Help with formula

[cartotech81]

I am pretty good at solving math problems as long as it is not a word problem. My problem is I have a word problem. This is not homework related, but still trying to wrap my head around it. I play a game and there is a way they calculate battles. What is given as an example is say you send a set of troops (could be any amount) that has a total offense 15,000 and the defense is at 20,000. The offense would lose 55% of their troops and the defense would lose 45% of their troops.

I have tried to figure out how they got these calculations but I am not sure. I thought maybe it would add the total of the two, then take 15K/35K to get losses on the one side, but that is only 43%. I am guessing their estimate could of just been averaged off, but want to get another opinion.

 

[JeffM]

I am pretty good at solving math problems as long as it is not a word problem. My problem is I have a word problem. This is not homework related, but still trying to wrap my head around it. I play a game and there is a way they calculate battles. What is given as an example is say you send a set of troops (could be any amount) that has a total offense 15,000 and the defense is at 20,000. The offense would lose 55% of their troops and the defense would lose 45% of their troops.

I have tried to figure out how they got these calculations but I am not sure. I thought maybe it would add the total of the two, then take 15K/35K to get losses on the one side, but that is only 43%. I am guessing their estimate could of just been averaged off, but want to get another opinion.

There are an infinite number of formulas that they might use, but probably only a few hundred that anyone sensible would actually use. Summing the weights, taking the ratio of the weights to their sum, rounding one to the nearest 5%, and finding the other as difference with 100% sounds like a good guess. You could test whether that is the probable formula by seeing whether it works on other weightings. Such a test may also determine whether the formula that you have come up with is a good approximation to whatever formula is actually being used.