Single post in CSY's Journal: Maths and Musings

Arceus 10k chain update and melan chances 1 Arceus Buff - Explanation So after seeking from clarification from Niet, it seems that the long-chain melan buff is literally just what is written on your Shiny Hunting page. This means that a 15% increase means that your chances have been increased by a multiplicative factor of (1+15%) = 1.15, a 30% increase means that your chances have been increased by a multiplicative factor of (1+30%) = 1.30, and so on. Here is a chart showing what the real buff is with accordance to the site numbers. I made an assumption that, with max boosts (shiny charms/ubercharms/lvl 7 radar/hm), your shiny chance is 1 in 25 and your albino chances are 1 in 150. That means your melan chances = (1/25) * (1/150) = 1 in 3750 This means that in 3750 hatched, you should statistically get 1 melan, not accounting for any long chain buff. The Buff column is represented as a decimal number but is equal to the corresponding percent - i.e. 15% = 0.15, 30% = 0.3, 45% = 0.45, etc. The Regular Buff column is the multiplicative factor. For example, at a 1000 chain, the buff is 15%. So the buff would be = (1/25) * (1/150) * (1+15%) = 1 in 3260.9 (Note that 1+15% is equivalent to 1.15) The Real Regular Buff column shows your Arceus adjusted melan chances based on the regular buff column. It is represented in the format of 1 in x, aka a 1000 chain is 1 in 3260.9, a 2000 chain is 1 in 2884.6, etc. I also plotted a graph to visualize the increase. It is linearly increasing because the difference between each factor is 15%. (Oh and it's represented in a decimal, aka 1000 would be 1/3260.9 = 0.000307, etc because as you can see the 1 in x has a different function entirely) 2 Addressing the discrepancy between Statistics and the Buff visible on the site This is what stumped me the most. According to the maths, a 4000 chain would yield a melan chance of 1 in 2343.75, but according to what statistics we have (including Akoomi's 44k Eevee chain, Muff's 25k Chikorita chain, my 16.5k Chimchar chain), it was previously postulated that the max arceus buff at 4k gave an ~1 in 1000 chance of hatching a melan. You might be thinking, maybe all of these are just lucky cases and I'm not looking at the cases where people's stats align with the maths if 1 in ~2.5k after max arceus buffs. However, as a hunter that constantly switches melan hunts, I personally feel that this 1 in 1k is pretty accurate. I'm only taking a look at one account (mine) for the ease of getting the relevant statistics as well as how luck should even out when considering one single account. For example, my long melan hunts including: Chimchar - 18 melans in 16.5k Fennekin - 11 melans in 9.5k Litwick - 4 melans in 5.6k All of this seem to suggest a higher, if not at least 1 in 1k melan chance after a 4k chain. Both Garthic and Niet have stated multiple times that no debuff has taken place and EVEN if we assume that they mean the agglomerate max buff hasn't been debuffed (aka you can still get the same chances after you max your chain to 10k), the max real regular buff would still only be 1 in 1500, which is lower than the previous statistics. So, unsatisfied with the results, I did a bit more maths to find a statistically adjusted factor if I wanted the 4000-chain to close in on 1 in 1k. The column statistics adjusted is just a hypothesis that there are some other undocumented factors that affect melan chances due to the discrepancy between the statistical evidence and what is shown on site. Call me a conspiracy theorist haha IMPORTANT NOTE HERE: This hidden factor thing isn't confirmed and there is literally no public announcement suggesting this. It's simply what I hypothesize based on HOW different the statistics and what is given to us on site is. I found a factor of about 87.5% seemed to put the 4000 chain closer 1 in 1000. Based on what is shown on site, I assume that this "hidden factor" does not change based on chain length. Anyways, a multiplicative factor of 87.5% (aka, base chance*(1+85.7%)) would put the melan chances of the 4000-arceus chain to 1 in 1250, with the maximum chance being at 1 in 800. Concluding remarks: I found that this "hidden factor" was quite necessary because that would mean that the buff values provided from the site was more than 134% off from our statistics. I do not know what the factor is, but assuming a 87.5% statistics-adjusted factor, the max boost would likely be at 1 in 800. Note that, if all previous statistical evidence remains close to the true real boost, the max boost would likely be even more potent than 1 in 800. (aka 1 in 700, 1 in 750, etc) 3 Explaining the "dimishing returns" So, the previous Arceus update created a lot of controversy about what "diminishing returns" meant. The Increase from last buff (RRB) column shows how much the buff has increased in terms of 1/x, where we find the absolute value difference in the decrease in x. Here, I only consider the Real Regular Buff (RRB) as given by site stats and not my statistics adjusted one. (Whilst I still don't believe the real regular buff is accurate based on statistical evidence, I'm just here to explain why the returns are diminishing... xD) To illustrate, when jumping from a 1000 chain to a 2000 chain, you go from 1 in 3260.9 to 1 in 2884.6. That means the increase from last buff would be = 3260.9-2884.6 = 376.3 What it meant by diminishing returns is that from a jump from a 0 to 1000 chain (489) gives a larger buff than a jump from a 1000 to 2000 chain (376). The longer your chain, the bigger your buff, but the smaller the jump. Oh and to end it off, here's a chart showing the "diminishing returns". The longer your chain, the bigger your buff but the smaller the subsequent increase 4 Concluding Remarks In this post, I've discussed the long-chain arceus melan buff and how it affects melan chances. I've also discussed the discrepancy between our statistics and what is shown on site, hypothesizing some other "buff" that should make up for the difference. If I've made an error anywhere or you think I've misinterpreted something, feel free to PM me to discuss ^^. I want to figure this out :) Might make one for non-Arceus users too... but unfortunately I don't have any statistics for that one, haha.