I don't follow your math.
Putting the question more simply. With all other things being equal (STAB, type effectiveness, ability boosts or lack thereof), how much base power does a pure damage move need to be on par with Aqua Cutter or Razor Shell? Whatever that number is, the answer to my previous question is that number times 1.25. (1.5/1.2 = 1.25)
Here's my take on that.
Almost every move with a high crit rate and 100% accuracy has a base power of 70 or lower.* From this I conclude that the 70 power high crit rate moves are on par with stronger high level moves, if perhaps not the absolute strongest; which would make them the equivalent of 90 or 95 base power. If we consider Cross Chop and Stone Edge to be peak move strength, making them the equivalent of a 100 base power move with no drawbacks (Earthquake, Gear Grind), and assume that 100 power with 80% accuracy is the same as 80 power with 100% accuracy, then the 70 power high crit rate moves are 10 power lower than that, which makes them the equivalent of a 90 power pure damage move. So 90*1.25 = 112.5 for Aqua Cutter.
As to Razor Shell. I go by the rule of thumb that a secondary effect is worth about 5 points of base power per 10% chance of the effect occurring. I'm much less sure of this for a high probability like 50%, and I'm more confident that this applies to a chance of inflicting a status condition than to a chance of lowering a stat; but my best guess is still that Razor Shell's effect is worth about 25 points of base power. Taking into account Razor Shell's 95% accuracy, that would make it on par with about a 95 power pure damage move, similar to Aqua Cutter. 95*1.25 = 118.75.
*(The only exception is Leaf Blade, but as I said, I consider that an anomaly stemming from Grass being considered weak in Gen 3. There's also the fact that Cross Poison also gets a 10% chance of poisoning, but similar to Leaf Blade, I think that's ignoreable on account of Poison being a weak attacking type when Cross Poison was introduced, before the addition of the Fairy type.)
Will take the math a little slower (and in Latex, which hopefully formats correctly for you. Give it a moment, if it does not format immediately.) Apologies if this is too slow. Feel free to scroll to everything past the math. Will factor in the critical this time too. Begins with the full damage formula:
LaTeX:
\[{\displaystyle {\text{Damage}}=\left({\frac {\left({\frac {2\times {\text{Level}}}{5}}+2\right)\times {\text{Power}}\times {\frac {A}{D}}}{50}}+2\right)\times {\text{Targets}}\times {\text{PB}}\times {\text{Weather}}\times {\text{GlaiveRush}}\times {\text{Critical}}\times {\text{random}}\times {\text{STAB}}\times {\text{Type}}\times {\text{Burn}}\times {\text{other}}\times {\text{ZMove}}\times {\text{TeraShield}}}\]
Ignores Targets, PB (Parental Bond), Weather, Glaive Rush, random (variation), type (effectiveness), other (mainly special cases), Z-Move, and Tera Shield. Will also remove critical
for now. Reintroduces that at the end. Pares the formula down to:
LaTeX:
\[{\displaystyle {\text{Damage}}=\left({\frac {\left({\frac {2\times {\text{Level}}}{5}}+2\right)\times {\text{Power}}\times {\frac {A}{D}}}{50}}+2\right)\times {\text{STAB}}}\]
Starts with Aqua Cutter this time.
Level = 100 for this, because why not?
A = Effective Attack. Will set this to 200.
D = Effective Defense. Will also make this 200. Leads to fewer terms to worry about.
Power = The move's effective power here. Sticks the Sharpness and Iron Fist boost in here too. Becomes 70 * 1.5 for Aqua Cutter and Sharpness.
STAB = Same-type attack bonus. Equals 1.5.
Plugs all those numbers in.
LaTeX:
\[{\displaystyle {\text{Damage}}=\left({\frac {\left({\frac {2\times {{100}}}{5}}+2\right)\times {{70} \times {1.5} }\times {\frac {200}{200}}}{50}}+2\right)\times {\text{1.5}}}\]
Simplifies this a little, in case of plugging in later moves. 42 * 200 / 200 / 50 = 0.84.
LaTeX:
\[{\displaystyle {\text{Damage}}=(({0.84}\times {70} \times {1.5})+{2})\times {\text{1.5}}}\]
Runs that through a calculator. Damage = 135.3 for a non-critical Aqua Cutter.
Adds the critical back in now.
LaTeX:
\[{\displaystyle {\text{Critical Damage}}=(({0.84}\times {70} \times {1.5})+{2})\times {\text{1.5}} \times {\text{1.5}}}\]
Technically could have just multiplied the previous number by 1.5. Went the longer route. Equals 202.95 damage on an Aqua Cutter critical.
Deals with one last calculation: average damage. Will not land criticals every time. Scores one 12.5% of the time at +1 critical. Deals regular damage the remaining 87.5% of the time.
LaTeX:
\[{\displaystyle {\text{Average Damage}}=({.125}\times {202.95})+({.875}\times {135.3})}\]
Equals
143.76 damage for the average Aqua Cutter hit.
Works backwards a little now. Begins with a formula similar to the one right above. Must figure out the damage of a different move, with a standard critical rate. Deals a critical hit 4.17% of the time, roughly. Fails to crit 95.83% of the time.
LaTeX:
\[{\displaystyle {143.76}=({.0417}\times {\text{Critical Damage}})+({0.9583}\times {\text{Regular Damage}})}\]
Knows Critical Damage = 1.5 * Regular Damage. Substitutes that in. (1/24) * (3/2) = 3/48 = 1/16 = 0.0625.
LaTeX:
\[{\displaystyle {143.76}=({.0625}\times {\text{Regular Damage}})+({0.9583}\times {\text{Regular Damage}})}\]
Created a formula with Regular Damage in both parentheses. Factors that out.
LaTeX:
\[{\displaystyle {143.76}={\text{Regular Damage}}\times ({.0625}+{0.9583})}\]
Adds the stuff in the parentheses. Divides both sides by that amount to get Regular Damage by itself.
LaTeX:
\[{\displaystyle {\frac {143.76}{0.0625+0.9583}}={\text{Regular Damage}}}\]
Regular damage = 140.8307. Must deal that much damage, non-critical to reach parity with Aqua Cutter.
Okay, then. Returns to an earlier formula. Replaced Sharpness's 1.5 multiplier with Iron Fist's 1.2. Removed Aqua Cutter's 70 base power with the "Base Move Power". Sticks the newly obtained 140.8307 number in for Damage.
LaTeX:
\[{\displaystyle {140.8307}=(({0.84}\times {\text{Base Move Power}} \times {1.2})+{2})\times {\text{1.5}}}\]
Solves for Base Move Power. Divides by 1.5 (STAB), subtracts 2, then divides again by (0.84 * 1.2). Turns into this:
LaTeX:
\[{\displaystyle \frac{\left(\frac {140.8307}{1.5}-{2}\right)}{0.84 \times {1.2}}={\text{Base Move Power}}}\]
Base move power = 91.158.
Math complete
The result: Aqua Cutter with Sharpness = a 91.158 power move affected by Iron Fist and no other effects, on average.
Feel free to point out any mistakes. Could have easily made one or two.
Edit: Missed the "without ability boosts" part. Uh...one second. Will edit that in shortly.
Edit2: No Latex this time. Takes a while to format.
Math Resume
Dropped Iron Fist and Sharpness. Kept STAB in. Assumed the same level 100, Attack = 200, and Defense = 200 Pokemon. Sped this up a lot. Used some heavy shortcuts, thanks to the formulas above.
Simplifies some of the damage formula the same way. 42 * 200 / 200 / 50 = 0.84.
Regular Aqua Cutter damage = ((0.84 * 70) + 2) * 1.5 = 91.2
Critical Aqua Cutter damage = 91.2 * 1.5 = 136.8
Average Aqua Cutter damage = (.125 * 136.8) + (.875 * 91.2) = 96.9
Piggybacks off of the prior formulas.
96.9 = (.0417 * Critical Damage) + (.9583 * Regular Damage)
Critical Damage = 1.5 * Regular Damage, of course. Factors out Regular Damage now.
96.9 = Regular Damage * ((1.5 * 0.0417) + 0.9583)
Regular damage = 94.921. Must hit this hard, non-critical.
Returns to the simplified damage formula, now with damage equal to 94.921.
94.921 = ((0.84 * Base Move Power) + 2) * 1.5
Solve for Base Move Power.
Base move power = ((94.921 / 1.5) - 2) / 0.84 = 72.953 power
Math over again
Aqua Cutter with no abilities = 72.953 base power move with no abilities and a standard critical rate, on average. Only adds an extra ~8.3% critical chance (at x1.5 damage), if you think about it. Hits for the standard amount 87.5% of the time still. Keeps the average much closer to the non-critical amount.
Edit3: Fixed an error. Again, feel free to point out any mistakes. Already made and corrected one.
