Probability of hitting an X frame window [entrpntr]

F (row) = size of input window, in frames                    ; NOTE: GB/GBC/GBA ~= 59.7275 fps
σ (col) = standard deviation of input timing, in frames

Assumes a calibrated timer setup with an offset that hits in the exact center of the desired window (mean = 0). Modeled with a normal distribution for a few arbitrary levels of precision, with 60 fps inputs in mind (std dev = σ; lower std dev = more precise). I used to be closer to σ = 1.25 with my input timing, then improved to 1.00, and now am somewhere between 0.90 and 0.95.

For 30 fps games, you would halve the σ from 60 fps games to get your precision level (or, equivalently, keep the same σ and double the size of the input window).

Excel command:    =TEXT(ROUND(NORM.DIST($A2/2,0,B$1,TRUE)-NORM.DIST($A2/-2,0,B$1,TRUE), 5), "0.00000")


***EDIT: A (work-in-progress) tool for calibrating manip offsets and calculating one's precision level can be found here: https://plnkr.co/edit/w0hvCuTtvJVC6qRAZhGE?p=preview.


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F \ σ        0.64       0.80       0.90       1.00       1.25     1.5625
1/256     0.00243    0.00195    0.00173    0.00156    0.00125    0.00100
1/128     0.00487    0.00390    0.00346    0.00312    0.00249    0.00199
 1/64     0.00974    0.00779    0.00693    0.00623    0.00499    0.00399
 1/32     0.01948    0.01558    0.01385    0.01247    0.00997    0.00798
 1/16     0.03894    0.03116    0.02770    0.02493    0.01995    0.01596
  1/8     0.07779    0.06227    0.05536    0.04984    0.03988    0.03191
  1/4     0.15485    0.12416    0.11046    0.09948    0.07966    0.06376
  1/2     0.30393    0.24534    0.21882    0.19741    0.15852    0.12712
    1     0.56534    0.46803    0.42149    0.38292    0.31084    0.25103
    2     0.88183    0.78870    0.73348    0.68269    0.57629    0.47783
    3     0.98091    0.93921    0.90442    0.86639    0.76986    0.66294
    4     0.99822    0.98758    0.97373    0.95450    0.89040    0.79945
    5     0.99991    0.99822    0.99453    0.98758    0.95450    0.89040
    6     1.00000    0.99982    0.99914    0.99730    0.98360    0.94514
    7     1.00000    0.99999    0.99990    0.99953    0.99489    0.97491
    8     1.00000    1.00000    0.99999    0.99994    0.99863    0.98953