Defending the technical calculations do not address the fact they are based on literally made up data.
They are not based on data at all, they are based on assumptions.
If you don't like the assumptions used, pick other assumptions (e.g. one orange and no bananas) and run the numbers for those assumptions instead. In fact, that's a great idea--run it for a wide range of assumptions--that's what I did to make the charts I posted in my first thread on this topic. Doing so will allow you to gain insight into how different assumptions change the probability of the desired outcome.
If that kind of insight is useful to you then you'll be better off for having done it. If you don't care about things like that then don't waste your time on it.
I'll try to explain what's going on with an example. Imagine that I'm designing a flood control system for a city. I want to know how my flood control system will handle 10 inches of rain in 24 hours so I run a simulation using standard, accurate, and accepted calculations. Then I run other simulations in inch increments from 5 inches of rain to 300 inches of rain in 24 hours. Now, without having to find any data at all about how much it is likely to rain on the city in a 24 hour period, I can still accurately answer questions about how the system is likely to handle various flooding scenarios. I now have a lot of insight into how the system will perform even though I've done no research at all into the rainfall data for the city.
I haven't done the research to determine if 300 inches of rain in 24 hours has ever happened, or could ever happen but I can still say what is likely happen if it DID happen. Likewise, when I started my test runs with 5 inches of rain, I'm not claiming that's the least amount of rain that could happen or that 5 inches of rain in 24 hours is likely to happen, but I am saying that IF it does happen now I know the likely outcome.
Now let's say someone keeps trying to assert that unverified "data" is being plugged into the algorithm. The fact is that NO data is being plugged in. Assumptions are being plugged in, and the results from a particular set of assumptions provide accurate insight into what would happen in that particular scenario--even if that scenario is unlikely to occur or even if it never happens at all.
In the same way, these calculations provide insight into the probability of various outcomes based on the input assumptions. A person can plug in a range of input assumptions covering the reasonable range of scenarios and gain insight into the outcomes.
So, now that you understand what's going on, what assumptions would you like me to run for you? Give me a few scenarios with reasonable hit rates, reasonable capacity numbers and the required number of hits for neutralization and I'll run the scenarios through the calculation so you can see the results.
...using probability formulas I dug out of my old college textbooks.
Your solution sounds more elegant than mine. I brute forced it with a spreadsheet that actually creates all the possible outcomes and then sums and weights the outcomes to get a final result. Not pretty, but accurate.
Again, the question is "how many rounds is enough" and you are trying to determine "enough for what?" The numbers are to quantify the "what."
Right. It's important to understand that they actually quantify sort of a best case scenario. There's nothing that tries to account for the possibility of being injured and having your hit rate degrade partway through the incident or maybe actually being unable to shoot your remaining rounds after that point. There's nothing that accounts for firearm malfunctions. There's nothing that accounts for fixating on a single attacker and continuing to waste shots shooting him even after he's been "neutralized" even though there's another attacker that needs "attention". There's nothing that accounts for being attacked in a way that doesn't even allow you to get to your gun and use it. There's nothing that accounts for the possibility that an attacker might be so hyped on adrenaline (or drugs) that he can soak up a whole magazine of solid hits (instead of just 2 or 3) and still keep coming.
In other words, there are many ways the outcome of a real world scenario with a determined attacker could actually be worse than the probabilities suggest. The probabilities just give you a feel for how things would play out, on average, if the outcome just boils down to what your hit rate is, how many hits you need, and how many shots you have on tap.
I can remember having the same thought when I finally got everything running. I thought that others might be interested in the outcomes and that's why I posted my first thread on this topic.
Obviously some people were interested, but posting the results opened my eyes in other ways. It appears that some people are very attached to their preconceptions.