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The mathematical models do not take into account any variables, only hit rate VS capacity.
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First of all, calling this a model is very misleading because it doesn't attempt to model or simulate anything. It is not a model, it is a probability calculation based on some very simple assumptions and three variables. The calculation takes the following variables into account. Hit rate. Number of hits required for "success". Capacity.
It does do not take any other variables into account because that's all it's designed to deal with.
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I personally do EVERYTHING to improve hit rate...
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An excellent strategy. There's nothing in the calculation that suggests otherwise and much to indicate that strategy will increase the chances of success.
Maybe this is an easier way to think of what the graphs do.
They can't tell us if we will succeed. They can provide insight into scenarios where success is very improbable. They can give us an idea of what kinds of scenarios (based on the three parameters of hit probability, number of shots required and capacity) are "workable" and which ones aren't. They allow us to vary those three parameters to see how they affect the workability of the scenario.
If you look at the case where the number of hits required is 1, the capacity is 15 and the hit rate is 90%, the chance of "success" (making your 1 hit before the magazine runs dry) is essentially 100%. Does that mean you are guaranteed to survive a gunfight based on that scenario? NOT AT ALL! There are all kinds of way you could still be killed. Maybe your gun jams, maybe the guy hits you in the brain with his first shot before you can even fire. Maybe you slip and fall and injure yourself and end up a sitting duck. All the graph tells you is that if you fail to "win" the gunfight in that scenario, it's very unlikely that failure was the result of an unworkable combination of capacity, hit rate and the number of hits required. Something else was likely the cause of the failure.
Now let's look at the case where the number of hits required is 6, the capacity is 7 and the hit rate is 30%. We can see the chances of success are very close to zero from the graph. This tells us something very important. It tells us that we have set up an unworkable scenario. Even if we get to expend all our ammunition and everything else goes perfectly, the odds of succeeding in making all the hits we need are just about nil. If we think that this is a scenario we want to prepare for, then the graphs tell us that a 7 shot gun is a very poor choice. Well, how could we improve the situation? The graphs let us change the capacity to 15 to see if different hardware might get us out of the "doomed to fail" situation.
Unfortunately that only improves our chance of making all the hits we need before running empty to about a 3 in 10 chance of success--and that's if everything else goes perfectly. Still pretty bad. Now we should start thinking that maybe a person with the skill level to only make 30% of their shots in a gunfight is in a really, really bad situation if they need to make 6 hits. And it looks like that's true matter how much ammo they carry and even if everything else goes perfectly. We've gained some valuable perspective about the limitations imposed by our skill level and equipment choice.
Can we predict how a given real world gunfight will go? No. There are simply too many variables involved. But we can get a rough idea of what capacity level is workable for a given situation and what capacity level would put the defender seriously behind the 8 ball in that same situation or maybe even make it virtually impossible to succeed.