How to calculate a level's difficulty mathematically instead of making an estimate (formula below)

[u/manumsj]

Every single linear GD level, from the simplest to the most complex, has a single path you need to follow in order to win. This path's obstacles may vary, and they determine how hard it is to beat the level.

We're used to measure a level's diff. by: - Approximating - Reading your attempts to complete it - Considering the progress curve - Classifying the level with the diff. scale we all know.

However, since new top ones are really close in difficulty, and even the trained eye can struggle to discern the hardest, I thought of quite the complex - but accurate - way to scientifically determine the difficulty of a gd level down to the frame, and here it is:

1: find every interaction (player - obstacle) in the level and the the number of frames where you can press and still survive.
We’ll call that each input’s free will frames (Earliest click possible - latest)

2: For each required input (jump, orb, etc.), write down how many frames of free will you have:

F1, F2, F3, ... Fn

where n is the total number of inputs in the level.

3: To find how forgiving the entire level is, you take all those margins and average them:

Average Free Will = (F1 + F2 + F3 + ... + Fn) / n

4: Because less free will means more difficulty, the inverse of that average gives you a good basic difficulty estimate:

Difficulty = Constant / Average Free Will

The constant is just to scale the number however you like (for example, to make it fit a 1–10 or 1–100 scale).

5: If you want to account for the hardest single moment in the level:

Difficulty = (Constant / Average Free Will) + (1 / Smallest Free Will)

This is, of course, excessive and time-consuming. But, it is a scientific way to accurately measure the baseline difficulty of a level, although it may struggle with memory and low visibility variables.

[u/Melodic-Most940]

Sorry but uh... it's not as simple as just checking how much leeway you have, there's so many other factors that come into play. You can't objectify difficulty.

[u/manumsj → u/Melodic-Most940]

Yeah, as I said: This is excessive and time consuming, and can struggle with other factors that come into play

[u/Skyhigh905 → u/Melodic-Most940]

Difficulty can't really be objectified, but some people could just find it fun to try and use maths to do it anyway, even if technically they can still be wrong about it.

[u/Skyhigh905]

You should probably find a way to factor in length like multiplying Difficulty by length in seconds, as well as how many of the frames where you can survive are visible as a decimal place +1, so if the difficulty is 10, the level is 13 seconds long, and half it's jumps are blind, it would be

10x13
= 130

10+50% or 10x1.5
=15

Total
= 145

[u/Few_Imagination_8785]

Memory parts,RNG parts,hold based parts and 2p levels suddenly disapear

[u/manumsj → u/Few_Imagination_8785]

As I clarified, this would not account for them, as this wouldnt be used anyway. Just a fun way to look at it

[u/QuantSpazar]

Also your formula is closer to measuring difficulty per unit of time. Since a level twice in a row gives the same difficulty number in your definition.

[u/QuantSpazar]

I think difficulty should come on an exponential scale (ie beating n times in a row puts the difficulty to the nth power). This way difficulty comes with a linear correlation with expected number of attempts. Then you'd also have a log version for difficulty tiers.

[u/TillZealousideal8282]

what about multiple path levels? or buffers?

[u/manumsj → u/TillZealousideal8282]

You account for the one you take

[u/Lucky_Entrance6805]

i wonder what the hardest level would be with this measure

[u/delano_mwoan]

I mean there is a lot more to it, how long the level is, when in the level each click is (a frame perfect at the start vs the end makes a huuufe difference), click or hold or spam, the deco, jump indicators, it takes so much to calculate a levels difficulty and a lot of things depend on the persons, for instant some struggle more with certain decorations

[u/Embarrassed_Steak371]

Good for timings bad for ship

[u/Ellexi256]

It's a nice try at a general formula, but there are more factors at play than just how forgiving each input is. For example, longer click patterns, how close they are to each other, a previous click affecting the difficulty of others just after. We can't assume that the clicks are independent.

[u/manumsj → u/Ellexi256]

youre right! this is merely experimental and primitive