in the meantime, they continue to do whatever it is that makes them an HPT in the first place, i.e. call fire on your HVT's (High Value Targets) or shoot down your aircraft.
Greater than 99% for a battery isn't good enough for you?
Your point of them "continuing to do whatever" is apropos. By devoting an entire battalion per target, when you have three targets to engage, you are allowing the second target an extra three minutes to do "whatever" and the third target an extra six minutes to do "whatever". Is nine full team-minutes of "whatever" an acceptable price to pay for gaining much less than one percentage point on an already overwhelming likelihood of destruction from a battery?
If you're really worried, target them with two volleys from the battery in a slightly open sheaf. If by some amazing bit of bad luck you fail to get them the first time, your second volley will still catch them, even if they do start moving. You can cancel the second volley if, as is most likely, the first volley does get them.
The actual, raw number is that each DPICM round has a 2% chance of killing a tank. So, if you drop over fifty rounds, 50 X 2%, you should, statistically, have 100% chance of killing the tank... hypothetically, there were 3 tanks, parked hub-to-hub, motorpool fashion, and you dropped 50 rounds on them, statistically, all three should be destroyed.
NOOOOOO! :hurt: :dead:
Sorry. Its just that you're killing me with this horrible misinterpretation of basic statistics. What you just said is equivalent to the following:
"I have a coin. I flip it twice. Since the chances of getting a heads result is 50%, and I flipped it twice, I therefore have a 100% chance of getting a heads result."
Clearly, that's just not true. It is, of course, completely possible that you will get two tails in a row. In fact, you have only a 75% chance of getting at least one heads result.
When you are conducting a number of trials, each with the same probability of success, each trial is random and unaffected by the success of prior trials, and you are looking for at least one success but don't care about additional successes (you can only kill a target once, after all) then you are working with what is called the "binomial distribution."
The problem with using simple addition is that you are "double-counting" successes. Consider the coin flip. You're going to flip it twice, and you want to see one heads result. The first flip has a 50% chance of producing what you want. So does the second. But, here's the important point: because the first flip has a 50% chance of success, the second flip has a 50% chance of being completely irrelevant; half the time, you will have already gotten the desired result. So, the second flip adds to the total success probability 50% of 50%. Adding a third flip obeys the same rules, i.e. it adds to the cumulative probability 50% of 50% of 50% for a total probability of 87.5% of getting at least one heads result. And so on. The essential point is that there will never be 100% probability. It will approach insanely closely as the number of trials increases, but will never quite get to that "guarantee" you're looking for.
You can also look at it from the opposite angle, which might be simpler for some. Multiply together the probabilities of *failure* instead to get the overall chance of failure for all trials together. Subtract from 100% to get the odds of at least one success.
So, for example, in the DPICM vs. dismount case, the odds of failure for a battery are 33% ^ 6, or 0.1291467969%. The odds of failure for a battalion are 33% ^ 18, or 0.0000002154%. So, committing those extra 12 tubes is buying you a whopping 1/7 percentage point improvement over a battery.
Still think its worth it?
As for the tank question, I already covered that in the prior post. 54 rounds would have about [1 - (.98 ^ 54 )] * 100 = 67% chance of killing a specific tank. The odds of killing all three tanks parked motor-pool style would be about ( .67 * .67 * .67 ) * 100 = 30%.
Now, if you fired 1,000 rounds at 1,000 tanks, you would have >95% chance of killing about 20 randomly selected tanks out of the group (1000 * .02 = 20.) But, as I said, that is a totally different question than asking what will happen with a relatively small number of rounds fired at a specific target.
This may sound like a lot of numeric wanking, but since artillery is essentially a game of statistics, I think the fundamentals are fairly important to understand.
--- Kevin
