Sure but what that gives you is the probability that at least 1 and no more than 3 leaders are created.

It doesn't tell you the most likely (expected) number of leaders that would be created per turn, which is 0

Your table gives all that information. Line one is the probability that zero leaders are created in any one run of sixteen CC DRs, 63.7 percent of the time. There's no point in adding it to the expected number of leaders created because .6372*0 = 0. Zero is the most likely number. It is also the median number. However it is not the expected number. The expected number is the sum of the number created times the chance of that number created. The expected number is 0.4444..., or sixteen divided by thirty-six. If in one-hundred player turns sixteen halfsquads attacked as described above, one would expect that forty-four leaders would be created.

To find the odds that at least one and no more than three leaders are created you sum lines 2-4, 0.2912… + 0.0624… + 0.0083…. This value is not particularly interesting to determining how "productive" (on average) the leader factory is because while it gives the probability, the "productivity" is probability times the value, i.e. the expected value. The value is, roughly, the percent of turns that at least one leader will be created, or put another way, the odds that one or more leaders will be created this turn. But you can get an exact answer by subtracting the probability that zero leaders are created this turn from one, i.e. 1 - 0.6372 = 0.3628 (approximately).

Similarly an event with a probability of one-tenth that produces ten leaders will

*on average* produce one leader per turn. On most turns (nine out of ten on average) it will produce zero leaders and on the tenth turn (on average) it will create ten. The event's median and most common values are zero, but its expected value is one.

JR