A statistics question

[Agback]

That Dex based monk is facintg 3x 1.575hp/rd (or 4.725hp/rd), while the Str based monk is facing 3x 1.75 hp/turn (5.25hp/rd). (Of course, that isn't technically correct if/when trogs start dropping, thus changing average damage output/round.)

Exactly. Strong Monk's first trog drops sooner, so he faces three foes for fewer rounds. Similarly, he faces two trogs for fewer rounds, and one trog for fewer rounds. If you work it out (as I did), facing three trogs means taking six times as much damage as facing one trog. Strong monk is ahead against one trog. He is six times as far ahead against six trogs.

And flanking bonuses to the trogs hurt Dextrous Monk more than they hurt Strong Monk.

 

[Dannyalcatraz]

We're making progress...I think.

1) How do you figure that flanking hurts the Dex monk more? Assuming optimal tactics, each of the 3 trogs gets +2 to attack, pumping the expected damage from the 3 attackers to 6.3hp/rd vs the Str monk and 5.25hp/rd vs the Dex monk. Both still collapse on turn 2 without dropping an opponent.

And this time, if the 2 monks have 18 hp instead of 9, the Str monk drops unconscious on round 3 having taken 18.9 hp of damage, never dropping a trog (because, as you pointed out, it takes him an average of 4.44 rds to do so), while the Dex monk at least survives to fight in round 4 (where HE drops after taking 21 hp of damage, never having dropped a trog).

2) What does the number "21" in your proof mean? I didn't see it defined, and it has me puzzled.

3) Your proof still assumes the Str monk and Dex monk use identical tactics- a static melee fight. A Dex monk would (properly played) emphasize HIS strengths. That would include using ranged attacks to soften up, harry or kill opponents (especially spellcasters), and using his superior damage avoidance to get into flanking positions. Yes, ranged attacks generally do less damage, but they DO still do damage that must be accounted for, and the Dex monk has the advantage here. While most monks' ranged attacks would come in the form of slings, daggers, and javelins, the heavy crossbow is still one of their weapons, and an elvish monk could use a longbow.

 

[Agback]

We're making progress...I think.

1) How do you figure that flanking hurts the Dex monk more?

Well, suppose that the foes hit Dextrous monk on A rolls out of 20. If they get a flanking bonus of +1, they will hit on A+1 rolls, which is an increase of 1/A*100%.

Exactly the same foes hit Strong Monk on A+1 rolls. With +1 for flanking, they will hit on A+2 rolls out of twenty, which is an increase of 1/(A+1) * 100%.

1/A > 1/(A+1).

For example, consider a foe that hits Dextrous monk on a roll of 20 only. Given a +1 they will hit twice as oftern, a 100% increase in their damage. The same foehits Strong Monk on a 19, with a +1, on an 18. That's three rolls out of 20 instead of 2, a 50% increase in expected damage.

And this time, if the 2 monks have 18 hp instead of 9, the Str monk drops unconscious on round 3 having taken 18.9 hp of damage, never dropping a trog (because, as you pointed out, it takes him an average of 4.44 rds to do so), while the Dex monk at least survives to fight in round 4 (where HE drops after taking 21 hp of damage, never having dropped a trog).

They both lose teh fight. Strong Monk does more damage before he drops because he dose 35% more damage per round. 3 * 1.35 = 4.05 > 4.

2) What does the number "21" in your proof mean? I didn't see it defined, and it has me puzzled.

I didn't define '20' either. 21 is 21, not a variable.

If you nead 20 to hit, you hit on one roll out of 20. If you need nineteen, you hit on two rolls out of twenty, if you need 18, you hit on three rolls out of 20, . . . , if you need a 10, you hit on 11 rolls out of 20, . . . , if you need a 1, you hit on 20 rolls out of twenty. In every case, the number of d20 rolls tht will succeed plus the number you need to roll adds up to 21.

The number you need to roll is ac-AB. So where the number of d20 rolls that gives you a success is N, ac-AB+N = 21, therefore N = 21 - ac + AB. Teh probability that you will succeed is N/20 = (21-ac+AB)/20.

3) Your proof still assumes the Str monk and Dex monk use identical tactics- a static melee fight.

It assumes that they use identical tactics, but not necessarily a static fight. No matter what tactics Dextrous Monk uses, Strong Monk can use the same tactics. He will hit more often, do more damage, put his foes down faster, and suffer fewer counterattacks. A higher proportion of the counterattacks will hit, but Strong monk is still ahead unless the foes have very low AC and very low AB.

That would include using ranged attacks to soften up, harry or kill opponents (especially spellcasters),

If you want to play an archer, a fighter is a much better choice than a monk.

and using his superior damage avoidance to get into flanking positions.

Dexrtrous Monk's advantage in tumble checks and reflex saves is 1/A * 100%, where A is his chance of making them. This advantage is only significant where A is small, ie. where the tactic is highly unreliable.

Supposing that Dextrous monk has 75% chance to make a tumble check and avoid an AoO, Strong monk has 70%. Strong Monk takes on average 20% more damge from teh occasionally AoO but dishes out 35% more damage on every round in mêlée.

Yes, ranged attacks generally do less damage, but they DO still do damage that must be accounted for, and the Dex monk has the advantage here. While most monks' ranged attacks would come in the form of slings, daggers, and javelins, the heavy crossbow is still one of their weapons, and an elvish monk could use a longbow.

If you want to play a longbow-using elvish monk you go right ahead. I consider such a build to be a concession that the high-DEX monk is worse in a mêlée than a strong monk, which is the propositionn that you asked me to prove.

 

[Dannyalcatraz]

A statistics question: comparing Dex and Str based monks

They both lose teh fight. Strong Monk does more damage before he drops because he dose 35% more damage per round. 3 * 1.35 = 4.05 > 4.

As you posted re Dex monk:

Monk hits on a roll of 13 or better, ie. 8 times out of twenty and does 5.5 hp per hit for an average of 2.2 hp per turn

And re: Str Monk:

Average damage output: 2.93 hp per turn

With 3 rounds before he falls to the assembled trogs, thats 8.79 points of damage dealt by the Str monk. But by surviving 4 rounds, thats 8.8 points of damage from the Dex monk before he drops.

Its not by much, but the Dex monk actually deals more damage in this combat than the Str monk.

If you want to play an archer, a fighter is a much better choice than a monk.

I'm not debating whether a fighter is a much better archer than a monk- I think we can assume that with the higher BAB, more weapon options, and more feats at their disposal, the fighter makes a much better archer/ranged warrior than the monk.

However, it makes no sense for a high dex PC not to use his abilities to the fullest, and that includes using ranged weaponry.

I mean, is a mage not going to use a weapon if someone gets too close for him to use a spell? No, of course not.

Thus, there is no reason a monk wouldn't use a sling or daggers or whatever his ranged weapon of choice is to damage foes before they close.

(Heck, he could even throw tanglefoot bags to really screw them over, further setting the table for ranged decimation.)

If you want to play a longbow-using elvish monk you go right ahead. I consider such a build to be a concession that the high-DEX monk is worse in a mêlée than a strong monk, which is the propositionn that you asked me to prove.

Not quite. What I said was:

Is a Dex-based monk REALLY worse in combat than a Str-based monk?

Combat would encompass both ranged and melee tactics.

And really, a Dex-build elvish monk with a bow isn't a consession- its the monk using all of his assets as best he can. Its the best use such a PC can make of his stats and weapons with which he is proficient.

 

[Dannyalcatraz]

I didn't define '20' either. 21 is 21, not a variable.

If you nead 20 to hit, you hit on one roll out of 20. If you need nineteen, you hit on two rolls out of twenty, if you need 18, you hit on three rolls out of 20, . . . , if you need a 10, you hit on 11 rolls out of 20, . . . , if you need a 1, you hit on 20 rolls out of twenty. In every case, the number of d20 rolls tht will succeed plus the number you need to roll adds up to 21.

The number you need to roll is ac-AB. So where the number of d20 rolls that gives you a success is N, ac-AB+N = 21, therefore N = 21 - ac + AB. Teh probability that you will succeed is N/20 = (21-ac+AB)/20.

Ah! I see what you're saying.

 

[Dannyalcatraz]

Agback, I made an error in the math when I doubled each monk's HP, I should have also added one to each one's BAB, because that is what happens when a monk reaches 2nd level. This would have affected their expected damage output.

So in a pure melee fight:

2nd level Dex Monk AB +3, AC 13, d6+2, 18 hp (average damage output: 2.48 hp per round) fighting 1 trog with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, the Trog expects to do 1.58/round. It will take the Trog 11.39 rounds to drop the monk...but he only has a little over 5 rounds to live.


2nd level Str Monk AB +4, AC 12, d6+3, 18 hp (average damage output: 3.25 hp per round) fighting 1 trog with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, the Trog expects to do 1.58/round. It will take the Trog 10.29 rounds to drop the monk...but he only has 4 rounds to live.

Advantage, Str Monk.

2nd level Dex Monk AB +3, AC 13, d6+2, 18 hp (average damage output: 2.48 hp per round) fighting 2 trogs with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, each Trog expects to do 1.58/round, for a total of 3.16/rd. By round 5, the Monk has dealt out 12.4 HP of damage, and the Trogs have dealt out 15.8 hp of damage. In round 6, one trog will drop, as will the monk (assuming simultaneous initiative). The monk will have done 14.88 points of damage.

2nd level Str Monk AB +4, AC 12, d6+3, 18 hp (average damage output: 3.25 hp per round) fighting 2 trogs with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, each Trog expects to do 1.75HP/round, for a total of 3.5/rd. In round 4, the Str Monk drops a trog (at 13hp exactly) and has taken 14 points himself. 3 rounds later, though, the remaining Trog drops the monk, after taking 9.75 damage himself. (That's a whopping 22.75 damage delivered by the Str Monk.)

Advantage Str Monk, possibly posthumously.

2nd level Dex Monk AB +3, AC 13, d6+2, 18 hp (average damage output: 2.48 hp per round) fighting 3 trogs with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, each Trog expects to do 1.58/round, for a total of 4.74/rd. In the 4 rounds it takes them to drop him, he deals out 9.92 points of damage.

2nd level Str Monk AB +4, AC 12, d6+3, 18 hp (average damage output: 3.25 hp per round) fighting 3 trogs with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, each Trog expects to do 1.75HP/round, for a total of 5.25/rd. In the 3 rounds it takes the trogs to drop him, he deals out 9.75 points of damage.

Pyrrhic victory, Dex monk- he does more damage and lasts longer before succumbing to the assembled Trogs. At higher levels of being outnumbered, neither monk survives more than 3 rounds.

 

[Agback]

2nd level Str Monk AB +4, AC 12, d6+3, 18 hp (average damage output: 3.25 hp per round) fighting 3 trogs with longspears, each AB +1, AC 15, d8, 13 hp. Because of the Monk's AC, each Trog expects to do 1.75HP/round, for a total of 5.25/rd. In the 3 rounds it takes the trogs to drop him, he deals out 9.75 points of damage.

You have miscalculated. The trogs need a 14 to hit, so their hit chance is 0.35. Their average damage per hit is 4.5. 4.5 * 0.35 = 1.575, not 1.75. Multiplied by 3 trogs, that is 4.725 hp/round, not 5.25. It takes the trogs 3.8 rounds on average to drop Strong Monk, not three rounds. In 3.8 rounds Strong Monk dishes out 12.4 hp to the trogs. That is 25% more damage than Dextrous Monk delivers.

 

[Dannyalcatraz]

You have miscalculated. The trogs need a 14 to hit, so their hit chance is 0.35. Their average damage per hit is 4.5. 4.5 * 0.35 = 1.575, not 1.75. Multiplied by 3 trogs, that is 4.725 hp/round, not 5.25

Are you sure? That 1.75 came from your single trog v. Str monk example.

Agback Post#9
Example: 1st-level monk with AB +2, AC 13, d6+2, 9 hp fights a CR 1 monster, say, a troglodyte with a longspear AB +1, AC 15, d8, 13 hp. Monk hits on a roll of 13 or better, ie. 8 times out of twenty and does 5.5 hp per hit for an average of 2.2 hp per turn, and the trog hits on a 12 or better (9 times per twenty turns) for 3.5 hp per hit, which comes out to 1.575 hp/turn. It will take the monk on average of 5.91 round to down the trog, in which time he or she will suffer 9.31 hp damage. In short, it's close, but we expect the troglodyte to win.

Now suppose that we swap the monk's 16 DEX for his 14 STR. His AB becomes +3, AC 12, d6+3, still 9 hp.The monk now hits on an 12 (9 rolls out of 20) for an average of 6.5 hp per hit. Average damage output: 2.93 hp per turn, The trog will go down in 4.44 combat turns. The trog now hits on 10/20 turns, and still does 3.5, for an average of 1.75 hp per turn. The monk now expects to survive the fight taking 7.78 hit points damage instead of 9.31.

Shall we go around again with the right numbers? What is the correct expected damage output per round per trog versus the Dex monk and versus the Str Monk?

 

[Agemegos]

Are you sure? That 1.75 came from your single trog v. Str monk example.

Then I miscalculated.

Trogs have AB +1. Dextrous Monk has AC 13. Trogs hit on a 12 or better, which is 45%. Trogs do 4.5 hp/hit. 45% of 4.5 is 2.025 hp/trog attack. Trogs have AB +1. Strong Monk has AC 12. Trogs hit on a 11 or better, which is 50%. Trogs do 4.5 hp/hit. 50% of 4.5 is 2.25 hp/trog attack. In avoiding damage, the advantage is to Dextrous Monk by 0.225/2.25 = 10%. This is independent of the number of trogs.

Trogs have AC 14. Strong Monk has AB +5 (with kama). Strong Monk hits on a 9 or better, which is 60% of the time. Strong Monk does d6+3, which averages 6.5. 60% times 6.5 is 3.9 hp/turn. Trogs have AC 14. Dextrous Monk has AB +4 (with kama). Dextrous Monk hits on a 10 or better, which is 55% of the time. Dextrous Monk does d6+2, which averages 5.5. 55% times 5.5 is 3.025 hp/turn. In dishing out damage, the advantage is to Strong Monk by 0.875/3.9 =23.4%, regardless of the number of trogs.

So regardless of the number of trogs, Strong Monk has a greater advantage. The ratio of damage suffered to damage done is what counts, and Strong Monk's ratio is better than Dextrous Monk's ratio by 20.4%. If there are enough trogs to beat either monk, Strong Monk does 20% more damage than Dextrous Monk. If there are few enough trogs that the monk wins, Strong Monk takes 17% less damage than Dextrous Monk. Somewhere in the middle, there is a fight that Strong Monk wins but that Dextrous Monk loses.

Shall we go around again with the right numbers?

You can if you like, but there is no point. I have done the algebra, I know how the numbers will turn out. The number of opponents doesn't matter. Strong Monk's advantage to hit gets bigger as the targets get harder to hit. Dextrous Monk's advantage to avoid damage gets smaller as the monks get harder to hit. And the opponents have to be feeble indeed before Dextrous Monk's advantage in avoiding damage overcomes both Strong Monk's advantage in hitting and his advantage in damage per hit.

 

[Dannyalcatraz]

Using your new numbers:

3 Trogs vs. 2nd lvl Dex Monk do 6.075hp damage/rd. He does 3.025 hp/rd. He drops in round 3, having taken 18.225 damage, and having dealt 9.075 hp damage.

3 Trogs vs 2nd lvl Str Monk do 6.75hp damage/rd. He does 3.9HP/rd. He drops in round 3 having taken 20.25 damage, and having dealt 11.7 damage.

If, however, instead of spears, the trogs have morningstars (which does 1d8 instead of 1d6), their damage per round jumps to 2.475/trog/rd versus the Dex monk and 2.75/trog/rd versus the Str monk.

Facing 3 Trogs armed thusly, the Str monk is nearly dropped in round 2 with 16.5 hp of damage, while the Dex monk has only taken 14.85 damage. Their damage outputs are unchanged.

Now, the only simple weapon that does 1d10 is the crossbow, but lets just assume that the monks are facing opponents that have the ability to use a martial 1d10 weapon without penalty, but also without any additional to hit bonuses- effectively identical to the Trogs, but with bigger weapons.

These opponents expect to do 2.925/rd each to the Dex monk (for a total of 8.775), and 3.25/rd each to the Str monk (for a total of 9.75 hp/rd). The Dex monk still survives to round 3, dealing 9.075 points of damage, but the Str monk does not, dealing only 7.8 points of damage.

The trend is obvious- the Str monk is in trouble if he is facing a number of opponents that are better equipped (as opposed to being more skilled or competent) combatants.

Thus, if your DM has a tendency to throw NPC “mooks” with Power Attack and big weapons, at the party, that Dex monk may be the better build for the campaign, because each time you get hit, it hurts more, but the mooks are less likely to hit because of their Feat.

Therein lies the source of my experience-based bias: when we run into numerous critters, the DMs I’ve been facing lately favor lots of opponents with BIG weapons and damage mods, but without good attack odds.