Skill Check

Success = 1 - 1 / (1 + exp(0.03 * (Attack - Defense))

where "exp" returns e raised to the power of the number that follows, the constant e equals 2.71828182845904, the base of the natural logarithm. EXP is a standard function for both Microsoft Excel and LibreOffice.

From http://www.calloffate.com/forum/forum_posts.asp?TID=191&PID=29738 :

Answer: srand - Casting spells uses a slightly different skill check curve than that used for all other skill checks. It has the same midpoint, but is steeper through the middle. So once you are over the 50/50 point, your casting gets reliable much faster than with a normal skill check curve. But conversely, under the 50/50 point your casting is much less reliable than with the normal skill check curve. I just found this out tonight, myself.

Example

Using this formula for a skill check of 500 generates the following chances of success:

Skill Success 300 0.2% 310 0.3% 320 0.4% 330 0.6% 340 0.8% 350 1.1% 360 1.5% 370 2.0% 380 2.7% 390 3.6%

Skill Success 400 4.7% 410 6.3% 420 8.3% 430 10.9% 440 14.2% 450 18.2% 460 23.1% 470 28.9% 480 35.4% 490 42.6%

Skill Success 500 50.0% 510 57.4% 520 64.6% 530 71.1% 540 76.9% 550 81.8% 560 85.8% 570 89.1% 580 91.7% 590 93.7%

Skill Success 600 95.3% 610 96.4% 620 97.3% 630 98.0% 640 98.5% 650 98.9% 660 99.2% 670 99.4% 680 99.6% 690 99.7%

You can easily generate success %s for any specific skill level using a spreadsheet by putting the skill level into cell A1, the difficulty in cell A2, and inserting the following formula into cell A3:

=1 - 1 / (1 + EXP(0.03 * (A1 - A2)))