Okay, I went a little crazy and decided to do some detailed analysis of the experience system used in DII. I haven't seen any of this info elsewhere and I guess I'll feel kinda stupid if someone points it out. I wanted to figure out what the optimal strategy is for getting xp or just figure out how the points are calculated. In particular, I wanted to find out if it's better to kill monsters in order from weakest to strongest or if you'll come out ahead if you kill stronger monsters first.
The bottom line:
- Kill monsters in order from weakest to strongest
Some more conclusion (including some we all already know):
- Never kill a creature that's the same level as you (you get the same number of points for a creature that's 1 level below you as at the same level)
- Never kill a creature that's more than 3 levels above you (there is a cap)
- Kill a creature that grants you fewer experience points before one that gives you more
- Use your mindread skill first where possible
- Complete quests or kill fixed point creatures last where possible
- A constant 10% Wisdom bonus will give you a net 4.8% bonus
How I figured this out (read at your own risk :-):
The last time I played, I kept a record of all the experience points I earned, the level I was at, the level the creature was at and what the creature was. Unfortunately I realized that you don't always get the same experience points based on the creature's level. There were some creatures that gave different experience points at the same level. The flying fortresses all seemed to be on their own sets of points. This means there is no simple formula based solely on your level and the creature's level.
I tried to save certain sets of creatures that each time I leveled up I would go kill, take notes and then reload so for one creature I was able to gather 26 data points.
I took the data I got for a specific enemy and dropped the data into a website (zunzun.com) that does data analysis to try to find formulas that match a given set of data. I discovered that there was no formula that exactly matched but quite a few that were really close.
FormulasOn the assumption that the developers didn't go out of their way to pick some esoteric formula, I identified the following formula that gives a very close approximation of the number of experience points you'll earn when you kill a creature:
xp = 3.333 * base / (hl - cl)^2
In this equation, hl is your hero level, cl is the creature's level and base is a base number that varies based on the creature. The base as I'm using it here is the number of xp you get when you kill the creature at the same level. This equation only applies to creatures that are -2 or lower level than you are. Creatures that are between +0 and +3 from you, the formula is exactly linear. Creatures that are +4 or higher are capped and you get the same value as at +3. Creatures that are -1 and +0 return the same number of points.
Example, there is a level 26 creature that when I killed while at level 26 I earned 1403xp. The number of xp I would earn if I killed this creature while at level 28 is:
3.333 * 1403 / (28 - 26)^2 = 1169
Which does exactly match the number of experience points I earned.
If the creature is between +0 and +3 of the hero, the formula is:
xp = base * (1 0.1667 * (hl - cl))
I also did some analysis to figure out if I could remove the need for the base. It turns out that most creatures do follow the same formula with only a minority acting as outliers. If I throw out the outliers, I was able to come up with a formula for calculating the base although it's even less accurate than the formulas above. Unfortunately the parameters are really esoteric and I couldn't come up with an obvious simplied form. That formula is:
base = (0.0213 + cl) / (0.0373 - 0.0008 * cl) - 43.4335
From my previous example with the level 26 creature, this formula spits out a base of:
(0.0213 + 26) / (0.0373 - 0.0008 * 26) - 43.4335 = 1446
This is a little off from the actual 1403 but it's reasonably close.
SimulationSo, armed with my equations, I set about creating a simulation. I chose a fixed pool of creatures of various levels and determined how many total experience points I would earn under various strategies. I know this doesn't exactly match a real games since you can't exactly chose which creatures to kill first; but it's just a simulation. With my fixed pool of creatures, here's what I found for the total xp along with the level you would have achieved:
Randomly chosen: 640,053 (level 26)
Just kill creatures at random. This is averaged over 5 different random simulations.
In Order: 819,916 (level 29)
This means kill the weakest creatures first.
In Order with 10% Bonus: 859,118 (level 29)
This means kill the weakest creatures first with a 10% bonus on each kill.
Backwards Order: 536,906 (level 25)
This means kill the strongest creatures first.
Backwards Optimized: 811,780 (level 28)
This means kill the strongest creatures first but obey the rules at the top (never kill creatures that are +0 or >+3).
So, the best of these (excluding the one with the bonus) is to kill the creatures in order. Doing an optimized backwards strategy is close as well but still not as good (and obviously impossible to actually do in the game). I can't rule out that there isn't something in between but I did let my random simulations run for a considerable amount of time and it never came up with anything close to the forward order, even when I reduced the pool size to reduce the number permutations.
