Author Topic: Maintenance and sustainable monetary value of equipment  (Read 3663 times)

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Offline WaltF4

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Maintenance and sustainable monetary value of equipment
« on: February 23, 2011, 06:06:51 AM »
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Some information in this post is now outdated. Please see my new thread for the updated information.




I have concluded a relatively simple test to determine the current rate of maintenance and the corresponding amount of equipment a character can afford to field. Over the last generation of my character, I have recorded my experience and gold multiplier for every round I have played since I could use my standard equipment. Additionally, I have kept track of the experience and gold I had when I first started using this set of equipment and have not purchased any items nor changed my equipment since beginning the test.  All rounds were played on the 100 man NA battle server while it was well populated. From a set of 482 rounds, I have determined the rate at which gold is lost to maintenance.

For these calculations I used the following values extracted from my test:
starting experience: 1136000 exp
ending experience: 8738000 exp
starting gold: 672310 gold
ending gold: 795081 gold
generation: 11
average multiplier: 2.19
equipment cost (buying price): 14220 gold

My character gained 7602000 experience and 122771 gold over this period. However 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+100 exp*(generation-1))

For my character:
gold gain/exp gain = 50 gold/2000 exp = 0.025 gold/exp

So without maintenance I would have gained: 
7602000 exp * 0.025 gold/exp = 190050 gold

Therefore, over this period I lost 67279 gold to maintenance. As gold gain, experience gain, and equipment breakage (to the best of my knowledge) are incremented at regular intervals, or clock ticks, it is perhaps best 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:
Number of ticks = (end exp-start exp) /((1000 exp+100 exp*(generation-1))*average multiplier)

For this set of data:
Number of ticks = 7602000 exp/ (2000 exp * 2.19) = 1735.6

The amount of gold lost to maintenance per tick was 38.8 gold. To determine the rate of maintenance, that is the gold lost to maintenance each tick per gold worth of equipment:
rate of maintenance per tick = (gold lost to maintenance per tick)/(equipment cost)

Using my values:
rate of maintenance per tick = 38.8 gold / 14220 gold = 0.0027

As this rate of maintenance per tick is normalized for generation, average multiplier, and equipment cost, it should be independent of character and player. While not necessary for further calculations for sustainable equipment value, the chance of breakage per tick can be determine from rate of maintenance per tick since the cost or repair is known to be 5% of the item buy price.

chance of breakage per tick = (rate of maintenance per tick)/(cost of repair)
chance of breakage per tick = 0.0027/0.05 = 0.054

This result shows a 5.4% chance of breakage for each item each tick. This chance of breakage is greater than values I have seen given by chadz, but could be the result of outdated change logs, the development team generally being a bunch of trolls, or the breakage checks not actually being synchronized with the experience and gold ticks.

Going back to the rate of maintenance per tick value of 0.0027, we can determine the sustainable monetary value of equipment using:
average equipment cost = 50 gold * (average multiplier)/0.0027

From the immediately preceding equation, it should be obvious that the average multiplier of a player is important to what equipment they can afford. Though player skill is a factor in your multiplier, it is not easily quantifiable and is beyond the scope of what I will attempt to cover here. Suffice it to say, average players will win about 50% of their games while good players would expect to win more while bad player would win less. From this assumption of 50% win rate, the average multiplier of the average player can be determined. Begin with the first round of play after joining a server the average player's multiplier would be:

1x for the first round (100% chance of 1x)
1.5x for the second round (50% chance of 1x and 50% chance of 2x)
1.75x for the third round (50% 1x, 25% 2x, and 25% 3x)
1.875x for the fourth round (50% 1x, 25% 2x, 12.5% 3x, and 12.5% 4x)
1.9375x for the fifth and following rounds (50% 1x, 25% 2x, 12.5% 3x, 6.5% 4x, and 6.5% 5x)

The following plot shows the cumulative average multiplier of a player as a function of rounds after joining a server.

(click to show/hide)

The most notable feature is the asymptotic approach to a 1.9375 multiplier. This means that players that play a few rounds in one sitting or between changing servers or having to rejoin servers would be expected to earn less gold and experience than player that play for extended periods. To put a scale to all of this, the average player who plays in 15 round sittings (about 1 hour on the 100 man NA battle server) could maintain 33730 gold worth of equipment continuously while an average player who plays in 30 round sittings could maintain 34880 gold worth of equipment continuously.




TL;DR version: You can continuously maintain an average equipment cost equal to your average multiplier times 18520 gold. Your average multiplier will most likely be a little less than 2x. Most players can have equipment worth about 35k without significant financial hardship.





Some information in this post is now outdated. Please see my new thread for the updated information.
« Last Edit: June 16, 2011, 04:53:26 AM by WaltF4 »

Offline Ishtar_Soup

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Re: Maintenance and sustainable monetary value of equipment
« Reply #1 on: February 23, 2011, 06:13:48 AM »
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Great Post,
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Offline Kong Ming

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Re: Maintenance and sustainable monetary value of equipment
« Reply #2 on: February 23, 2011, 06:21:46 AM »
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There's some awesome bar going out to a certain annoyingly good Awlpiker for this post.  Nice work.
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Offline Freland

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Re: Maintenance and sustainable monetary value of equipment
« Reply #3 on: February 23, 2011, 11:03:54 AM »
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One thing to add:

There is one little trick to actually come as close as possible to the average 1.9375 multiplier: Only leave the server after you have lost a round. That way it does not matter how many rounds you are playing in one session.

And btw great post +1 awesome  :)
« Last Edit: February 23, 2011, 11:12:47 AM by Freland »
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Offline Tigerclaw

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Re: Maintenance and sustainable monetary value of equipment
« Reply #4 on: February 23, 2011, 01:43:04 PM »
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Very nice piece of work, Walt.

Offline Brutal

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Re: Maintenance and sustainable monetary value of equipment
« Reply #5 on: February 23, 2011, 02:03:05 PM »
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Very nice post indeed.
It does confirm what most people say about the upkeep: that you can maintain about 35 000 worth of equipment (i still make money with 37 000 gold of equipment).

ps: WaltF4 you should highlight the important part of your post and conclusion for the lazy readers.

Offline Fluffy_Muffin

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Re: Maintenance and sustainable monetary value of equipment
« Reply #6 on: February 23, 2011, 05:03:16 PM »
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An awesome point for you sir
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Offline Murrogh

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Re: Maintenance and sustainable monetary value of equipment
« Reply #7 on: February 24, 2011, 12:37:49 AM »
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Good analysis. Lots of people complain about running out of money with light gear and this shows that a player can use medium gear and still break even.

I think that the 1.94 average multiplier may be a little low though. You assume that the probability of winning any given round is 50%. This is true on average, however, wins are correlated so that if you win one round after autobalance, you are more likely to win the next. This allows some players to remain with high multipliers.

A better model may be a Markov Chain where the probability of winning the first or second rounds of a map are 50-50 but a team that won after balance has a higher chance of winning again. This model would lead to the conclusion that the average multiplier is higher in servers with a higher win limit because a stronger team has a chance to stay together.


Offline Kung Fu Jesus

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Re: Maintenance and sustainable monetary value of equipment
« Reply #8 on: February 25, 2011, 12:01:11 AM »
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Math is hard.

+1 for Walt.
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Offline WaltF4

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Re: Maintenance and sustainable monetary value of equipment
« Reply #9 on: February 26, 2011, 07:32:17 AM »
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You assume that the probability of winning any given round is 50%. This is true on average, however, wins are correlated so that if you win one round after autobalance, you are more likely to win the next. This allows some players to remain with high multipliers.

What you are saying is true, and the effects are observable in my records; however, degree-of-team-stacking is hard to quantify. A somewhat exaggerated demonstration of what you are saying can be seen in the following a pair of 11 round strings, both with a 50% win rate:

Set 1:   Start (1x multiplier), win, loss, win, loss, win, loss, win, loss, win, loss
or
Set 2:   Start (1x multiplier), win, win, win, win, win, loss, loss, loss, loss, loss

The average multiplier of the first set of rounds is 1.45x while the second set of rounds is 2.27x. So, everyone can take some comfort that when stacked teams are streamrolling the fun out of the game, your net experience and gold gain will normally be greater than with back and forth games.

I have worked through a slightly different version of the previous model that incorporates a win rate other than 50%. The newer version yields average multipliers that are in good agreement with my data if the lower multipliers for the first, second, third, and fourth rounds after joining the server are ignored. It seems that the increase in average multiplier due to the win-streaks effect that Murrogh mentioned approximately offsets the early round reductions, at least for sets of games with between 40% to 60% win rate. The only difference in the newer model is that the probability of winning or losing is no longer assumed to be equal. The following figure shows the probability tree of wins and losses that I used to determine the win-loss permutations out to the fifth round. After the fifth round, there is no change in the tree as the maximum multiplier remains 5x. 

(click to show/hide)

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 some data points extracted from my records.

(click to show/hide)

In short, the previous model underestimated the average multiplier, even at 50% wins, as win-streaks do have an observable increase on the average multiplier. However, the previous conclusion was conservative enough to remain accurate: the average multiplier of the average player will most likely be a little less than 2x and such a player can support equipment worth about 35K.



EDIT: Corrected a few typos and bolded the newer conclusion, which happens to be the same conclusion as my previous post.
« Last Edit: February 26, 2011, 05:36:02 PM by WaltF4 »

Offline SeQuel

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Re: Maintenance and sustainable monetary value of equipment
« Reply #10 on: February 26, 2011, 07:53:17 AM »
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TL;DR?

Offline Magikarp

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Re: Maintenance and sustainable monetary value of equipment
« Reply #11 on: February 26, 2011, 07:16:45 PM »
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Great Post,
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Offline EliteDragon

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Re: Maintenance and sustainable monetary value of equipment
« Reply #12 on: February 27, 2011, 07:11:24 AM »
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I just learned something amazingly awesome today. Great job Walt.

P.S. You still annoy the hell outta me when I have to fight you.

Offline Maira

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Re: Maintenance and sustainable monetary value of equipment
« Reply #13 on: February 27, 2011, 07:28:51 AM »
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Math is hard.

+1 for Walt.


It's simple really, I had to use a board, two rather, but here it is:

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Re: Maintenance and sustainable monetary value of equipment
« Reply #14 on: February 27, 2011, 08:08:51 AM »
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I have a theory

some items are fine broken for instance black armour (you only wear it to look cool).
If it aint broke dont fix it.


or save up and use expensive gear in long/short stints until you've got no cash in your sky rocket and start over again with cheap gear

ps: sky rocket is an Australian term for pocket

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