Genfanad Max Hit and DamaGE (2 Pi)
2 Pi's Max Hit and Damage Rolls Theory
Max hit
Max hit is based on 2 factors: effective Strength level (effStr) and Power bonus (Pow). The effect of combat level difference on your damage output only kicks in when fighting enemies 4+ levels above your melee combat level, and will be disregarded in this topic.
Effective Strength level is obtained from
effStr = L + S + P
where L is your base strength level, S is the combat stance boost (0 for Accurate/Defensive, 1 for Controlled, 3 for Aggressive) and P is the current boost from a Strength potion (starting at +7, decreasing by 1 every 2 minutes).
Power bonus Pow is as shown in the combat menu.
Your max hit can then be calculated with the following formula:
M = 1/500 * (effStr + 15) * (Pow + 125) - 3
This result is NOT rounded at this point, as decimals will have an influence on your average damage output. More details about this formula are given down below.
Damage rolls
A random hit H is obtained as follows: - Take 3 random samples (x1, x2, x3) from a uniform distribution on the interval [0, 1] - Average these 3 random samples: x = 1/3 * (x1 + x2 + x3) - Multiply with max hit and round up: H = ceil(M * x) The expected value (average) of H can be calculated with
E(H) = (M + 1) / 2
Because damage is rounded only in the final step, the decimal values of M determine how likely you are to see your integer max hit. For example, with M=3.2 you are able to hit a 4, but you will see it less often than with M=3.9.
The averaging of the 3 random samples also forces the hit distribution to be heavily weighted towards the center, as shown in this probability density graph.
Extra information
Due to the multiplicative nature of the max hit formula, it's not as simple as just saying "+1 max hit every x strength levels, +1 max hit every y power bonus". Rather, the increase in max hit per strength level is dependent on your power bonus, and vice versa. As such, you should always consider both values when choosing between unlocking better gear (higher power) or training strength.
The max hit formula can be visualized using a colormap as shown below, with strength (horizontal axis) ranging up to 100 and power (vertical axis) up to 200. Contour lines (lines of constant M) are drawn at max hit intervals of 5.
To get more insight, this colormap can be "sliced" horizontally or vertically by selecting a constant value for either strength or power, and drawing the function of max hit versus the other variable. In the graph below, this is done for strength values of 1, 20, 40 and 60, corresponding to slicing the colormap vertically at those points along the x-axis.
Similary, this can also be done for constant power values of 0, 25, 50, 75 and 100 as shown below.
Lastly, by drawing the max hit formula as a function of both variables and interpreting max hit as "height" we can draw it as a 3D surface. Extending the ranges of strength and power into the negatives (purely theoretical of course), we can observe a shape known as a hyperbolic paraboloid, more commonly known as a saddle surface, and resembling a Pringles potato chip.
This information is from 2 Pi as found in the Genfanad Skilling Methods Discord