View Single Post
Old 01-08-2018, 01:49 PM   #192
larsdangly
 
Join Date: Dec 2017
Default Re: The Fantasy Trip

Re. the stat optimization issue raised above, and in the other major thread:

Melee presents players with a 'trade space' having several different axes. But the major two trades you can make are:

1) Exchange 1 point of DX for 1 point increase in the expected value of a successful attack + 1 point increase in your effective hit points.

2) Exchange 1 point of DX for 1 point of armor protection.

(I'm ignoring some little corners of the equipment table where these general rules break down).

There are then a couple of equipment-related trade offs you can make:

1) Decrease damage done by 1 in exchange for being able to use a weapon in HTH
2) Decrease damage done by 0.5 to 1 in exchange for being able to use a weapon either thrown or in melee
3) Choose between getting 1 free point of protection or a 1 point increase in damage done (i.e., shield vs. 2 handed weapon)
4) Decrease damage done by 1 in exchange for pole weapon properties

There are a few more narrower trade offs like those in this second list.

So, when you make optimization decisions, your primary thought should be the DX vs. damage done+HP vs. protection trades, and secondarily the narrower trade offs you make about weapon properties.

Part of the complexity of the game is that these trades are close to balanced within certain ranges in ST and DX, and the weapon trade offs have values that are situational and so depend on tactical decisions.

The main ST vs. DX trade off primarily depends on where you are on the DX scale. The easiest way to evaluate this is by calculating the expected value of the difference between the average number of turns it would take you to kill a foe vs. the number of turns he or she would take to kill you.

For reference, two combatants with ST 12, DX 12, no armor, a buckler and a broad sword (each, of course!). Each has a chance to hit of 0.74, an expected value for damage of 7, protection of 1 and 12 hit points. Thus, each will reduce the opponent's HP by [(0.74 x 7) -1] = 4.2 per turn (on average), meaning 2.8 turns are required to kill the foe (and, conversely, you yourself will survive for 2.8 turns, on average).

These sorts of calculations properly should consider the 'tails' to the distribution of outcomes (double and triple damage; odds of very high or low damage rolls; odds of broken or dropped weapons). It is actually quite easy to build Montecarlo models to simulate all this on a spread sheet, but it isn't really worth talking through the details so I won't.

Let's imagine you match one of the combatants described above vs. someone with ST 11, DX 13, a short sword and buckler. Now damage done per turn is [(0.838 x 6) -1] = 4.0. It will take 3.0 turns to kill your foe, whereas you will be killed in 11/4.2 = 2.6 turns. That was a bad trade. The reason why it was a bad trade is that an adjusted DX of 12 has higher odds of success than your intuition might suggest, and going up one more to 13 only increases your success chance by a little under 10 %. That is, you are already on the path of diminishing returns for raising DX, but traded away a significant fraction of your average damage done per turn.

As another example, consider someone with a cutlass, chainmail, large shield, ST 10 and DX 14 (adjusted to 10). This person has an expected damage done per turn of 5 x 0.5 = 2.5; if he fights the first sort of foe above, this is reduced to 1.5 points of damage taken by his foe per turn, meaning it will take 8 turns to kill him. But that foe will do you (on average) only 0.2 points of damage per turn, so it will take you basically forever to get killed. This would seem to indicate the heavily armored ST 10, DX 14 foe will always win. But this is because the simplest way of calculating expected value breaks down as average damage done approaches the value of protective armor. In reality, the broadsword wielding attacker will do 1 or more point of damage about every other turn, and has about a 1 in 4 chance of doing several points of damage (just combining the chance of success with the probability of each damage outcome). A case like this needs a full Montecarlo sort of model to describe correctly. If you do that, you find the combatants are actually still pretty closely matched.

Edit: the actual average damage done in excess of armor, per turn, by the broad sword wielder is something like 1.6-1.7 points (considering the chance of a hit and the chance of each damage outcome). So, the two combatants are chipping away at each other at a very similar rate, and our ST 12, DX 12 combatant is actually still pretty close to the peak statistical outcome, even when we consider trade offs of armor and 2 points worth of trade offs of ST for DX.

This rolls over pretty fast to higher ST because your chance to hit drops fast as DX goes below 10-11.

Last edited by larsdangly; 01-08-2018 at 02:38 PM.
larsdangly is offline   Reply With Quote