Fun with Numbers.

[Amechra]

Basically, I was taking a glance through the FFd20 site, and I saw that their version of the Fighter has an ability that gives you a +2 to damage, and rerolls any 1s on damage rolls, ad infinitum. Let's refer to it as "Fury", because why not?

What this translates to (after some AnyDice calculations) is a +2 to damage and then, on top of that, +1 to average damage and +2 to minimum damage for every 2 dice that you're rolling.

If you reroll anything less than 3 ad infinitum, that translates to +1 to average damage and +2 to minimum damage per die.

In other words, it builds up the more dice you are throwing around, which is a neat little dice manipulation (it's faster if you have a dice roller; then you can just roll 1d5+1 or 1d4+2.)

So, let's say two fighters have 18 Strength, and are using a  greatsword against a monster with an AC of 15. Let's assume that they have no bonuses to damage except Strength, with the exception of:

1. Fighter 1 has Fury.
2. Fighter 2 has Weapon Specialization.

The average damage for Fighter 1 is 2d5+10, compared to 2d6+8 from our friend Fighter 2.

Fighter 1 deals 12 - 20 damage, with an average of 16 damage.
Fighter 2 deals 10 - 20 damage, with an average of 15 damage.

Let's assume that they later pick up a weapon that deals 6d6 damage (why not?)

The average damage for Fighter 1 becomes 6d5+14, compared to 6d6+8 from our friend Fighter 2.

Fighter 1 deals 20 - 34 damage, with an average of 32 damage.
Fighter 2 deals 14 - 34 damage, with an average of 29 damage.

I like it, at the very least.

[Amechra]

Hi, I'm back!

I've got another fact to share:

A * D * (20 + B * C) / 400 = E

You see that equation?
A is your chance to hit a given AC, divided by 5.
B is your critical multiplier minus 1; set this to 0 if you are attacking something immune to critical hits.
C is your chance to threaten a critical, divided by 5; it can't be higher than A.
D is your average damage.
E is your average damage dealt in either a round or an attack.

To get per round, you sum all the percent chances to hit before dividing by 5.

Now, I've been playing around with this equation, and I've seen some pretty interesting facts.

For example, let's say that you're playing a Whirling Frenzy Barbarian, or using Rapid Shot, and you want to know when to use your extra attack; well, as long as you can hit on at least a 5, you should totally go for the extra attack; your chance of hitting with the extra attack grows far faster than it would otherwise.

[Jackinthegreen]

I've got a spreadsheet with equations similar to that in your second post, but it takes a few more things into account.

=(((E6)*(20-C6-F6))+(((20-F6)/20)*(E6)*C6*D6)+((F6/20)*(E6)*(C6)))/20

Breaking it down, E6 is average weapon damage, C6 is crit chance/5 (so a 20 would be a 1), D6 is the crit multiplier, and F6 is the chance to miss the attack.  The spreadsheet has an A and B column, which are devoted to the Attack Bonus and Defender's AC, respectively.  The F column is B-A, but has an enforced minimum of 1 to account for automatic misses on a 1.  I think it takes into account ties going to the player, but I'd need to really look through the math to make sure.

The first part [((E6)*(20-C6-F6))] is average weapon damage not including critical damage.  Notice that it subtracts both the miss chance and the crit chance.

The second part [(20-F6)/20)*(E6)*C6*D6)] is the chance of being a successful critical.

The third part [((F6/20)*(E6)*(C6))] is the chance to have a failed crit and instead deal normal weapon damage.

All of those add together, and then it's divided by 20 to get the average weapon damage factoring in crits and misses.  For instance, if it was a weapon that did an average of 5 damage and had 20/x2 crit, and only missed on a 1, its average damage would be 4.9875.


I need to port it from Excel over to Google Docs one of these days...  I also need to update it to have a column with bonus to confirming crits.

I don't remember the poster's name, but I saw some calculations posted and immediately put them into Excel, then after tweaking the equation (and getting help with making sure it was correct) went to town on calculating various effects, mostly Power Attack and the like.  Part of what lead me to do that was wanting to figure out the math for Arcane Duelists.

Once I can get my crap organized I'll post a full thread on AD math, as well as for Power Attack and other things.


You might get something out of these topics:
http://www.minmaxboards.com/index.php?topic=6429.msg96496#msg96496
http://www.minmaxboards.com/index.php?topic=6417.msg96196#msg96196

[SorO_Lost]

After reading the posts, I think I am way to simple

I use 100 - (Average AC by CR - Attack Bonus * 5) for a hit rate percentage.
For damage it's (non-crit average * none-crit range) + (crit damage * crit range) / 20.
Scale damage by hit chance (ie 15dmg @95% hit is 14.25) and you're looking at your "DPS".

Technically, it doesn't factor the d20 roll at all. I use it to look at Class based comparisons.