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| #1FrogReaverAug 17, 2015 20:30:49 | If I have the option of choosing to do +10 damage in round 1 of a combat vs doing +20 damage in round 4 of a combat how do I choose what the better options is?
We all know that generally speaking, Damage Now is better than Damage later. But how much better is it? That's the question this thread is meant to explore.
I'd like to offer one possible simple formula for making this clear mathematically.
Converting Damage in round n from now to Damage NOW; F(n) = Damage * (3/4)^(n)
Basically for each round removed from now we take 75% of the damage.
So in the above example I would plug in 20 * (3/4)^3 = 8.4375 < 10. Therefore using this metric it would seem it's better to take the +10 damage NOW as opposed to waiting till round 4 to get the +20 damage.
Now this isn't to say that my formula doesn't need tweaks or that there isn't a better formula for comparing these things but I'm viewing it as a starting point and as a thought provoking point. Any thoughts? |
| #2NevvurAug 18, 2015 0:38:27 | IMO, there's too great a variety of situations in combat to get reliable use from this function. No matter how much you refine it, this is white room analytics taken to an extreme. I don't mean to be a naysayer; I hope this thread takes off and produces a handy tool for tacticians like myself. Just seems like there's way too many variables to consider, and that in the process of reducing everything to averages, the function won't even be relatable to an "average combat," whatever that is.
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| (Reply to #2)FrogReaver |
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| (Reply to #3)Nevvur |
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| #5NoctaemAug 18, 2015 5:03:56 | From what the 4e CharOP board figured out, when it comes to a comparisson between the two exclusively, damage now is always better than damage later because damage later has a chance of not happening. Ongoing damage from 4e being a great example. If you have the choice of dealing 10 damage now vs 10 damage later at the start of a creature's turn via ongoing damage, it's always better to do damage now. The only situation where that might not be true is if the damage later is so high that it clearly defeats the purpose of taking actions to deal damage now and is assured to happen. I expect that 5e is the same thing. Dealing damage now means that you can prevent damage from being returned and remove a threat before it can presumably fulfill its role. Imo, shoot first ask questions later. |
| #6melloredAug 18, 2015 5:27:36 | Well... damage now is only better if it kills something.
i.e. Facing an enemy with 100 HP, then it doesn't matter if you deal 5 + 5+15 damage, or 15+5+5 damage. But it matters very much when facing something with 10 HP.
So how often do you fight things capable of surviving damage now? Need some monster manual analisys for this. |
| #7NoctaemAug 18, 2015 6:22:29 |
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| #8melloredAug 18, 2015 6:32:09 |
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| #9bidAug 18, 2015 9:05:00 | I think damage-now vs damage-then is mostly ressource management. As long as you lose the same amount of HP it does not matter when it happens. (Except if you get down and lose a turn.)
Pure whiteroom simplification, you start with 5 monsters, kill 1 per turn and they do 1 damage each: - 4 + 3 + 2 + 1 = 10 - 5 + 4 + 1 + 0 = 10 with delayed damage Here you could not kill on the first round but kill 3 on the 3rd, same result.
Damage now will kill earlier and save from lost HP. - no nova round from dead monsters, - lost lost round from going uncounscious
In that sense, damage on round 1 is worth 5x while damage on round 3 3x and damage on round 5 1x. It should not be .75 * .75 * .75 * .75 but .8 * .75 * .66 * .5 before considering nova. |
| #10CooperjeraAug 18, 2015 10:38:23 | The one thing that this question reminds me of is the net present value of money. I haven't looked at those sets of equations in some time; however I feel they may be an improved starting point. If one assumes the damage output by the character is investment into an account and damage output by the enemy is deduction from the account then a net present value can be found. However, the interest rate of investment is what would need to be defined. In most cases I don't feel the interest would have a value greater than zero, but that may not work the equations.
The damage output by the enemy can be a function of enemies remaining and their respective level. The number of enemies remaining will be a function of their HP. It would seem reasonable to use the median damage and HP values from the monster creation table in the DMG. The damage output by the character would be a function of its HP. In other words there is no damage output by the character if it's dead. If you assume a hard encounter then the HP total is set. The set HP of values puts a limit on the investment duration. Again, once HP is gone on either side of the encounter then damage output stops.
The above system should help determine, in a white room, the net present value of an encounter and when it would be best to hit hard. Of course, this all comes from a 2 minute brainstorm and while I write the post. It could be really far off or more complicated than it needs to be. |
| #11MechaPilotAug 18, 2015 12:35:22 |
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| (Reply to #11)bid |
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| #13Tempest_StormwindAug 18, 2015 14:29:49 |
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| #14transcendantviewerAug 18, 2015 15:16:17 | I don't place much stock in Spike Damage v. DoT. If you want to really feel effective and remain that way, you should make use of both to give yourself a high consistent damage output as well as a continengency in case you stop hitting. That way, you're at least always helping somehow. |
| #15MechaPilotAug 18, 2015 19:41:46 |
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| #16MechaPilotAug 18, 2015 19:54:56 | @Tempest_Stormwind:
I'm going to both agree and disagree with you here.
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| #17Tempest_StormwindAug 18, 2015 20:42:42 |
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| (Reply to #15)bid |
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| #19MechaPilotAug 18, 2015 22:50:55 |
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| #20MechaPilotAug 18, 2015 23:06:28 |
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| #21YunruAug 19, 2015 5:58:01 | Why calculations? "Can I kill/remove something without too much overkill?" If yes: do it! If no: "How can I do the most damage/removal with what I've got?" . Also only worrying about the last hit point is wrong: you want to minimize the damage taken, because that HP sponge has to last the entire day. |
| #22SorsohkaAug 19, 2015 6:18:01 | This is all depend on what value YOU give to waiting.
I fight Bugbears (27HP), I can cast fireball dealing 28 damages NOW or I can cast vitriolic Sphere dealing 20 damage now then 15 damage next round, well we can both agree that fireball is better then vitriolic sphere in this situation.
now if we are fighting stronger monster with 34 HP each now between fireball doing 28 damage NOW or vitriolic sphere doing 20 now then 15 next round, vitriolic sphere become better.
FInally in a situation where you got the BBEG with 50HP surrounded with an army of 24HP monster, does fireball killing all the minion now is better or worse then vitriolic which will cause more damage tot he BBEG is more usefull, that is YOUR personal opinion. Personnly I prefer the fireball in this situation since killing all thoe minion, will greatly reduce the damage on teh party, and the fighter go far better abilities to deal single target damage to that BBEG, and as a spellcaster my job is to fireball the minions and cast haste on the fighter, then I can turn on my gameboy and play pokemon while the fighter kill the BBEG. |
| #23Mommy_was_an_OrcAug 19, 2015 8:27:29 |
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| #24MechaPilotAug 19, 2015 9:05:40 |
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| (Reply to #19)Cooperjera |
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| (Reply to #20)bid |
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| (Reply to #25)FrogReaver | For the most part I prefer simple equations. Dealing with the almost exponetional complexity of calculating "chance to kill" in any subsequent rounds just makes dealing with such a stat not worth it even if the results are more accurate. Then factoring in the additional exponential effect that dealing with any error at all in such calculations and its an impossible task IMO.
Basically what I want is a system that can allow me to weight damage now vs damage later. I know damage now is better. However, I'm not sure how much better. I know that any result I get will be a general result and not apply to every situation. I'm okay with that as long as whatever method we use applies to a decent majority of situations.
As such so far I'm most interested in the finance equations because finance deals with present values and future values all the time. So some modified finance equation is probably the easiest method and I think we all try then we can probably nail down a decent approximation equation that works in most situations.
So basically, I want an equation that doesnt make a variable out of monster hp because. Though we may have to start at equations that use monster hp as a variable to get an idea for how things work and how we might can remove it.
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| #28Tempest_StormwindAug 22, 2015 11:54:55 |
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| #29FrogReaverAug 21, 2015 20:12:47 | Tempest, If we assume that damage now is more valuable than damage later then we also must assume that monster damage now is worse for us than monster damage later. As such you will have to take that fact into account on both sides of the equation and not just 1.
I envision a formula that consists of 2 functions: f(x) = the equation for the future value of the damage outside any context g(x) = the context of what that damage actually does
my hope is that f(x) will not depend in any way on g(x)
And the final result f(x)*g(x) = would yield the future value of the damage in context of what you are fighting.
For my purposes all I care about is f(x) while you care about everything.
By the way, does anyone know a way to estimate the average number of rounds a monster with known hp will live given some average DPR values? |
| (Reply to #29)bid |
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| #32Tempest_StormwindAug 22, 2015 0:32:07 | Not to mention, mine does account for that. A monster will have a lower threat index later in the fight due to a higher kill rate against it; the threat index will only be higher later in the fight if the monster has a desperation attack or something. In other words, they're a bigger threat when dealing damage now vs damage later. I argue that there is no way to answer this question without knowing at least an estimate of g(x), as I said above. |
| #33YunruAug 22, 2015 3:47:13 | Hex is a great example of more damage later being better than more damage now. Although probably in part due to "later" including "later in the same turn". |
| (Reply to #31)FrogReaver |
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| (Reply to #32)FrogReaver |
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| #37YunruAug 22, 2015 9:40:42 | Yes but unless you action surge it doesn't do more damage until your second turn. |
| #38Tempest_StormwindAug 22, 2015 10:36:06 |
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| (Reply to #38)FrogReaver |
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| (Reply to #26)FrogReaver |
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| #41halvgrimAug 23, 2015 2:47:40 | Lets make a model based on a single player fighting a crowd of small monsters. The damage delivered by player on nth turn is called pd(n). Now we can define the cumulative damage delivered by player on nth turn (The total damage that the player has delivered)
PD(n) = pd(1)+pd(2)+.... pd(n)
We assume that whenever we deal 1HP of damage to a crowd of monsters, the damage output of the crowd will decrease by a factor a. (The more damage we deal, the less we will receive on subsequent turns). This means that whenever the monsters have received x damage, their damage output will have decreased by a*x. We assume that the monsters initial damage output is mdstart, and we insert x=PD(n). Nowe we can calulate the monsters damage output on the nth turn.
md(n) = mdstart - a*PD(n)
Here we have assume that the player wins initiative. we can also define the cumulative damage delivered by monsters on nth turn
MD(n) = md(1)+md(2)+.... md(n)
A litttle calculation yields
MD(n) = (mdstart - a*PD(0))+(mdstart - a*PD(2))+(mdstart - a*PD(3))......(mdstart - a*PD(n)) MD(n) = n*mdstart - n*pd(1)- a*(n-1)*pd(2) - a*(n-2)*pd(3) -....a*(1)*pd(n) |
| #42Coredump00Aug 23, 2015 7:32:35 |
I fully understand and condone doing math because its fun.... but this is a question that can't be answered in any usuable way.
Given a set group of PCs, and given a set group of enemies.... we could model some approximations of the relative value of 'current' and 'future' damage. But even then it would depend on how much current and future damage. (1hp now is going to be roughly equal to 1 hp later; 100hp now is worth a whole lot more than 100hp later.) So we will have a list of approximations of various damage levels... and even those are just white room, since the actual values will be dependent on the actual dice rolls.
So we will have a list of approximations of various damage levels that will not be overly reliable...... and that is only for a specific set of PCs against a specific set of enemy creatures.....
Have fun with the modeling exercise.... but I see no feasible way of getting an applicable 'rule of thumb' to use in discussions.
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| (Reply to #42)FrogReaver |
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| #45Tempest_StormwindAug 23, 2015 9:34:57 |
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| #46YunruAug 23, 2015 9:57:30 | DPR is based on finite variables, thus we can use the law of averages. This... isn't. |
| (Reply to #45)FrogReaver |
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| #48Tempest_StormwindAug 23, 2015 10:25:56 |
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| #50Tempest_StormwindAug 23, 2015 10:29:05 |
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| (Reply to #50)FrogReaver |
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| (Reply to #48)halvgrim |
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| (Reply to #49)halvgrim |
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| #54MechaPilotAug 23, 2015 13:27:04 |
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| (Reply to #40)bid |
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| #59Tempest_StormwindAug 23, 2015 14:40:44 |
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| #60FrogReaverAug 23, 2015 15:28:48 | Dang it's weird how auto loan interest rates don't change once you have the loan. It's weird how CD interest rates do not change once you take out the CD. It's weird how many credit cards have fixed interest rates too... |
| #61MechaPilotAug 23, 2015 15:31:13 |
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| #62MechaPilotAug 23, 2015 15:37:20 |
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| (Reply to #62)FrogReaver |
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| #65MechaPilotAug 23, 2015 16:13:27 |
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| (Reply to #59)bid |
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| #67Illumina_or_RagnarokAug 23, 2015 18:36:10 | I looked at some practical examples to try and get a feel for this.
One is the first example you gave, slightly modified - Is 10 damage round 1 better than 20 damage round two? ' The answer is 20 damage rouned 2 is always better - if the 10 damage wouldn't kill the enemy and it otherwise survives until round two. I am going to treat the chance of killing an enemy with an initial attack as a situational know, that is, it is pretty apparent when this will occur (much like it is pretty apparent when you should choose AoE spells over single target spells). That leaves the chance of the enemy getting killed before the damage hits as the rate of discount. It is my experience a mean encounter will have ~4 enemies and take ~4 turns, and it turns out that, typically, one enemy per turn is eliminated. If there are no tactics used (i.e.,don't focusfire the enemy with DoTs), this leads to a discount rate of ~25% per turn. With coordinated tactics, this could be a higher, but if you factor in lost damage from other options (direct damage) and the fact that focus-fire tends to be the best option, that would drive it down, so I am going to say a rough discount of 25% is a reasonable estimate at a high level.
Another scenario I looked at - Valor Bard 10 and Haste - Lone PC - No bonus action attacks, 100% hit chance assumed for simple math. - No value was given to any feature of haste other than the extra attack.
The question is this - when does it pay back to sacrifice 2 attacks on round 1 to get 3 attacks every following round? The metric I was looking at was enemy turns taken.
First I looked at this against a solo monster, how many hp would it take before haste would "pay-off"? Turns out that about 8 hits worth of damage is the crossover point (turns out that with hit chance factored in this becomes 8 attacks, so the crossover point is still about round 3-4). With resource expendatures, this says it really doesn't make sense to cast haste unless the encounter is going to last at least 4 rounds.
What about with hordes of one hit kill minions? How many minions would there have to be before it makes sense to cast haste? My numbers show the crossover point was 12 enemies, so it was not beneficial to cast haste unless the encounter would last until round 6 (if haste is not cast), pretty rare in my experience!
I take this to show that, for encounters that are typically between these two extremes, this pays off on about round 5.
The interesting part is that, If you look at a formula that shows a summing of 1 attack per turn starting on round 2, discounted at a rate of 0.25% per turn, and see when that sum exceeds the 2 base attacks that could be done the inital round, it happen on round 5.
I realize there could certainly be a lot of more detailed analysis that could be done on this, but as a rough value, I would say a discount of 25% per turn is a good estimate. |
| #68halvgrimAug 23, 2015 22:07:33 | A years ago someone made a combat simulator in Excel. It could be interesting to create something similar to show the effects of missing heaviside-functions, wasted damage and randomness.
https://www.reddit.com/r/DnD/comments/21ele2/a_dd_v35_excel_battle_simulator_to_see_what/
EDIT: Or maybe that is what Ragnarok already did... |
| (Reply to #64)Cooperjera |
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| #70CognomenAug 28, 2015 12:04:44 |
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| (Reply to #70)bid |
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| #72YunruAug 28, 2015 14:46:49 | But there is a sharp drop. Bexause the target will have died or cured itself with increasing chance each turn. |
| #73CognomenAug 29, 2015 15:57:23 | I see what you're getting at, bid, but, like Yunru, I think that a sharp early drop is appropriate. Any delay introduces a huge amount of uncertainty, as issues like deaths, healing, positioning, terrain changes, concentration failures, the end of combat, and other actions the PC might need to perform, to say nothing of all the actions, bonus action, and reactions of both allies and enemies, make predicting futurities unreliable. I don't mean white-room predictions, either. The enemy casts a wall spell, and suddenly he's out of range; an ally casts thunderwave and blasts all the pirates over the gunwale. These things happen in real games, and they are predictably unpredictable.
As far as there being less fall-off in more-remote rounds, there are a few things to consider. First, I would expect there to be a notability threshold, a minimum damage that one can always do on the present turn. Thus, any result below, for example, 5 would be beneath consideration, and whether the future-damage number was 20/5 or 25/6 would be immaterial. Second, far-remote damage should retain at least appreciable value. If the player is estimating responsibly (i.e., not trying to plan way out past the realistic end of combat, such as considering a delayed-blast fireball for round 11), then the action being considered has some chance of doing its full damage. Thus, I think a more-regular decay, such as every turn representing a half-life, would be too aggressive. Third, game design sets limits on these kinds of decisions, and the more remote a turn is, the less likely it is that the player has access to it. The majority of far-remote cases will be long-duration buffs like haste or hex/er's mark, which a) usually provide adequate damage in the first few rounds to justify their casting and b) have the potential to really break the usual rules for spell-slot efficiency, in some cases lasting through multiple encounters, so may not be quantifiable in the same way as direct-damage actions anyway*. A final reason that there should be less decay in far-remote rounds, combat slows down. Your allies run out of spell slots, run out of rages, run out of ki points. Thus enemies die more slowly and things become slightly less unpredictable from round to round. Call it the heat death of the multiverse.
The problems I see with a multiplicative scheme like you have suggested are, first, that the coefficients seem to be chosen at random.Your example is "{10*5 13*4 16*3 20*2} or {50 52 48 40}" but why not {10*4 13*3 16*2 20*1} or {40 39 32 20}, which creates a different set of priorities? And second, that the numbers this outputs aren't directly comparable to anything in the game mechanics, so that it requires the additional operation of dividing all outcomes by the "now"-turn coefficient to convert them into "now" damage.
*I had a thought about this as I was typing, but I'm going to have to give it some more thought. |
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| #75CognomenAug 31, 2015 9:52:49 |
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| #77FrogReaverAug 31, 2015 22:41:54 | I think I've figured out what I want to figure out.
Suppose you are fighting X enemies and you can kill Y per turn (T).
The damage you take on a given round will be given be: Damage taken (T) turns into comabt =[ X-Y(T) ] * (Monster DPR)
Damage on turn1 = X - Y.... Damage on turn2 = X - 2Y.... Damage on turn3 = X - 3Y.... .... Damage on turnT = X - 3T ----------------------------------------------- Total Damage taken on turn2 = 2X - 3Y Total Damage taken on turn3 = 3X - 6Y Total Damage taken on turn4 = 4X - 10Y Total Damage taken on turn T = TX - [ T(T+1)/2 * Y]
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The below equation is good for uniform damage and a discrete integer number of monsters killed on a turn.
Total Damage taken after turnT = [ TX - ( T(T+1)/2 * Y ) ] * (Monster DPR)
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This is just a starting point. I need to look at the equation and consider fractional kill rates not just integer kill rates. Sometimes it will take to 2 rounds to kill a monster and so that kill rate would be 1/2. My equation isn't totally accurate for such.
Also I need to find a way to consider non-uniform kill rates between turns.
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After this work is done, it may be possible to draw conclusions without actually needing to estimate kill rate itself. It may be enough to know that damage and kill rate are directly proportional. Thus the change from kill rate to damage may happen easily enough (hopefully)
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