So I recently started using Oblivion Heirlooms to try out different builds, and got to thinking that it would be a lot easier to calculate for PvP damage if I could find a formula to translate PvE damage. So I got together with a friend (and invited a priest along the way for healing) to test out the damage of the "basic attack" or auto attack and create this formula. What ensued was a several hour long brain teaser, which we mostly completed to my satisfaction. If anyone wants to add more data to this effort, and/or has better math skills (and is able to calculate the last bit that we couldn't) PLEASE respond below.
So what we decided was that in order to create our formula, we needed 2 different formulae- a formula to calculate player damage in PvE, and a formula to calculate player defense results against PvP damage (this was the hard part). The data given to us by the game is our atack rating, our defense rating, and the damage of hits both given and recieved. Using this information, we created a graph (which turned out surprisingly linear) and used it to create our formulae.
We started with PvE damage. We calculated this by attacking the NPC in the criminal area that tells you how long your crimes condemn you. My friend and I both used fighters, and each of us used 2 different weapons (with different attack ratings) and had different strength values (in order to factor out strength in the formula). We each hit the NPC 10 times with each weapon (excluding hard hits) and he recorded the data. I wish I had asked him for that data at this point, but it was quickly and easily discovered that the average player damage against the NPC was "Playerattack(2) + Strength(2) = Average damage" with an margin of error of 6 points of average damage.
EDIT: After further review, this information is correct for the FIRST hit of any auto attack. We had only recorded first hits originally as we were looking for repeatable data, and hadn't taken into consideration the combo multipliers inherent to each type of weapon. More data will be tested in this field when the game goes live.
Next we set out to determine the effect of player defense in PvP situations, given the average damage in PvE. What set us back (about an hour of head-scratching) was that the two were completely separate. We ended up disregarding the above formula in order to calculate pure character defense in PvP situations vs character attack in PvP situations. Collecting the data was rather easy (although this is where we called in a priest, since it involved hitting each other repeatedly). We collected this data by first taking off all of our armor (although as a fighter >Lv18 I had 10 passive defense) and hitting each other 10 times (again disregarding hard hits) and collecting the data. We would then add on 1 piece of armor at a time and record the new data onto a graph, with the X coordinate being armor and the Y coordinate being average damage. Unfortunately, we were forced to scrap half of this data when it did not add up due to the fact that the level difference between us caused him to hit me for significantly less (damage per attack point) than I hit him for with similar defense stats. For the record, I was Lv.21, and he was Lv.13. We then took the data obtained by me hitting him (NOTE: there was no effect that I did more damage to him based on level, which will be made clear by the formula) and calculated a deceptively simple formula for PvP defense with the resulting graph. GRAPH DATA IS AS FOLLOWS: 5,119; 22,98; 44,83; 58,73; 75,55; 98;30 The graph formula is: IF (Playerdefense<Playerattack) then Playerattack - Playerdefense = Average damage with a margin of error of 5.5 points. The effects of having a player defense significantly higher than player attack got really crazy on our graph, and I attribute this to the compression effect required to keep damage at a positive number. We were unable to calculate this data, and again, if anyone would like to take a shot at it, please go ahead and post the results here.
The great part of having these formulae is that we can use them to calculate more precise data on skill damages and attack powers by plugging the attack damages into these.
PLEASE NOTE THAT THIS EXPERIMENT IS JUST THAT, AN EXPERIMENT. THIS IS FAIRLY SOLID EVIDENCE, BUT THERE REMAINS MARGIN OF ERROR AND POSSIBLE CONFOUNDS LIKE DEFENSE TYPES (such as pierce vs. bash).