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Arceus "Nerf" Update - Visualizing the changes
This post was made following this update in the changelog. In addition, Niet has given the following pieces of information in regards to the Arceus buff.
And in reply to my question about the previous Arceus buff:
So in case anyone was interested - here's an explanation of what this all means, theoretically.
(Graph made by me on Geogebra. It's literally f(x) = x and g(x) = ln (x) + 2 if anyone's interested)
Here is a nice little graph. Imagine the x-axis is your chain (where the x-axis - the horizontal line - is number hatched. You can take 1 unit = 500 hatched, or 1 unit = 1000 hatched, it doesn't matter as there are no numbers... yet ^^. If anyone happens to have a 4k+ arceus chain, please PM me xD)
Now, imagine the Y-axis is your melan multiplier. What do i mean by melan multiplier?
Well, a x2 multipler would increase your chances by 2. Aka if the original melan chances were 1 in 1000 (just as an example), x2 mulitplier would mean your chances are now 1 in 500.
Again the "melan multiplier" axis is an arbitrary number. That means 2 units can literally be x0.1, x0.2 or x1000. It's arbitrary, as I don't have the actual numbers.
The green line is the present buff, the red line is the previous buff.
As you can see, before the 3rd unit on the horizontal line, the green line is above the red line, meaning that the melan multiplier, before the 3rd unit, of the greenline is higher than the red.
This means that in shorter chains, the melan multiplier now is higher than before. By... a lot, actually
Logarithim also... sucks. Because it means the increase decreases really quickly. You can see after the 3rd unit on the horizontal line, the red line is much higher than the green one.
This means that in longer chains, you used to get more melans before than now - thus the nerf.
This model hopefully helps you visualize what the changes mean. None of the values are actual representations of PFQ's numbers! ^^
QUOTE
- The effect of Arceus Rank on Melanistic chances has been reduced
- (Conversely) the base effect of very long chains on Melanistic chances has been somewhat raised
QUOTE originally posted by Niet
@CSY: Actually it's logarithmic in effect, meaning that (as you describe) the effect is stronger at the first kick, but then lessens. So the difference between 1k and 2k is much bigger than the one from 3k to 4k.
But yes, as you conclude, the bonus is actually designed to help chains sooner, without turning them into Melanistic farms.
QUOTE originally posted by Niet
It used to be linear under the effects of the bug.
(Graph made by me on Geogebra. It's literally f(x) = x and g(x) = ln (x) + 2 if anyone's interested)
Here is a nice little graph. Imagine the x-axis is your chain (where the x-axis - the horizontal line - is number hatched. You can take 1 unit = 500 hatched, or 1 unit = 1000 hatched, it doesn't matter as there are no numbers... yet ^^. If anyone happens to have a 4k+ arceus chain, please PM me xD)
Now, imagine the Y-axis is your melan multiplier. What do i mean by melan multiplier?
Well, a x2 multipler would increase your chances by 2. Aka if the original melan chances were 1 in 1000 (just as an example), x2 mulitplier would mean your chances are now 1 in 500.
Again the "melan multiplier" axis is an arbitrary number. That means 2 units can literally be x0.1, x0.2 or x1000. It's arbitrary, as I don't have the actual numbers.
The green line is the present buff, the red line is the previous buff.
As you can see, before the 3rd unit on the horizontal line, the green line is above the red line, meaning that the melan multiplier, before the 3rd unit, of the greenline is higher than the red.
This means that in shorter chains, the melan multiplier now is higher than before. By... a lot, actually
Logarithim also... sucks. Because it means the increase decreases really quickly. You can see after the 3rd unit on the horizontal line, the red line is much higher than the green one.
This means that in longer chains, you used to get more melans before than now - thus the nerf.
This model hopefully helps you visualize what the changes mean. None of the values are actual representations of PFQ's numbers! ^^
Limitations
This is a model and is thus oversimplified. Here are some limitations of my model in case anyone is interested:
1) Arceus buff increases as a floor function - aka it increases every 1k. In my model, it seems like the buff continuously increases per egg, but in reality, it only jumps every 1k
2) Arceus buff stops at 4k. You can't go any higher after 4k - which to be honest, shouldnt be a big issue given the nature of the log function - and that it will "tend" to a certain melan multiplier number
3) The graph is literally just a random function!! It doesn't represent ANYTHING but the idea behind it all
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