Energy Enhancements are too good at +1 (math)

[Nail]

The equation for expected damage per attack looks like this:

A = P{D[1+Pc(Mc-1)] + Db}

where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier
Db = Bonus Damage dice that are not multiplied by a confirmed critical

Keep in mind that at low probabilities to hit, the Pc gets smaller than the normal value:
Pc = Min (threat range/20, P)

 

[FreeTheSlaves]

...actually, your crit numbers are off. Sorry! Your crit number should be 1.1.

Shouldn't it be 5% if the confirmations are successful 1/2 the time for a 19+*2 weapon?

Btw, nice formula, it probably pays for all to use that layout for clarity.

 

[Nail]

+3 longsword
0.6 * ((4.5base + 4dam +3sword) * 1.1crit) = 7.59

+1 flaming burst longsword
0.5 * (((4.5base + 4dam +1sword) * 1.1crit + (0.10confirm * 5.5flaming burst)) +3.5flame) = 7.25

Fixed that for you. It's easy to get turned around........

 

[Nail]

Shouldn't it be 5% if the confirmations are successful 1/2 the time for a 19+*2 weapon?

Lemme dig out the algebra.....

 

[Nail]

Okay....let's try this:

Normally (without critcals or burst), the expected damage per attack is:

A = PD

Pretty simple. Then we add in the criticals....and we can be a bit tricky here, since criticals actually just add damage to the normal damage. They add one less than the weapons multiplier, i.e. a x2 multiplier just adds one "extra damage", while a x3 multiplier adds two "extra damages".

extra damage = D(Mc-1)

Then we put in the chance to threaten......

=Pc*D(Mc-1)

....and finally multiply the whole thing by the chance to confirm the critical. Fortunately that's the same chance as the normal chance to hit (barring a feat, obviously)

A = PD + PDPc(Mc-1)

where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier



How's that so far?

 

[Coredump]

Lemme dig out the algebra.....

Actually it is pretty easy.

His logic was good, 10% threaten, 50% confirm leads to 1.05 crit, but.....

He calculated the 50% twice. Once in his 'head' to come up with the 1.05, and once in the beginning of the equation (the 0.6 or 0.5)

 

[Nail]

For a long sword, with a 19-20/x2 threat and crit, the numbers are:

Pc= 0.10
Mc= 2

so the factor that you multiply weapopn damage to get expected extra damage from criticals is:

Pc(Mc-1) = 0.10(2-1) = .1

 

[FreeTheSlaves]

Once in his 'head' to come up with the 1.05, and...

Tis true, I only really developed 'instinctual' maths.

 

[Nail]

Actually it is pretty easy.

Not really.

 

[Nail]

You know....just from an "ease of use" stand point, I'd have rather that the "burst rule" used the same dice as the original energy enhancement, i.e. +1d6.