stable, etc, the advantage moves in the F-86's direction. As the planes move farther apart, the advantage moves to the 20mm. However, for any distance, the probability of equal hits always falls in favor to the F-86.
Given the Navy analysis of one 20mm equal three .50s, at about 5% probability of strike (five projectiles hitting out of one hundred), the F9F and F-86 are roughly equal in fire power, below 5% probability of strike, the F9F delivers more damage, above that, the F-86 is more effective, at least according to probability.
It also must be noted here that one poster pointed out that the armament of the F-86 is lighter than the F9F, although a couple of seconds less in firing time. Equal being equal, both are probably equal in weight per firepower. I did not check his numbers.
It is apparent to me that the six M-3 machine gun battery on the F-86 was reasonably equal in effectiveness and weight to the four M-2 cannon on the F9F, and for the Korean War, was as state-of-the art as the 20 mms, not just a "tweaked", old gun. I think the claim that the Korean War F-86 was under-gunned is a myth.