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Overall Statistics on Artisan's Energy
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The first thing I was interested in is, for the 40.7 billion suimulations, how many times did we get 100% Artisan's Energy (engaged the pity-system). Below are the results, note that this is
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across all simulations, so base rates as well as every possible enhancment material combination.
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to +7891215
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# of Simulations that Hit Max Artisan's Energy535252825249002775966139727673671167507527
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% of Simulations that Hit Max Artisan's Energy0.20%0.92%2.84%5.99%7.18%
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As expected, the later upgrades with lower base rates are where we hit the pity-system the most. Also going back to the point from the welcome sheet, it is a notable percentage, which
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means ALOT of failed upgrades. Of the 40.7 billion simulations run, we hit the pity-system on 5.53% of them.
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Overall Statistics on Base Upgrades
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Here are some overall statistics from the individual base rate analyses you will find in the following sections. These statistics are based on only the simulations done using the base
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upgrade rates (no enhancement materials). So the appropriate way to interpret these numbers is to say "these statistics describe what I expect to happen if I upgraded all my gear
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starting at +6 and ending at +15 never using any enhancment materials. I have layed this out into three catagories, the most lucky player's experience, the average player's experience,
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and the most unlucky player's experience. As should be obvious, neither extreme will happen, and if it does it didn't and you are lying :)
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The Most Lucky PlayerThe Average PlayerThe Most Unlucky Player
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Fails 0 timesFails 146 times.Fails 486 times.
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Probability of2.2182E-34%Probability of 50%Probability of2.5475E-71%
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1 in every4.508E+33people1 in every 2 players1 in every3.925E+70people
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From +6 to +7
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Here are the statistics for upgrading from +6 to +7 if you do not use any enhancment materials.
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The base success rate is 60% and the adjusted success rate is63.18%
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Which means the average number of attempts to succeed is1.58
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Which means on average we should expect to fail the upgrade0.58 times
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Number of attemptsNumber of SimulationsPercentage of SimulationsCumulative Percent
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1299885460.0%60%
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2132148726.4%86%
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34890869.8%96%
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41485333.0%99%
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5420400.8%100%
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This number highlighted in green is the percentage of people hitting the pity-system.
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The way to understand the cumulative percent is "by this number of attempts, cumulative percent of people
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have achived their upgrade"
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From +7 to +8
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Here are the statistics for upgrading from +7 to +8 if you do not use any enhancment materials.
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The base success rate is 45% and the adjusted success rate is49.30%
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Which means the average number of attempts to succeed is2.03
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Which means on average we should expect to fail the upgrade1.03 times
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Number of attemptsNumber of SimulationsPercentage of SimulationsCumulative Percent
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1224961445.0%45%
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2136071727.2%72%
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375033415.0%87%
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43745657.5%95%
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51665643.3%98%
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6982062.0%100%
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From +8 to +9 (and +10 and +11)
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Here are the statistics for upgrading from +8 to +9 if you do not use any enhancment materials.
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These are the same rates as going to +10 and +11 as well.
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The base success rate is 30% and the adjusted success rate is35.49%
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Which means the average number of attempts to succeed is2.82
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Which means on average we should expect to fail the upgrade1.82 times
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Number of attemptsNumber of SimulationsPercentage of SimulationsCumulative Percent
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1149973230.0%30%
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2115479723.1%53%
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384359616.9%70%
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458632511.7%82%
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53838987.7%89%
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62387584.8%94%
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72928945.9%100%