So today at 4am I had a thought that went something like this: “You know, it would be pretty handy to have the exact formula for percentage stats”, and then it hit me - it’s actually incredibly easy to calculate, allow me to explain.
This one goes out to you @NoBanana.
The actual maths
We know it’s an expression with a logarithm, so it’s gotta be something like this:
%Increase = alogb(StatAmount)
But we don’t want that stinky base b logarithm, so we do some basic transformations.
Step by step in here
alogb(x) =
aloge^(ln(b))(x) =
(a/ln(b))ln(x)
Notice how a/ln(b) is still a constant, so we can write it as just some c.
Now we have this:
%Increase = cln(StatAmount)
Now we know that 160 of a stat grants a roughly 50% increase in effect, so we plug those numbers in and get:
c = 50/ln(160) = 9.851…
Since the 50% increase is just a rough estimate, we can conclude that actually c=10.
In conclusion, we can calculate (or at the very least approximate with high precision) the effectiveness of some amount of a percentage stat by using this formula:
%Increase = 10ln(StatAmount)
One caveat
Because of the nature of the logarithmic function (namely giving negative infinity for values approaching 0, look at graph below) and depending on the implementation of it, the actual formula could be %Increase = 10ln(StatAmount + 1) to account for you having 0 of every stat by default, but could also use the exact formula given above and account for when you have 0 of a stat in a different way.
But we can never know this without insight into the actual code.
I got that from memory, but I changed it to 160 now and still checks out since it was an estimate by Vetex anyways.
About the log talk, I agree that it’s a bit messy, markdown and html don’t seem to have the best API for maths expressions.
Don’t sweat it though, logs aren’t scary at all, it’s just if you’re unfamiliar with the notation the sudden influx of letters in maths might make your brain hurt a bit.
This is a good start, but it’s certainly nothing conclusive. The formula could be far more complex than just log(stats)*constant, and we don’t really have enough datapoints to make any assertions.
I took a swing at something like this myself a while back - vetex made the change based on a suggestion from a (now deleted) suggestion by Meta, so I scaled one of the example formulas meta gave to fit the single datapoint we have.
Both are logarithmic scaling for percentile stats, but they’re radically different in curve and range.
Graph
X axis is stats (0 to 2500 is the amount given by a full set of enchantments from levels 0 to 5000).
Y axis is bonus multiplier (50% is 0.5).
ln(stats)*0.1. (150*ln(0.33*stats+4)^3)*0.00005
Simply put, we need more data points. I think the best way to do it is to record a bunch of clips of running down a straight path with different agility sets, and then look back at the video to time how long each attempt took. This isn’t perfect, but the other stats are much harder to measure.
I’ve kinda been planning on doing this myself at some point, but never got around to it.
We may or may not have found the formula for how much effect each point of a percentile stats (things like magic size, agility, etc) is worth.
We know that 160 points is worth +50% effect, but aside from that vetex told us nothing so nobody’s known how it works (except vetex) since it was added in the fishing update.
It’s the inverse of an exponential (if I remember correctly an exponential is like n^x solve for x)
I don’t remember much about it since I’m stupid as well ;-;
So every mathematical operation has an inverse (opposite), which you can use to “undo” the operation.
The inverse of +n is -n.
The inverse of *n is ÷n.
The inverse of n² is √n.
The inverse of xⁿ is logₓ(n).
For example: 5⁴ = 625 log₅(625) = 4.
You can do some fancy shenangans with logarithims, but a logarithmic formula is just one that uses a logarithm. They typically look like this:
It quickly goes up, then curves off and stops increasing.
Vetex uses one for stats like magic size and agility because he wants stats to quickly get to the point where they’re good, but not keep going up to ridiculous amounts at endgame.
We don’t know the exact details of the formula though - that’s what this thread is for.
True, I just put 2500 into my thing and got a measly 78%. I now sincerely hope I’m wrong about all of this.
Let’s just hope more data points or the big man himself prove me wrong, because casting speed is the most fun stat imo and I’m not settling for a 75% increase from a dedicated build.
It gets worse - put 500 in and you get 62%.
If this formula (or anything similar) is correct, then mixed builds will be so ridiculously good that nothing else is worth considering - you can have 80% in your favourite stat, or 60% in agility, size, speed, cast speed and destruction all at once, plus a bunch of power and defence.
Dedicated builds are guaranteed to suck, regardless of the formula, because the standard build will be almost as good in every stat.
This is a common issue with all logarithmic formulae (which is why I’m trying to get the formula - so I can explain properly why it’s bad), but so far no luck. Let me know if you find the time to run up and down a long path.
For sure. Somebodys doing an unholy amount of 100m dashes after school tomorrow, or today actually.
But time to cash in those 4 hours of sleep, I’m not waiting for another 4am idea this time.
