| Post/Author/DateTime | Post |
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| #1FrogReaverFeb 12, 2015 0:07:10 | I wanted to make a thread that had math formulas and explanations for calculating some fairly complex D&D related numbers.
Some of the basic formulas I eventually want to include are: 1. generalized formula and/or techniques for solving complex DPR calculations 2. Chance to do X damage with a given weapon or fighting style 3. Defensive formulas 4. Benefits of spells like shield 5. Benefits of feats like defensive duelist 6. Anything else
Much of this work is already present in other places and will simply need moved over and properly indexed. If anyone can thing of something they believe belongs here feel free to post it and I will include it when I get time. |
| #2FrogReaverFeb 12, 2015 10:39:50 | My current pet project is about trying to evaluate a characters chance to do at least X damage on a turn (weapon attacks). I think this may make for a more realistic comparison than DPR (especially in the early game where 1 attack can often kill a monster)
For a single attack: Let C be the chance-to-hit,
Then for a one handed weapon with a 1dN damage dice, the chance to deal at least a particular damage amount is: N + stat damage = 1/N * C (N-1) + stat damage = 2/N * C (N-2) + stat damage = 3/N * C ... ... ... 2 + stat damage = (N-1)/N * C 1 + stat damage = (N)/N * C -------------------------------------------------------- Example 1d4, +3 stat bonus (no extra +damages) 1/4 * C = (chance to deal 7 damage) 2/4 * C = (chance to deal at least 6 damage) 3/4 * C = (chance to deal at least 5 damage) 4/4 * C = (chance to deal at least 4 damage)
***remember that C is the characters chance to hit the given target (you cannot deal damage without hitting) ---------------------------------------------------------------------------- It's quite a bit more complex to evaluate the chance of a great weapon user that has the great weapon fighting style that allows rerolls on 1's and 2's
Let C be the chance to hit,
(1/N + 2/N^2) * C = N + stat Damage 2(1/N + 2/N^2) * C = (N-1) + stat damage .... .... (N-2)*(1/N + 2/N^2) * C = 3 + stat damage [(N-2)*(1/N) + (N-1)*(2\N^2)] * C = 2 + stat damage [(N-2)*(1/N) + (N)*(2\N^2)] * C = 1 + stat damage -------------------------------------------------------------- Example 1d6 + 3 stat bonus (no extra +damage) (1/6 + 2/36) * C = (chance to deal 9 damage) 2(1/6 + 2/36) * C = chance to deal at least 8 damage) 3(1/6 + 2/36) * C = chance to deal at least 7 damage) 4(1/6 + 2/36) * C = chance to deal at least 6 damage) [4(1/6) + 5(2/36)] * C = chance to deal at least 5 damage) [4(1/6 + 6(2/36)] * C = chance to deal at least 4 damage) ---------------------------------------------------------------------------- Calculate weapons with 2dN damage dice
Let C be the chance to hit, (assume no odd sided dice)
1/N^2 = 2N + stat Damage 2(1/N^2) = (2N - 1) + stat Damage ...... ...... (N-1)*(1/N^2) = (2N - (N-2)) + stat damage (N)*(1/N^2) = (2N - (N-1)) + stat damage (N-1)*(1/N^2) = (2N - N) + Stat Damage (N-2)*(1/N^2) = (2N - (N+1)) + Stat Damage ...... ...... 2(1/N^2) = 3 + stat Damage 1/N^2 = 2 + stat Damage --------------------------------------------------------------------------- Example 2d6 + 3 stat 1/36 * C = 15 damage 3/36 * C = at least 14 damage 6/36 *C = at least 13 damage 10/36 * C = at least 12 damage 15/36 = at least 11 damage 21/36 = at least 10 damage 26/36 = at least 9 damgae 30/36 = at least 8 damage 33/36 = at least 7 damage 35/36 = at least 6 damge 36/36 = at least 5 damage
-------------------------------------------------------------------------- Calculate a 2dN damage dice weapon that rerolls on 1's and 2's
-------------------------------------------------------------------------- The final part will be to find a method to scale this to multiple attacks
More Calculations will be coming tomorrow!
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| #3FrogReaverFeb 13, 2015 0:13:41 | Halfling reroll new probabilities
probability of rolling 1 = (chance to roll a one(gets rerolled)) * (chance to roll a one) = 1/20*1/20 = 0.25% probability of rolling X in the range of 2-20 = (chance of rolling X) * (chance of rolling 1(gets reroll))*(chance of rolling X) = 1/20 + 1/20*1/20 = 5.25%
New cumulative chance to hit formula
Let M = target AC, Let A = attack bonus
(21 + A - M) * 5.25% = chance to hit For M - A > 1 .025 = chance to hit for M-A <= 1
5.25% = chance to crit |
| #4FrogReaverFeb 12, 2015 0:07:39 | Reserved 3 |
| #5FrogReaverFeb 12, 2015 0:07:46 | Reserved 4 |
| #6FrogReaverFeb 12, 2015 0:07:53 | Reserved 5 |
| #7FrogReaverFeb 12, 2015 0:08:01 | Reserved 6 |
| #8FrogReaverFeb 12, 2015 0:08:08 | Reserved 7 |
| #9FrogReaverFeb 12, 2015 0:08:16 | Reserved 8 |
| #10FrogReaverFeb 12, 2015 0:08:24 | Reserved 9 |
| #11FrogReaverFeb 12, 2015 0:08:39 | Reserved 10 |
| #12TheNovaLordFeb 12, 2015 2:14:38 | www.Paizo.com They love this stuff Enjoy |
| (Reply to #12)FrogReaver |
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| #14TheNovaLordFeb 12, 2015 11:12:49 | Reducing a free flowing d20 game to a pile of numbers, play paizos pathfinder for such math |
| #15JamwesFeb 12, 2015 11:47:43 | I look forward to seeing this guide completed and having a resource for the math behind it all. I don't build power characters, but I like to see how my goofy character concepts stack up. I hope you have this added to the guide of guides so that I can find it again when I want to crunch some numbers. |
| (Reply to #15)FrogReaver | Thanks. I don't know how to get it linked in the guide of guides. Do you know how? Also, any help on formatting would help.
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| #17Tempest_StormwindFeb 12, 2015 21:23:01 | I'll help with it (gladly) when I get back. |
| #18JamwesFeb 13, 2015 6:21:18 |
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| #19melloredFeb 13, 2015 10:53:28 | Halfling...
base chance of success * 1.05
i.e. 50% chance to hit/save = 52.5% 5% chance to crit = 5.25% |
| (Reply to #19)FrogReaver |
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