Prestige Math

A little bit of a breakdown on our previous Fighter12 vs. Fighter6/Weapon Master6 comparison.

Doing the Numbers

For the purpose of this article, we will be using the two otherwise identical Warhammer users from our previous Prestige class breakdown

We will name the Straight Fighter Roland and the Weapon Master Ogami for the sake of personalizing this mess.

We will arm them each with a Warhammer +2, Plate Mail +2, a Large Steel Shield +2, and give them the unremarkable hit point total of 78 (max for first level, average henchforth with a +1 con bonus).

Each fighter is reasonably aware of his opponent’s capabilities. These are 12th level characters, and it is reasonable that each has a bit of a reputation. For this reason, both will make an attempt to break his foe’s weapon during the first round of combat. Roland has two advantages here, his higher initiative and his ability to attack weapons without drawing attacks of opportunity (provided by the Improved Initiative and Sunder feats). Ogami has a single advantage, an extra +1 to attack granted by his class ability Superior Weapon Focus.

Abilities Breakdown

&nbsp Roland Ogami
HP 78 78
AC 25 25
Att +19/+14/+9 +20/+15/+10
Dmg 1d8+8 1d8+8

Who goes first?

Naturally, Roland will likely go first, with his +5 initiative bonus as opposed to Ogami’s +1. All math aside, there is a 66% chance that Roland will go first.

Roland’s Sunder Attempt

66% of the time, Roland will have the jump on Ogami. If he attempts to attack Ogami’s warhammer, an opposed attack roll is made. Due to Ogami’s extra +1 from Superior Weapon Focus, Roland will hit 47.5% of the time.

Due to the +4 damage from Roland’s Strength, +2 damage from Weapon Specialization, and +2 damage from his weapon’s enchantment (enhancement bonus), Roland does 1d8+8 damage. A +2 Warhammr (the target of this attack) has a hardness of 7 and 7 hit points (each magical “plus” adds one to the hardness and hit points of an item). The harness is effectively reduced back to 5 by Roland’s weapon (see the Attacking an Object rules in the PHB for a proper explaination). Roland must do 12 damage to break Ogami’s warhammer, a 62.5% chance.

Sunder Odds

Provided that Roland wins initiative (66% chance) and hits Ogami’s Warhammer (47.5% chance) and subsequently does adequate damage to break it (62.5% chance), Ogami is disarmed and at a severe disadvantage. There is a 12.9% chance of all of this happening.

Ogami Tries To Sunder

Same situation, but this time Ogami gives it a try. He likely won’t go first (34% chance of him having the upper hand in initiative) but he is likely to still have his weapon (87.1%).

Ogami has a 52.5% chance of hitting Roland’s weapon, provided that Roland hasn’t already clobbered Ogami’s hammer. Roland gets an Attack of Opportunity as a result, and has a 75% chance of hitting Ogami on it (with his total of +19 to attack, hitting is a fairly trivial matter). There is a 10% chance that this will be a critical blow, which can do a total of 48 damage. While this is a lot of hit points on a single blow, it is not enough to drop Ogami, so Ogami’s attack gets resolved in any case.

Once Ogami’s blow has landed, Ogami may opt to use his Ki Damage ability, thereby ensuring that Roland’s weapon is broken (100% chance).

Overall, there is a 87.1% chance that Ogami will get a good shot at Roland’s hammer, with a 52.5% chance to hit, for a total of a 45.7% chance that Roland will be hammerless after Ogami goes.

How to Improve Roland’s odds

There are a couple of gambits for Roland to take that may assist him.

Power Attack

Often underutilized, Power Attack can make Roland’s attack of Opportunity really count for something, though the odds are far slimmer. To drop Ogami, Roland will need to critical for at least 78 damage. 50 Will prompt a “death by massive damage” saving throw, but 78 will do the trick. If Roland wants to hope for a critical, then hope he rolls an 8 on his damage roll (for 16 damage), he can remove 10 from his base attack bonus and put it into his damage, for a total of +9 to attack, 1d8+18 damage. However, only a critical or poor luck on Ogami’s end will prevent Roland from being disarmed, so he may as well go all-in: +7 to attack, 1d8+20 damage.

On a roll above a 18, Roland will hit Ogami’s 25 AC. On a roll of 19 or 20 this hit will be a critical (thanks to Roland’s Improved Critical feat). This critical strike will do (1d8+20)*3 damage. Anywhere from 63 to 84 damage. The remaining random element is the 1d8 for damage. A roll of 6 or better will do the trick (a 37.5% chance).

All told, there is a 3.75% chance that Roland will fell his opponent before his weapon is harmed.

Spring Attack

Roland also has the Spring Attack feat, which entitles him to the ability to move, make a standard-action-attack, and move again (only covering a single move’s worth of ground, naturally). Suppose he were to take advantage of this, provoking an attack of opportunity, but generating an additional one for himself as well?

Presuming that Roland wins initiative (66% chance), he makes his attack and withdraws 10 feet.

Ogami’s Free Shot

Ogami gets a free shot against Roland, against an AC of 29 (Mobility grants Roland a +4 to AC against such Attacks of Opportunity). Ogami has a 55% chance of hitting, and if Ogami chooses to try to eliminate his foe immediately, he may shunt some of his attack bonus into his damage. For a roll of 19 or 20 to be adequate to hit Roland’s improved AC, Ogami will only be able to shunt 10 of his base attack bonus into damage, for a total of 1d8+18 damage with a 10% chance to critical. Ogami may improve his critical multiplier to *4 up to 3 times per day, and if this is a critical, it would be a good time to do so. This would leave his damage range of (1d8+18)*4 which ranges from 76 to 104 damage. There is a 87.5% chance that a crit thusly empowered will drop Roland like a bad habit (an 8.75% chance overall).

Roland’s First Attack of Opportunity

If Roland survives this attack of opportunity, Ogami will be provoking two attacks of opportunity against himself by attempting to break Roland’s weapon (one for movement, one for attacking Roland’s weapon). The first attack of opportunity will be against an AC of 29, as Ogami has the Mobility feat as well.

Roland, with his +19 to attack, has a 55% chance of striking Ogami on his way in, with a 10% chance of it being a critical blow. On average, Ogami is likely to do 12.5 damage with a non-critical blow, or about 37.5 with a critical. Overall, 16.875 damage will be done to Ogami, so we’ll use this (no use following every possibilility, so let’s use a minimum damage of 9).

Having probably done a little damage to Ogami with the movement-provoked Attack of Opportunity, Roland takes his second Attack of Opportunity when Ogami strikes at his hammer. There is a 55% chance that Ogami is now reduced to 69 hit points or fewer. This means Roland’s target damage has been reduced for his hopes of a critical. There is still a 10% chance of a critical on this strike, which will still do (1d8+20)*3 damage. This time Roland will only have to roll a 3 on that 1d8, a 62.5% chance, or a 6.25% chance of dropping Ogami right then and there.

Spring Attack/Power Attack Combo Summary

If Roland decides to break away after failing to smash Ogami’s hammer (87.1% chance of failure) Ogami will have a 8.75% chance of dropping him on the way out (if he uses his Power Attack to fullest extent). If Roland survives, there is a 55% chance that Ogami will take at least 9 damage while pursuing Roland. If Ogami is thusly damaged for 9 points, there is a 93.75% chance that he will survive to strike at Roland’s warhammer, with a 47.5% chance of succeeding.

So here are the chances of a particular outcome:

  • Roland goes first, Roland breaks Ogami’s weapon before Ogami acts: 12.9%
  • Roland goes first, Ogami kills Roland on an attack of Opportunity: 7.62%
  • Roland goes first, Roland kills Ogami on an attack of Opportunity: 5.05%
  • Roland goes first, Ogami breaks Roland’s weapon: 36.45%
  • Ogami goes first, Roland kills Ogami with Attack of Opportunity: 1.23%
  • Ogami Goes first, breaks Roland’s weapon: 15.48%
  • Ogami Goes first, Roland breaks Ogami’s weapon: 8.17%

All of these numbers assume that the Fighter is trying to take down the Weapon Master ASAP to avoid being eventually whittled to death by the Weapon master’s extra +1 attack bonus. Why exactly the Weapon Master would try to power attack and attack his opponent’s weapon in leiu of a perfectly-formidible +20/+15/+10 attack routine is quite beyond me, however. In two to three rounds the Weapon Master is likely to make mulch of the fighter without relying upon crits to get him there. Presuming that there are other opponents availble, the Weapon Master is unlikely to provoke attacks of opportunity upon himself unless there is a clear need to, so this all-or-nothing one-round combat tactic is quite improbably to see in actual gameplay.

Advice to a straight Fighter against a Weapon Master

Get a bow. Stay away. Use Mobility and Spring Attack to not be anywhere near your opponent and his superior melee skills.

Advantage: Weapon Master

The optional maximum damage, optional improved critical multiplier, and additional +1 to attack are all formidable elements of the Weapon Master’s arsenal. Toe to toe against another melee opponent, these skills will serve him quite well.

Then Why not be a Weapon Master?

One word: flexibility. The pursuit of a single weapon, or weapon type is ultimately foolish. As the saying goes “specialization breeds weakness.” In our next look at Prestige Classes, instead of continuing to pursue Warhammer excellence, Roland will have, at 6th level, taken up the fair art of Archery. We’ll put Ogami versus this new fighter and see how they do. Time allowing, perhaps we’ll put the two of them on horseback.