Calculating fumbles

[Akisa]

I'm looking for formula to calculate chances of rolling a fumble, and prove that the higher levels with more attacks the higher chances of fumbling goes up.

[Person_Man]

Critical Fumbles are not RAW. And thus there isn't an explicit RAW formula for calculating them.

And in most cases, they make character who depend on attack rolls significantly weaker then characters who don't depend on attack rolls.

But if you assume that a character makes a Critical Fumble on a roll of a natural 1, then you assume that there is a 5% chance of a Critical Fumble per attack roll. So it's simple multiplication. # of attacks per round (inclusive of attacks of opportunity) * 5% = % chance per round of a Critical Fumble.

[Maginomicon]

A million people on this forum would probably agree with you that fumbles become more likely as you level up or have more attacks.

What's the context for your specific inquiry though? If you're trying to argue with your GM about whether to use fumbles, perhaps you'd be better off trying to compromise with your GM instead of rejecting his use of fumbles.

For example, you could compromise with him by using this "Diminishing Returns" fumble system (http://www.giantitp.com/forums/showthread.php?t=317155). The system in a nutshell: fumbling requires a number of confirmation rolls equal to your number of iteratives, confirmation rolls are versus touch AC, and if any of the confirmations hit, it's a miss instead of a fumble).

[Bakkan]

Critical Fumbles are not RAW. And thus there isn't an explicit RAW formula for calculating them.

And in most cases, they make character who depend on attack rolls significantly weaker then characters who don't depend on attack rolls.

But if you assume that a character makes a Critical Fumble on a roll of a natural 1, then you assume that there is a 5% chance of a Critical Fumble per attack roll. So it's simple multiplication. # of attacks per round (inclusive of attacks of opportunity) * 5% = % chance per round of a Critical Fumble.

/mathpedantry on

Technically, (# of attacks) x 5% gives you the expected number of critical failures per round, which is higher than the chance of getting at least one critical failure a round (for an easy proof, if you have 20 or more attacks [but still finite], your expected number of critical failures is at least 1, but you still have a nonzero chance of getting no critical failures). To calculate the chance that you'll get at least one critical falure in a round, it's easiest to calculate the chance that you'll get no critical failures, which is (95%)^(# of attacks), and then subtract that value from one.


For instance:
{table=head]# of attacks | Chance of getting at least one crit fail | Expected number of crit fails per round
1 | 5.0% | 0.05
2 | 9.8% | 0.1
3 | 14.3% | 0.15
4 | 18.5% | 0.2
5 | 22.6% | 0.25
6 | 26.5% | 0.3
7 | 30.2% | 0.35
8 | 33.7% | 0.4
9 | 37.0% | 0.45
10 | 40.1% | 0.5
11 | 43.1% | 0.55
12 | 46.0% | 0.6
13 | 48.7% | 0.65
14 | 51.2% | 0.7
15 | 53.7% | 0.75
16 | 56.0% | 0.8
17 | 58.2% | 0.85
18 | 60.3% | 0.9
19 | 62.3% | 0.95
20 | 64.2% | 1
21 | 65.9% | 1.05
22 | 67.6% | 1.1
23 | 69.3% | 1.15
24 | 70.8% | 1.2
25 | 72.3% | 1.25
26 | 73.6% | 1.3
27 | 75.0% | 1.35
28 | 76.2% | 1.4
29 | 77.4% | 1.45
30 | 78.5% | 1.5
31 | 79.6% | 1.55
32 | 80.6% | 1.6
33 | 81.6% | 1.65
34 | 82.5% | 1.7
35 | 83.4% | 1.75
36 | 84.2% | 1.8
37 | 85.0% | 1.85
38 | 85.8% | 1.9
39 | 86.5% | 1.95
40 | 87.1% | 2
41 | 87.8% | 2.05
42 | 88.4% | 2.1
43 | 89.0% | 2.15
44 | 89.5% | 2.2
45 | 90.1% | 2.25
46 | 90.6% | 2.3
47 | 91.0% | 2.35
48 | 91.5% | 2.4
49 | 91.9% | 2.45
50 | 92.3% | 2.5
[/table]

/mathpedantry off

All this being said, the expected number of crit fails per round is likely the better measure of how bad something is, but the chances of getting at least one fail each round is interesting.

[skyth]

Yeah, it's hard to calculate the chance if you don't know the specifics. You have to define what a fumble is. Is it a natural 1, is it missing by a certain amount, is it a natural 1 followed by another roll to determine if it's a fumble?

All of those would have different math to determine what the chance per fumble is and if being better (more attacks) causes the chance to fumble to go up.

[Hua]

We use a natural 1 is a chance of fumble.
The confirmation roll is a DC15 Reflex save. At higher levels, when people are more skilled, it is less likely to happen. At lower levels, it can still be a fumble but won't be every time.

We have used this for a couple decades now and it works well for us.

[Bakkan]

That's an interesting idea. In order to keep your fumbles/round from increasing, as you gain attacks you have to gain enough Reflex to pass the DC 15 check reliably.

/mathpedantry on

The formula for number of fumbles per round while making N attacks per round and having a Reflex save of R is F = 0.05N*0.05max(14-R,1). Let r be a character's reflex save at level 1. Then at level 1 he is making 0.0025(14-r) fumbles per round. We want 0.0025Nmax(14-R,1) to be less than this, which means we want 14-R to be less than (14-r)/N, which reduces to R being greater than 14 - (14-r)/N.

The table below shows the necessary Reflex saves to have the fumbles/round be no greater than with a single attack as additional attacks are granted.
Reflex Save at Level 1 | 2 attacks |3 attacks | 4 attacks | 5 attacks | 6 attacks | 7 attacks
-2 | +6 | +9 | +10 | +11 | +12 | +12
-1 | +7 | +9 | +11|+11|+12|+12
+0|+7|+10|+11|+12|+12|+12
+1|+8|+10|+11|+12|+12|+13
+2|+8|+10|+11|+12|+12|+13
+3|+9|+11|+12|+12|+13|+13
+4|+9|+11|+12|+12|+13|+13
+5|+10|+11|+12|+13|+13|+13

Hmm, seems like this works well at higher levels and number of attacks as +10- +13 is not unreasonable even for a poor save. It looks a little painful for poor Ref folks right about level 6 (or earlier with TWF), though.

[Studoku]

If you're trying to calculate an appropriate rate for fumbles, this post from a previous thread should help:


Critical Fumble Rule:
If at any time a DM shall propose using a "critical failure" or "fumble" table of any sort in a 3.X game, the players are to beat the DM with folding chairs until each of them has accidentally struck himself with his chair at least once, while keeping a count of the number of strikes made before this happens. Then, the average rate of such "fumbles" as generated by a table full of nerds swinging improvised weapons will establish the maximum probability of a "fumble" within the game mechanics for a level 1 Commoner (note that this already will probably require rolling multiple Natural 1's in succession to confirm a fumble), with the probability dropping by at least an order of magnitude per point of BAB of the attacking character. Thus a full-BAB character at level 20 might have to roll 20+ Natural 1's in a row to before you even bother glancing at the Fumble Table.

[Person_Man]

We use a natural 1 is a chance of fumble.
The confirmation roll is a DC15 Reflex save. At higher levels, when people are more skilled, it is less likely to happen. At lower levels, it can still be a fumble but won't be every time.

We have used this for a couple decades now and it works well for us.

If it works for you so be it. But more attacks still equals more failure, especially at low levels. (Pity the Ranger, Monk, and Totemist). And even at higher levels, it still screws players with more attacks, since you auto-fail Saves on a roll of a 1. It seems like a built in way to encourage spellcasters and psionics.