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Putting a Difficulty Level to achieving a certain Accuracy

posted
Total Posts
9
Evening
2,464 posts
Joined December 2012
Topic Starter
Evening
Wanted to know the community opinions about if the calculated difficulty is reasonable with the achieved accuracy as shown by the spoiler box below

Not sure if i should go with DIFF1/SQRT(DIFF1)/DIFF2 or any thing else so I'd like some inputs in this basically

Difficulty is relative to itself, there isn't really any unit/reason behind if it's 1.0 or 100, it scales accordingly
SPOILER
ACC  -  DIFF1  -  SQRT(DIFF1)  -  DIFF2  -  SQRT(DIFF2)  

100.00	1.703	1.305	--------	--------
099.75	0.976	0.988	--------	--------
099.50	0.799	0.894	0.828	0.414
099.00	0.677	0.823	0.669	0.335
098.50	0.613	0.783	0.602	0.301
098.00	0.570	0.755	0.558	0.279
097.50	0.537	0.733	0.526	0.263
097.00	0.510	0.714	0.500	0.250
096.50	0.488	0.699	0.478	0.239
096.00	0.468	0.684	0.460	0.230
095.50	0.451	0.672	0.443	0.222
095.00	0.435	0.660	0.429	0.214
094.50	0.421	0.649	0.416	0.208
094.00	0.409	0.640	0.404	0.202
093.50	0.397	0.630	0.393	0.196
093.00	0.386	0.621	0.383	0.191
092.50	0.376	0.613	0.373	0.187
092.00	0.366	0.605	0.364	0.182
091.50	0.357	0.597	0.356	0.178
091.00	0.348	0.590	0.348	0.174
090.50	0.340	0.583	0.340	0.170
090.00	0.332	0.576	0.333	0.167
089.50	0.325	0.570	0.326	0.163
089.00	0.318	0.564	0.320	0.160
088.50	0.311	0.558	0.313	0.157
088.00	0.304	0.551	0.307	0.154
087.50	0.298	0.546	0.301	0.151
087.00	0.292	0.540	0.296	0.148
086.50	0.286	0.535	0.290	0.145
086.00	0.280	0.529	0.285	0.143
085.50	0.275	0.524	0.280	0.140
085.00	0.269	0.519	0.275	0.137
084.50	0.264	0.514	0.270	0.135
084.00	0.259	0.509	0.265	0.133
083.50	0.254	0.504	0.261	0.130
083.00	0.249	0.499	0.256	0.128
082.50	0.244	0.494	0.252	0.126
082.00	0.240	0.490	0.248	0.124
081.50	0.235	0.485	0.244	0.122
081.00	0.231	0.481	0.239	0.120
080.50	0.226	0.475	0.235	0.118
080.00	0.222	0.471	0.232	0.116
079.50	0.218	0.467	0.228	0.114
079.00	0.214	0.463	0.224	0.112
078.50	0.210	0.458	0.220	0.110
078.00	0.206	0.454	0.217	0.108
077.50	0.202	0.449	0.213	0.106
077.00	0.198	0.445	0.209	0.105
076.50	0.194	0.440	0.206	0.103
076.00	0.190	0.436	0.203	0.101
075.50	0.187	0.432	0.199	0.100

More on DIFF 2 Spread

SPOILER
ACC  -  DIFF2  -  SQRT(DIFF2)
099.69	1.451	0.725
099.68	1.176	0.588
099.67	1.098	0.549
099.66	1.050	0.525
099.65	1.016	0.508
099.64	0.990	0.495
099.63	0.968	0.484
099.62	0.949	0.475
099.61	0.933	0.466
099.60	0.919	0.459
099.59	0.906	0.453
099.58	0.894	0.447
099.57	0.884	0.442
099.56	0.874	0.437
099.55	0.865	0.432
099.54	0.856	0.428
099.53	0.849	0.424
099.52	0.841	0.421
099.51	0.834	0.417
099.50	0.828	0.414



Interesting things:

Probability of hitting at a certain MS, 000 means the probability of hitting between 000 and 001 ms from the note
PROBABILITY     MS (MILLISECOND) 
0.0895	000
0.0840	001
0.0785	002
0.0729	003
0.0675	004
0.0622	005
0.0571	006
0.0521	007
0.0474	008
0.0430	009
0.0388	010
0.0350	011
0.0314	012
0.0281	013
0.0250	014
0.0223	015
0.0198	016
0.0176	017
0.0155	018
0.0137	019
0.0121	020
0.0107	021
0.0094	022
0.0083	023
0.0073	024
0.0064	025
0.0056	026
0.0049	027
0.0043	028
0.0038	029
0.0033	030
0.0029	031
0.0025	032
0.0022	033
0.0019	034
0.0017	035
0.0015	036
0.0013	037
0.0011	038
0.0010	039
0.0009	040
0.0007	041
0.0007	042
0.0006	043
0.0005	044
0.0004	045
0.0004	046
0.0003	047
0.0003	048
0.0003	049
0.0002	050
0.0002	051
0.0002	052
0.0001	053
0.0001	054
0.0001	055
0.0001	056
0.0001	057
0.0001	058
0.0001	059
0.0001	060
0.0000	061
0.0000	062
0.0000	063
0.0000	064

if you're interested in the calculations

https://docs.google.com/spreadsheets/d/ ... sp=sharing
Last edited by Evening , edited 6 times in total.
Elementaires
658 posts
Joined January 2013
Elementaires
yes
Evening
2,464 posts
Joined December 2012
Topic Starter
Evening

Elementaires wrote:

yes
pls
Jinjin
891 posts
Joined September 2013
Jinjin
cute ' w'

may look into this more when i have the time

edit: I did take a look at the spreadsheet but aaaaa i'd suggest organizing the sheet further, because it's kinda hard to understand the intentions for each of the calculations / data tables that you have done. Maybe write a sentence or two of explanations? That would help people give better feedback
Full Tablet
2,543 posts
Joined September 2011
Full Tablet

Evening wrote:

Edit:
Forgot this was in this too, this shows the probability of players hitting within a certain range, the distribution is one-sided however and note that this is a cumulative statistic, it's supposed to have and asymptote at 1.0 probability but stuff happens
Instead of using trapezoids, you could use the exact integrals of the formula (they are simple for the formula used) you came up with.

With:
a = 1.42482
b = 0.765566
c = 0.136078

Your graph formula is:

It's definite integral from 0 to x is:
The limit at infinity of that integral is: (This is the value of the sum all the x-values in the table)

So, the cumulative probability (from 0 to x+1) is:
The "Trapezoid Area" would be replaced by the differences of cumulative probability between rows:

Note: Logarithms are using base "e", "LOG" in excel by default uses base 10, "LN" uses base "e".
Evening
2,464 posts
Joined December 2012
Topic Starter
Evening

Full Tablet wrote:

Evening wrote:

Edit:
Forgot this was in this too, this shows the probability of players hitting within a certain range, the distribution is one-sided however and note that this is a cumulative statistic, it's supposed to have and asymptote at 1.0 probability but stuff happens
Instead of using trapezoids, you could use the exact integrals of the formula (they are simple for the formula used) you came up with.

With:
a = 1.42482
b = 0.765566
c = 0.136078

Your graph formula is:

It's definite integral from 0 to x is:
The limit at infinity of that integral is: (This is the value of the sum all the x-values in the table)

So, the cumulative probability (from 0 to x+1) is:
The "Trapezoid Area" would be replaced by the differences of cumulative probability between rows:

Note: Logarithms are using base "e", "LOG" in excel by default uses base 10, "LN" uses base "e".
yea this really helped make the calculation way more accurate and neater, thanks a ton for this, though i'm having trouble calculating at a 0.1 x increment interval (you've calculated in a 1 x increment intervals) for some weird reasons unknown, it adds up to >1 this time

would be great if you can help out again of course

iJinjin wrote:

I did take a look at the spreadsheet but aaaaa i'd suggest organizing the sheet further, because it's kinda hard to understand the intentions for each of the calculations / data tables that you have done. Maybe write a sentence or two of explanations? That would help people give better feedback
Not sure if the intention really got through but like I actually wanted to ask if the difficulty relativity of getting a certain percentage is reasonable, not really anything about the spreadsheet mainly, if you're interested:

I've used 30 random selected scores to approximate a logistic curve (because it fits best for some weird reason) and scaling it down so that the area is 1.0 in total, pretty much using that as a probability curve to calculate probabilities and stuff

I've scaled down the hit error ranges by a certain multiplyer as a difficulty changing factor and wanted to ask if the output is reasonable basically, i'll amend the post to make it clearer
Full Tablet
2,543 posts
Joined September 2011
Full Tablet

Evening wrote:

yea this really helped make the calculation way more accurate and neater, thanks a ton for this, though I'm having trouble calculating at a 0.1 x increment interval (you've calculated in a 1 x increment intervals) for some weird reasons unknown, it adds up to >1 this time

would be great if you can help out again of course
For a step size of s (in the previous formulas I used s=1).
The cumulative probability (from 0 to x+s):
The Area (differences between rows):
Evening
2,464 posts
Joined December 2012
Topic Starter
Evening

Full Tablet wrote:

Evening wrote:

yea this really helped make the calculation way more accurate and neater, thanks a ton for this, though I'm having trouble calculating at a 0.1 x increment interval (you've calculated in a 1 x increment intervals) for some weird reasons unknown, it adds up to >1 this time

would be great if you can help out again of course
For a step size of s (in the previous formulas I used s=1).
The cumulative probability (from 0 to x+s):
The Area (differences between rows):
it worked out perfectly, thanks a lot again
FrenzyLi
258 posts
Joined April 2015
FrenzyLi
What a nice read!
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