HOLF Players' Guild Forum

I am, at long last, getting around to some PATE revisions, and is my habit, I will discuss the changes on this forum for player views and comments. I reserve the right to make all decisions myself, but you all are fairly smart and experienced, and I have done well by incorporating as many of your views and suggestions as I can, and will continue to do so.

The first problem I want to discuss is damage in PATE battles. There have been a lot of complaints about this, most of them in one-sided battles, where the winning side seems to take a lot more damage than it should. Jim Voege, who I hope will be able to return to this discussion, argued strongly that damage needs to be settled first and victory second (which is the reverse of the way it's done in GITM, for which Jim said it was correct). Having looked at the code carefully, however, I think the problem is slightly different. The problem is that the way damage is calculated is flawed. There is an initial damage level for the winning fleet, which I think is being set well; the problem is that actual damage to each ship is not closely linked to the damage level for the fleet as a whole. The reason is that in Napoleonic naval battles, some ships sink and others get away scot-free. That is, the amount of damage taken by each ship in the battle has a high variance. (If it doesn't, then in a large fleet action, either a) Every ship on the losing side sinks and every ship on the winning side takes 3 damage points but none sink, or b) Every ship on the losing side take 4 damage points but none sink, and every ship on the winning side takes 2 damage points and of course don't sink. Neither of this outcomes is realistic. The ship damage has to work such that the losing side takes 4 points plus or minus 4 and some sink, and the winning side takes 2 points plus or minus 4 and some sink but not as many.)

The problem, in a nutshell, is this: 2 points plus 4 is 6 points and the ship sinks, but 2 points minus 4 is -2 points and the ship does not repair two points of damage. Instead, -2 damage becomes 0 damage. That means when you get really bad luck, your ships sink, but when you get really good luck, you get no benefit from it because -3 and -2 and 0 are all the same result. That is, the random results are trimmed off at the limits of 0 and 5.

As a result, if you have a lot of ships taking these random rolls, and each one is for a relatively low amount of damage, you end up taking a lot more damage than you should, because your +6 and your -4 don't average out to +1 like they would if it wasn't for the rounding to 0. Instead they become +5 and 0 and they average out to +2.5, meaning you've taken twice as much damage as you should have. The problem is that if you're supposed to average 1 point of damage, then you're getting a lot more negative results trimmed to 0 than you're getting high results trimmed to 5, so your average rises. (The reverse is true if you're expecting to take 4 points of damage; you get more high results rounded down to 5 than you get negative results rounded up to 0, and your expected damage falls. This causes fewer complaints but is conceptually the same problem, just the opposite side of the coin.)

One solution, the one I think Jim V had in mind, was to do the ship by ship damage first and then decide who won. But that wouldn't solve the trimming problem. I think instead the solution is to deal with the trimming problem directly.

The way I intend to do that is to keep track of the actual damage handed out to ships, not just to the average level, and adjust the running average as actual damage is taken. Consider, for example, a case where you have 10 ships and the battle calls for you to receive 10 points of damage. As the code stands now, it would give 1 point plus or minus 5 or 6 to each of your ships, and because all your negative results would get trimmed to 0, you'd probably take 30 or 40 points. With the adjustment, for each point you actually take, the program will reduce the amount you have left to give to the remaining ships. That is, say your first ship takes 4 damage points; the program will reduce your remaining damage to 6 points. Now instead of taking an average of 1 point of damage, your remaining ships will taking only 6/9 = 2/3 of a point. When your remaining damage drops to 0 points, your ships will stop taking damage. All the rest will get off scot-free.

What this means is that in total, fleets will take an amount of damage that is much more closely related to the amount they're supposed to take, in contrast to the current situation where those two things can be quite different.

The changes will be most noticeable in one-sided battles where one side has a lot of ships receiving very little damage, and the other has just one or two that are supposed to receive a lot. With the current system there's lots of chances for the side with a lot of ships to get hosed on their die rolls. With the new system, once they've been hosed enough times to hit their damage level, the rest of their ships won't take any damage.

We'll have to test this out in a PATE test game, but that's the current plan. It has the (big, to me) advantage of being a relatively simple change to me.

Comments welcome.

Steve