A statistics question

[Agback]

I'm not rounding

Yes you are.

By taking 9.075 points of damage per round, the Str Monk (who has 18hp) takes an expected 18.15 hp of damage by round 2, dropping him.

No. He doesn't take 9.075 points of damage every round. He can take any integer amount from none to 24 on any given round. It is only on average that he takes 9.075, and on average he lasts 1.98 rounds. When you treat that as definitely dying before his third round starts you are rounding off. Sometimes he will die in the first round without gloving the trogs at all, sometiimes he will kill all three without taking a scratch. You cannot treat this distribution as a definite outcome at teh expected value.

The Dex monk with the same HP takes only 17.55 hp of damage in the same time- he survives to round 3 just barely.

No, he survives on average for 2.05 rounds. Which is on average 0.07 rounds longer than the strong monk. When you treat that as definitely surviving for a whole extra round you are in effect rounding off. And screwing up. You cannot treat an expected survival time of 1.98 rounds as definitely dying after making two attacks. You cannot treat an expected survival time of 2.05 rounds as definitely surviving to make a third attack.

This isn't quite right. The Str monk got in trouble because each change in the scenario featured opponents with a higher expected damage per round being done to the monk- but damage per round is affected by several hidden variables. And it is the expected damage/round the monk recieves that is the key to a monk's survivability...and his ability to deal damage in later rounds.

No he didn't. He got in trouble because your invalid rounding habits worked out to his disadvantage in that particular scenario.

The number of opponents affects it. Number of attacks affects it. Their equipment affects it. Their to hit and damage bonuses (of whatever source- str, class features, etc.) affect it.

Their hit bonus does alter the percentage by which the strong monk outclasses the dextrous monk. The better the opponents' AB is, the greater the advantage to the strong monk.

Number of opponents, their damage output, and their number of attacks do not alter the comparison between the strong monk and the dextrous monk.

In reality any of these variables that significantly increases the expected damage/round affects the Str monk more adversely than the Dex monk. A foe or foes that hits often but doesn't hit hard could still have an expected damage/round equivalent to the 3 trogs in the last example- as could a foe with a huge weapon but poor accuracy, or a moderate weapon with moderate accuracy.

You are quite wrong about that. If you can't see why from the algebra and explanations I posted above I am just going to have to ask you to believe me. I am a math whizz. I did an entire major in statistics.

 

[Agback]

That's a fair point. The trouble, however, is that such a feat becomes wasted when you reach a sufficent level that your tumble is high enough that it always passes.

Not wasted. It frees up skill points for other skills. Which is what eth dextrous monk's DEX bonus is doing at that point.

I think you've misunderstood my point. Combat in D&D is frequently about more than standing in front of your foe and trading blows. Monks, in my experience, excel in their tactical versatility. It is not their ability to stand and deliver damage but their ability to move suddenly to different and tactically more important positions on the battle field that makes them scary foes.

True. But a strength-based monk build still enjoys those advantages. And when those advantages get him to strategic points on the battlefield he hits more often and harder than the dex-based monk, to an extent taht is proportionately greater than the extent to which he takes more hits. Both strong monks and dextrous monks move suddenly to unexpected and tactically advantageous positions: the strong monks take greater advantage when they get there.

 

[Dannyalcatraz]

He can take any integer amount from none to 24 on any given round. It is only on average that he takes 9.075, and on average he lasts 1.98 rounds.

Exactly- if that is the average damage per round, then we can expect the Str monk to drop in round 2...on average.

And that is the format you yourself set up in your first trog example.

No, he survives on average for 2.05 rounds. Which is on average 0.07 rounds longer than the strong monk. When you treat that as definitely surviving for a whole extra round you are in effect rounding off.

Fine, but the point remains that he does survive longer on average in a situation where the Str build cannot statistically expect to get out of round 2, and he can expect to survive into that 3rd round.

And the trend remains- the more damage the monks' foes expect to dish out, the more that AC difference matters.

 

[nogray]

What I think Agback was essentially saying is that you can't add a full round of damage from the Dexterous Monk, but only 0.07 rounds worth of expected damage. The difference there is significant. The Dexterous Monk only survives an average of 0.07 rounds longer (as an average value), but you are treating it as if he survived a full round longer. If you are dealing with statistical averages, you have to discard any integer-based effects, like "suviving into round 3."

The Strong Monk, over an average of many combats, survives 1.98 rounds, dealing 3.9 hit points per round (if I'm grabbing the correct numbers) for a total expected damage of 7.72 (3.9 * 1.98). The Dexterous Monk suvives 2.05 rounds dealing 3.025 hit points each round for a total expected damage of 6.20125 hit points (3.025 * 2.05).

When dealing with average cases, all rounding off must be avoided when possible.

 

[Agback]

ine, but the point remains that he does survive longer on average in a situation where the Str build cannot statistically expect to get out of round 2, and he can expect to survive into that 3rd round.

On average. the dextrous monk will last one fourteenth of a round longer than the strong monk, not a whole round longer. There is about one chance in fourteen fights that the dextrous monk will last an extra turn and get an extra attack. You cannot treat that as a certainty of getting an extra attack.

And the trend remains- the more damage the monks' foes expect to dish out, the more that AC difference matters.

No, that is not correct. And you won't be able to discern whether it is correct or not until you start treating the averages correctly.

 

[Dannyalcatraz]

Thanks nogray, you and Agback are absolutely right on that- it took me tracking down my old stats book today to figure out what my error was.

Now, onto the ranged combat.

Here, the Dex monk has the advantage in both AC and Hit probability.

Because of the Str bonus, the Str Monk gets a bigger damage kick from using the Javelin- 1d6+2 (for an average of 5.5 per hit)- but the Dex Monk does the same damage with a heavy crossbow. If there is only one round of ranged combat, the Dex monk should stick with the heavier weapon.

Because of the superior rate of fire, however, the Javelin is preferred when ranged combat would be protracted. While doing only 4.5 per strike, the Dex monk still hits more often and has the AC advantage.

If the Str monk is hitting 10/20, he's doing 2.75/rd, while the Dex monk is hitting 11/20 for 2.475/rd.

Assuming the 3 Trogs have spears to throw and have the same to hit for melee as ranged:

In the 2.96 rounds it takes the Trogs to drop the Dex Monk, he does 7.33 points of damage.

In the 2.67 rounds it takes the Trogs to drop the Str Monk, he does...7.33 points of damage.

 

[jeffh]

Except that any item a Dex monk would take to boost Str could be acquired by a Str monk- its a wash. The only stat changes that matter are those inherent to the PC.

Thus, the only real difference in Dex/Str progressions will occur as the 2 PCs level up- the Dex monk will likely continue to stress his Dex advantage, the Str Monk his Str. One will boost his damage production, the other his AC and Initiative mods.

This is not entirely true. Both will have to decide between these items at various stages of their career, though it is true that they will eventually want both. Very early on, a monk is unlikely to be in a position to get both a Strength and a Dexterity item (and will also run into the problem that the +2 versions of these occupy the same slot). Later on, the monk might be able to afford a +6 boost to one stat but only a +4 to the other. There are decisions to be made all the way up the level chart, not just when the monk gets his four-level boosts. (However, it remains true that neither Strength nor Dexterity is likely to remain static for any monk that is played through 20 levels.)

 

[Dannyalcatraz]

This is not entirely true. Both will have to decide between these items at various stages of their career, though it is true that they will eventually want both.

It is a wash in the sense that there is no item out there that a Dex Monk could acquire that a Str Monk couldn't, and vice versa- just like the Feats.

That is, if we were to assume a hypothetical in which the Str monk has a Belt of Giant Strength, there is no reason to think that the Dex Monk wouldn't get equal utility out of the Str boost and wouldn't choose to acquire such an item.

Or to put it a different way, if the comparison is between 2 monks with the same equipment, the equipment doesn't matter unless it actually gives them different benefits, usually because they have other different attributes (racial abilities, feats, etc.) so that the same item interacts with those attributes to give them different abilities- factors that we're ignoring.

For example, that BoGS would have more benefit to the Str Monk than the Dex Monk if the Str Monk has Power Attack and the Dex Monk doesn't.

A Dex Monk, OTOH, would get more benefit from a Dex boosting item than a Str Monk if he has Combat Reflexes and the Str monk doesn't.

 

[jeffh]

factors that we're ignoring.

We?

Only presidents, editors and people with tapeworms have the right to use the editorial "we".
- attributed to Mark Twain

 

[Victim]

Prioritizing Dex instead of Str initially usually indicates a design choice that will lead to different item choices though. If you decide to pick Dex over STR, the same reasons will apply when it's time to buy to your first stat booster, or a few AC items vs Mighty Fist. Item choices usually aren't mad in a vacuum.

Man, if you frequently get to use all the AoOs from Combat Reflexes... Even using reach weapons, I almost never see characters needing more than a handful of AoOs. With 5ft steps, tumble, reach, special movement, etc AoOs don't come up that often. And when they do, the threat of having many extra AoOs is almost as good as the actuality. It's easy to 'flood' a target with AoOs to land a key move if they only can take one, but once they demonstrate extras, it's usually not worth the extra damage to push their limits. Eating 1 attack to grapple an enemy with close quarters fighting can be worthwhile. But taking 2 such attacks with the possibility of more tends to discourage that tactic.