I have completed an updated study of the rate of maintenance in cRPG 0.223. This study used the same system of data collection as
my previous study on this topic that was preformed in February 2011. This amounts to recording the amount of gold and experience gained over a given set of rounds, the multiplier each of these rounds was player with, and value of the items equipped each round. To simplify the experiment, I play every round with the same set of equipment. All rounds were played on the NA battle servers. From a set of 915 rounds, I have determined the rate at which gold is lost to maintenance.
I have reused the same equations and variables as the last study since they are still correct (with a modification for the newer generational bonus) and are still the most direct method I have found. To save everyone else the trouble of switching back and forth between posts, I will reproduce the calculations here in their entirety.
The following values are need to for the complete derivation and are taken from records explained above:
starting experience: 1041390 exp
ending experience: 9853970 exp
starting gold: 1499164 gold
ending gold: 1771701 gold
generation: 12
average multiplier: 2.23
equipment cost (buying price): 9686 gold
My character gained 8812580 experience and 272537 gold over this period. This amount of gold gain has been reduced due to maintenance. The gold gain without maintenance is proportional to experience gain and character generation such that:
gold gain/exp gain = 50 gold/(1000 exp+30 exp*(generation-1))
With a values of generation greater than 16 counting as 16. For my character:
gold gain/exp gain = 50 gold/1330 exp = 0.0376 gold/exp
So without maintenance I would have gained:
8812580 exp * 0.0376 gold/exp = 331353 gold
Therefore, over this period I lost 58816 gold to maintenance. As gold gain, experience gain, and equipment breakage are incremented at regular intervals, or clock ticks, it is easier to look at these tick time units instead of number of rounds. The number of ticks included in this set of games can be determined as:
Number of ticks = (end exp-start exp) /((1000 exp+30 exp*(generation-1))*average multiplier)
Again, values of generation greater than 16 count as 16. For this set of data:
Number of ticks = 8812580 exp/ (1330 exp * 2.23) = 2971.3 ticks
And the amount of gold lost to maintenance per tick is:
58816 gold / 2971.3 ticks = 19.79 gold/tick
To determine the rate of maintenance, that is the gold lost to maintenance each tick per gold worth of equip items, the following equation is used:
rate of maintenance per tick = (gold lost to maintenance per tick)/(equipment cost)
Using my values:
rate of maintenance per tick = 19.79 gold / 9686 gold = 0.0020
This rate of maintenance per tick is normalized for generation, average multiplier, and equipment cost so it is independent of character and player. We can determine the sustainable monetary value of equipment using:
average equipment cost = 50 gold * (average multiplier)/0.002
From the immediately preceding equation, it should be obvious that the average multiplier of a player is important to what equipment they can afford. Unfortunately, the development team has not included a multiplier tracker or even a win-to-loss tracker. However, an average multiplier can be approximated using the probability tree below:
This probability tree shows all of the possible permutations of results for the first 5 round of play after joining a server. After the fifth round, there is no change in the tree as the maximum multiplier remains 5x and the tree branches into identical pairs indefinitely after the fifth round. The probability of each result can be determined by multiplying the chance of winning or losing at each branch needed to reach a particular result. For example, to reach the 4x multiplier in the fifth round requires a loss, then a win, a second win, and finally a third win. With a 60% win rate and 40% loss rate the probability the 4x multiplier in the fifth or following rounds would be:
Probability of a 4x multiplier in the fifth or following rounds = ( Chance to lose)*(Chance to win)*(Chance to win)*(Chance to win)
Probability of a 4x multiplier in the fifth or following rounds = 0.4 * 0.6 * 0.6 * 0.6 = 0.0864
This process is repeated for all 16 permutations of the fifth and following rounds. The following figure shows the theoretical average multiplier as a function of win chance along with a 10 data points extracted from 100 round strings of my last 1000 recorded rounds.
From this plot it can be seen that the average player with a win rate of about 50% have an average multiplier of about 2x and that experimental values for average multiplier for a given win rate are within 0.2x of the theoretically predicted value.
The most significant result of this new maintenance study is that the rate of maintenance has been reduced as the breakage chance is now actually the 4% claimed by the development team, instead of the ~5.4% it was in February, and the average player can now continuously maintain an average equipment cost of about 50000 gold, instead of the about 38000 gold as was the case in February.
TL;DR version: The average player can now continuously wear an average equipment cost of about 50000 gold.