# most efficient baal running

##### Diabloii.Net Member
most efficient baal running

OK, so i'm no math wiz - actually i'm quite bad at math, but i'm trying to figure this out, so here goes... according to d2data, Baal on /players 1 has an 18.75% chance of rolling a no-drop. as i understand it, bosses actually roll 7 items, but only drop six and discard one. i think this means that even if you roll one no-drop you still get 6 items, right? if that is correct, then at /players 1 setting, each of the potential drops actually counts for (1-.1875) = 0.8125 items time 7/6 = .94792. so, at /players one, if you can kill baal every two minutes, for example, you will get an average of (6*.94792*30) items per hour, or 170.6 items. if on the other hand, you kill baal at players 3, the no-drop goes to virtually 0% (i'll figure it is actually 0 for these calculations), but it takes you 4 minutes to kill baal, then you get (6*15) = 90 items per hour. this would mean that in order to have it be more efficient to kill baal at players 3 than 1, you can only go at 94.7% the speed you do it at players 1!!!

i don't know how hitpoints stack up, but i'm guessing that at /players 3 baal has 3 times as many hitpoints, meaning that unless you use some sort of attack that takes a set fraction of his hitpoints off every time (CB or static field), then you will actually get many more items per unit time spent running baal on a lower players setting! OK, so now tell me how wrong i am! :bow:

#### Ravenforce3

##### Diabloii.Net Member
Your calculations make sence, even if I can't check them outright. Even if it is wrong, at least you look good being so. :teeth:

#### gnomb

##### Diabloii.Net Member
What are the chances Baal will roll more than 1 no-drop in a particular run?

##### Diabloii.Net Member
gnomb said:
What are the chances Baal will roll more than 1 no-drop in a particular run?
each individual item has an 18.75% chance of being a no-drop, so there is an .1875^2 = 3.5% chance of rolling two no-drops.

#### StellarDust

##### Diabloii.Net Member
OK, so i'm no math wiz - actually i'm quite bad at math, but i'm trying to figure this out, so here goes... according to d2data, Baal on /players 1 has an 18.75% chance of rolling a no-drop. as i understand it, bosses actually roll 7 items, but only drop six and discard one. i think this means that even if you roll one no-drop you still get 6 items, right? if that is correct, then at /players 1 setting, each of the potential drops actually counts for (1-.1875) = 0.8125 items time 7/6 = .94792. so, at /players one, if you can kill baal every two minutes, for example, you will get an average of (6*.94792*30) items per hour, or 170.6 items. if on the other hand, you kill baal at players 3, the no-drop goes to virtually 0% (i'll figure it is actually 0 for these calculations), but it takes you 4 minutes to kill baal, then you get (6*15) = 90 items per hour. this would mean that in order to have it be more efficient to kill baal at players 3 than 1, you can only go at 94.7% the speed you do it at players 1!!!

i don't know how hitpoints stack up, but i'm guessing that at /players 3 baal has 3 times as many hitpoints, meaning that unless you use some sort of attack that takes a set fraction of his hitpoints off every time (CB or static field), then you will actually get many more items per unit time spent running baal on a lower players setting! OK, so now tell me how wrong i am! :bow:
Before I start, let me say that I am not quite sure how correct my info are, so don't blame me for it (especially at 1:30 AM).
A few things to point out. First of all, your calculation of Baal's expected number of drops in player 1 is wrong--you can only multiply 7/6 by 0.8125 IF Baal can drop all 7 items if he rolls 7, but he can't. So you have to take that in to account--the expected number of items is 0.8125 * 7 / 6 - (7 C 7) (0.8125 ^ 7), which will give you 5.45374, so you can expect 5.45374 * 30, or about 164 items (yeah... I know many of you who read this is going to say, "uh... so?" but this value is more precise). Secondly, I think your theoretical figures aren't very realistic. Considering the fact that it will take the same time to get to Baal in both cases, it is quite unlikely that the time it takes to kill Baal would take that much longer in Player 3 than 1 (of course, unless the build is just really inefficent against Baal; in which case Player 1 would be a better idea).

##### Diabloii.Net Member
i think you're right about the 5.45 items per run thing... i was trying to figure out how to do that. regarding the time to kill baal... if baal has 3X the number of hitpoints at players 3 vs 1, then it should take ~3X as long to kill baal if the skill you are using does the same amount of damage at any players setting. my hammerdin still does 7200-7300 damage whether baal has 100,000 hitpoints or 300,000. if you are using a skill that is more effective at higher players setting (like static field or crushing blow) then you are right, it shouldn't take that much longer. i can attest that it takes my hammerdin quite a while to kill baal on players 3 - especially since i have to go back to town to get more potions half way through. oh yeah, and the 2-4 minutes thing was just an example, but the 94% slowerthing should still hold true.

#### Borlag

##### Diabloii.Net Member
Crushing Blow reduces the targetâ€™s current life by a certain amount, depending on the attack type and the kind of target. Against normal monsters, it reduces 1/4 of their current life when youâ€™re using a melee attack, and 1/8 when youâ€™re using a ranged attack. Against bosses, itâ€™ll reduce 1/8 of their current life if itâ€™s a melee attack, or 1/16 if itâ€™s a ranged attack. Against mercs and players, itâ€™ll reduced 1/10 of their current life if itâ€™s a melee attack, and 1/20 if itâ€™s a ranged attack. PvP penalty doesnâ€™t affect Crushing Blow, but the damage dealt is reduced by Damage Reduction % items, so itâ€™ll be less effective against monsters with Damage Reduction, and against opponents with a lot of Damage Reduction. Crushing Blow only takes into account the base life of the monsters at players 1, so itâ€™ll be less effective when there are more players in the game
actually according to this it's not...check the last 2 lines

#### strijdje

##### Diabloii.Net Member
mm interesting, so still IMO its better to run baal @ players1, simply cause u can do more runs in less time..

#### StellarDust

##### Diabloii.Net Member
i think you're right about the 5.45 items per run thing... i was trying to figure out how to do that. regarding the time to kill baal... if baal has 3X the number of hitpoints at players 3 vs 1, then it should take ~3X as long to kill baal if the skill you are using does the same amount of damage at any players setting. my hammerdin still does 7200-7300 damage whether baal has 100,000 hitpoints or 300,000. if you are using a skill that is more effective at higher players setting (like static field or crushing blow) then you are right, it shouldn't take that much longer. i can attest that it takes my hammerdin quite a while to kill baal on players 3 - especially since i have to go back to town to get more potions half way through. oh yeah, and the 2-4 minutes thing was just an example, but the 94% slowerthing should still hold true.
I don't think Baal has 3X the HP in player 3, but more like 2.9 or so. Yeah it probably won't make THAT much of a difference. But in my experience it usually takes a long time to get to Baal and I play sorc a lot so... And yes, Borlag is right, CB is independent of the amount of players.

#### Thrugg

##### Diabloii.Net Member
The effect of extra players on HP is reasonably straightforward in 1.10 (much simpler than 1.09). For each additional player the monster gets +50% of his base HP. So for two players he has 1.5x HP, 3 players 2x, ..., 8 players 4.5x.

However, the amount of time it takes to run there, kill his minions etc has to be counted in too. Time to do a run will increase quite a bit slower than the number of Baal's HP. And it may even depend on your charctaer class. The right players setting will vary from char to char. You are, at least, thinking about it the right way. Drops per hour is the key to MF.

#### Fafner

##### Diabloii.Net Member
I think waiting for all the stupid Minions to spawn actually takes longer than killing Baal with an efficient build. So this debate may be moot as I think the slow step is there. Just my \$0.02.

#### Nightfish

##### Diabloii.Net Member
I did a few runs on all player settings and found that for my purposes players 1 was the best option.

##### Diabloii.Net Member
just for clarification, i was referring only to how long it actually takes to kill baal. since you can choose the players setting you want before entering the world stone room, you can kill baal at any setting. clearly the most time is spent getting to baal, not actually killing him.

that actually brings up another interesting question. the players setting has no effect on champion/unique drops - its always one item (or gold or rune...) and a mess of potions. but regular monster are another matter entirely. is it mathematically efficient to run the WSK on /players 8 given the increased potential for an item drop from a normal monster, given that this is going to slow down your runs by a certain amount? and since normal monsters have a VERY small chance of dropping a unique item, is the extra time spent killing these monsters who have such a slim chance of dropping a unique/set, worth it when champions/uniques and baal have a much higher probability of dropping a magical (and thus a set/unique) item. this type of calculation is way beyond my poor mathematical skills, and i don't have ready access to the proper formulae to even begin working on it anyway.

#### Nightfish

##### Diabloii.Net Member
is it mathematically efficient to run the WSK on /players 8 given the increased potential for an item drop from a normal monster, given that this is going to slow down your runs by a certain amount?
Summendar (I think it was him anyway) answered that question quite some time ago. The answer was "no".

#### Thrugg

##### Diabloii.Net Member
True, but it wasn't necessarily best to go at p1 either.
Very fast walking chars will probably be more efficient at p1, but if you walk slow but hit hard, p2 or even p3 will look better. Again the right thing to do is time your runs at various settings.

I can't find Sumendar's old post of course, but I can probably reproduce his figures.
Assuming a monster density of about 160 regular monsters / 6 champs / 8 bosses - which seems to be right for the Pit, and won't be far different for WSK, you expect:

Uniques
p1 - (160 * 16/160) + (6 * 37/100 * 32/7) + (8 * 58/62 * 32/7) = 60.4
p2 - (160 * 16/98) + (as above for champs, uniques) = 70.5
p3 - (160 * 16/79) + (as above) = 76.8
p4 - (160 * 16/70) + (as above) = 80.9
p5 - (160 * 16/66) + (as above) = 83.1
p6 - (160 * 16/63) + (as above) = 85.0
p7 - (160 * 16/62) + (as above) = 85.7
p8 - (160 * 16/61) + (as above) = 86.3

Don't worry about what the units are - it's just a relative comparison - the important thing is you want to maximise the above number for players x, divided by your time to do a run on players x. That is the setting you should use for finding uniques.

It isn't the same for runes. With uniques, "most" get dropped by boss monsters, even at p8, because bosses are much more likely to drop a unique item. But for runes, boss monsters don't get such a big advantage. For them, the calculations are

Runes
p1 - (160 * 2/160) + (6 * 3/100) + (8 * 4/62) = 2.70
p2 - (160 * 2/98) + (as above for champs, uniques) = 3.96
p3 - (160 * 2/79) + (as above) = 4.75
p4 - (160 * 2/70) + (as above) = 5.27
p5 - (160 * 2/66) + (as above) = 5.54
p6 - (160 * 2/63) + (as above) = 5.78
p7 - (160 * 2/62) + (as above) = 5.86
p8 - (160 * 2/61) + (as above) = 5.94

So again, if you are hunting for runes, you want to maximise the above number divided by your run time, over all players settings.