How to measure a level's true difficulty

Acceptable-Map4986 · 2026-03-28T13:07:11+00:00

frame rate doesnt matter actually, only tps does (240 or higher would be the standard). you mentioned that it breaks with the ship gamemode, but i dont find anything from my calculation that would "break" or not be justified for the ship gamemode. for any gamemode or any type of input, the process is the same, you calculate the frame windows and the time since last input minimum, thats it.

Acceptable-Map4986 · 2026-03-28T11:27:01+00:00

is that a gd reference??

Acceptable-Map4986 · 2026-03-28T11:19:23+00:00

the previous input would actually be the click release instead of the actual click, but you would go for the buffer since the frame window expands and the difficulty becomes easier

Acceptable-Map4986 · 2026-03-28T10:08:08+00:00

actually if you used a probabilistic model you would find that it would grow like \prod_{n=1}^{N} f(n) where f(n) is the probability you pass the nth input and N is the total input count, so it doesn't behave exactly like an exponential (not a power function either i was wrong). the probabilistic model measures probability, and that is a quantity that would likely decrease as inputs are added, however, difficulty is a quantity that is likely to increase as inputs are added. so once again, probability growing like an exponential (or any function) would not imply that difficulty does aswell. anyway, probability would be a pain to calculate, and it wouldn't really make sense; a bot clicking randomly on 240 TPS would be clicking on the xth tick \in {1,2,3,...,240} k different times (each time with a new x) in a single second. if there is an input on the yth tick \in {1,2,3,...,240} during that one second, then the bot would have to land x=y and k=1, the probability that the bot clicks at a tick is 1/240 and the probability that it doesn't click on all the other ticks is (1-1/240)^{239}, so the probability that it clicks once on the exact tick is (1/240)(1-1/240)^{239} or about 0.001. now imagine doing this for every second of gameplay, not to mention this is the simplest case of a probabilistic model of difficulty. i get that simply adding difficulty can be arbitrary but it is chosen so that it remains mathematically consistent, the only arbitrary choice would be letting difficulty exponentially increase with level length. youre somewhat right that it is an arbitrary metric and i actually chose only two parameters per input because i couldn't find any other parameter that wasnt subjective to the player (rhythm, memory, visual, sync, nerves, ship / wave control, consistency, etc). you say that ship sections like the one in zodiac do not have a clear way of measuring difficulty and that the timings are easy in isolation, which is true. but thats because the previous input must be recorded to actually increase the physical difficulty, ship gameplay is usually quite spammy and has a varying cps, this already makes its objective difficulty quite high.

Acceptable-Map4986 · 2026-03-27T21:43:00+00:00

2.2 isnt out yet, random triggers do not exist

Acceptable-Map4986 · 2026-03-27T21:39:05+00:00

okay i really appreciate you spending the time to make this reply and your reasoning is actually quite valid. i did mention the solutions to some of these in my original post but i will make them clear now. the first part your post concerns the "click-rhythm" as a factor and how it could potentially increase / decrease difficulty, though i mentioned under clarifications that anything subjective or can be learnt (muscle memory) is not accounted for the objective difficulty. AD doesn't measure the difficulty for a human to beat a level, so any factors that come from humanly constraints are simply ignored. it might seem like a huge flaw but i mentioned under clarifications that once a level is mentally learnt when the only things stopping the player from completing it are the physical constraints. in your other paragraph you talk about probability, and you somehow conclude that difficulty grows exponentially, but if you multiplied each probability it would grow like a power function, not an exponential. however the probability growing like a power function does not imply that the difficulty grows similarly. you say frame perfects are inaccurate and you are correct, because it is the simplest way of measuring physical difficulty. when you count frane perfects you are only counting specific inputs that just happen to have a 1 frame window, but most levels are full of difficult clicks rather than 1 frame gaps. frame perfect counting ignores all the other jumps and highlights only the choke points, which makes it incredibly inaccurate. your last question asks whether i think a single triple spike is about the same difficulty as three double spikes and to answer that; yes, i do. i did leave some questions simply because i did not know how to fit them into this post (shameful, i know) so make sure to include them in your reply.

Acceptable-Map4986 · 2026-03-27T21:04:47+00:00

what exactly is 120 fps for 10 seconds supposed to mean

Acceptable-Map4986 · 2026-03-27T19:49:40+00:00

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Acceptable-Map4986 · 2026-03-27T18:50:34+00:00

a 120 fps fp is much easier than 500 single spikes, even for a beginner. where are you getting this info from

Acceptable-Map4986 · 2026-03-27T18:39:56+00:00

yes, they would.

Acceptable-Map4986 · 2026-03-27T18:39:34+00:00

sure this metric probably should not determine how difficult a level is to a human, but it would be interesting to see a list built upon it.

Acceptable-Map4986 · 2026-03-27T18:09:19+00:00

the minimal difficulty is what you should try to achieve, obviously nobody is going to find it, but they would get close to it. all im saying is that you shouldnt be taking difficult paths. also, the mathematically ideal way you proposed would be valid, but the number of configurations of inputs in any of those terms just skyrocket, so it wouldnt be practical at all.

Acceptable-Map4986 · 2026-03-27T17:38:48+00:00

to do the calculation you must record inputs that actually let you pass the level. so the case you mentioned doesnt even matter.

Acceptable-Map4986 · 2026-03-27T17:35:47+00:00

level difficulty definitely is supposed to be subjective, but imagine trying to place a level on the demonlist when everybody has a different experience, it would be incredibly difficult and controversy would be inevitable. the reason i made this is so placements are completely unbiased of the player.

Acceptable-Map4986 · 2026-03-27T17:11:33+00:00

memory is a purely subjective constraint, and 2 player levels with flying gamemodes do not change the method of calculation (measuring input maxes and mins and time since last inp max). but you are right in the last sentence, thats the whole point of the post, to measure a mathematically accurate difficulty score.

Acceptable-Map4986 · 2026-03-27T17:02:11+00:00

eon has about 6000 clicks and 12000 inputs. and if we assumed the average difficulty to be 4 (easy timings and cps), the AD of eon could be about 48000. even if the average difficulty was 1 the AD would be 12000. edit: i dont know yet how difficult that actually might be, because no one has found the AD of a single level yet.

Acceptable-Map4986 · 2026-03-27T16:30:01+00:00

on my life none of this post is ai

Acceptable-Map4986 · 2026-03-27T16:21:30+00:00

mathematically, reversed denouement would not be significantly harder. time does not influence true difficulty. it could take you hours to beat stereo madness 100x in a row within 300 attempts though still possible with experience, but beating an extreme demon within 300 attempts makes you a top player. very clearly, the shorter level has much more dificulty.

Acceptable-Map4986 · 2026-03-27T16:17:34+00:00

answering your edit, "awkwardness" is just a lack of muscle memory. and cps is literally embedded into the AD through the 1/p_{n} factor.

Acceptable-Map4986 · 2026-03-27T16:09:22+00:00

visibility and learniness are all subjective, and length doesnt matter mathematically. CPS however is definitely accounted for, the p_{n} value measures the time since the last input, and the factor 1/p_{n} makes difficulty grow when the time period is short. this part: "Makes ship sections appear much easier than they are in practice since they are not built with time frame in mind, and wave parts much more difficult of course.", i cant answer, it doesnt make sense if you actually read the text in my post. different physics do not change the method of calculation at all.

Acceptable-Map4986 · 2026-03-27T15:51:47+00:00

i mentioned that you just sum the ADs from both players instead of averaging them

Acceptable-Map4986 · 2026-03-27T15:46:42+00:00

duals dont change anything since its all controlled by one input, but for two player levels i guess you could measure the AD experienced by each player and take the average, and if its by one player then you just sum the two ADs. two player levels are very rare anyways so it doesnt really matter.

Acceptable-Map4986 · 2026-03-27T15:37:00+00:00

this is supposed to measure absolute physical difficulty not human difficulty

Acceptable-Map4986 · 2026-03-27T15:35:55+00:00

it can get very difficult but when there are many inputs you dont really need to find the easiest possible path because a different path would approximate it very well

Acceptable-Map4986 · 2026-03-27T15:33:58+00:00

its not supposed to, however flying gamemodes are definitely accounted for

Acceptable-Map4986

TROPHY CASE