Diablo® III

PVP Balanced System Analysis

Hi, I would like to inform the general community of my ideas on how the PVP system could be balanced and possibly expedite its release (if the ideas are accepted by Blizzard)! First of all, I am an applied mathematician and I have used my talents to aid others in calculating effective strategies in various games in my free time. While the mathematical analysis of games isn't a topic I specialize in (I specialize in computational physics), the formulas used in these games aren't too mathematically complex.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Introduction

Now to begin the talk of PVP! I believe an effective PVP system should be accessible to all players on roughly an even footing; however, in doing so I do believe there should be customization of the characters to promote diversity (it would be boring to directly overwrite everyone's stats to some fixed template for PVP).

Currently, with the PVE system, player damage is on average very high and as such would lead to very short battles. On the other hand, some players have very high health and can survive a very long time. I believe that roughly 99% of the matches would consist of 1 of 4 cases:
  • (i) Player 1 can kill player 2 in seconds.
  • (ii) Players 1 and 2 can kill each other in seconds.
  • (iii) Player 1 cannot kill player 2 due to life sustainability and damage mitigation.
  • (iv) Players 1 and 2 cannot kill each other due to life sustainability and damage mitigation.

  • To counteract this I believe several adjustments must be made on various parameters to try to prevent these 4 cases most of the time. The adjustments must be made to Damage Per Second (DPS), Effective Health (EHP), Crowd Control (CC), and Life Sustainability (LS). Here I propose formulas for the following by using a standard value and logarithmic diminishing returns after that standard value is attained.

    Consider the following formulas and explanations:

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    DPS Scaling

    Set a standard reference for DPS and denote it by sDPS. This will be the scale that player damage will be adjusted on. Next, set a diminishing returns factor and denote it by dmfD. This will affect how quickly additionally DPS will be attenuated beyond the standard reference. Introduce a multiplicative factor which will attenuate DPS and denote it by dscale. Lastly define PVPDPS as the adjusted DPS used for PVP.

    Now the formulas become:
  • If (DPS <= sDPS), then dscale = 1.00
  • If (DPS > sDPS), then dscale = (1 + dmfD* log(DPS / sDPS)) * sDPS / DPS
  • PVPDPS = DPS * dscale

  • This equation allows for some flexibility by adjusting sDPS and dmfD. By decreasing dmfD, it is possible to make diminishing returns steeper and by setting dmfD to 0, everyone's PVPDPS will be hard capped at the sDPS.

    As an example, if a player has 200,000 DPS and sDPS is 50000 and dmfD = 1.00 then the dscale becomes roughly 0.4 and the player's PVPDPS becomes roughly 80000.

    The PVPDPS will be adjusted by multiplying the damage-per-hit by the dscale multiplier as defined above. This will allow players to maintain high critical chance and attack speed but will lower the damage-per-hit in doing so.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    EHP Scaling

    Start by calculating a player's EHP amounts, these amounts may be different depending on they type of damage (e.g. melee, ranged, poison, etc.) and they player's resistances to those types as well as overall mitigation from armor, skill, passives, etc. This EHP calculation should include dodge and block chance. And for the block amount calculation, use an attacker that hits for the sDPS amount. Without loss of generality, let EHP denote the EHP of any particular type of damage as the formulas will be the same.

    Now set a standard reference EHP and denote it by sEHP similar to sDPS for DPS. Again, also set a diminishing returns factor dmfE similar to dmfD for DPS. Introduce a multiplicative factor which will attenuate EHP and denote it by escale. Lastly, PVPEHP will denote the adjusted EHP used for PVP.

    Now the formulas become:
  • If (EHP <= sEHP), then escale = 1.00
  • If (EHP> sEHP), then escale = (1 + dmfE* log(EHP / sEHP)) * sEHP / EHP
  • PVPEHP = EHP * escale

  • The flexibility of the equation is the same as for DPS. The way PVPEHP will be implemented won't be by decreasing a player's EHP but instead by increasing the damage taken by the player by a factor of 1/escale. This effectively allows players to penetrate absurd defenses by increasing the damage they do to those targets.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    CC Scaling

    This system can be simply the current CC system used for elites except with the CC cap at 100% instead of 65% as used in PVE. This will enable players to only temporarily lock their opponent down (stun/freeze/etc.) without the ability to permanently prevent a player from doing anything.

    In addition, a knockback adjustment should be made similarly to CC by reducing the amount knocked back with subsequent attacks which inflict knockback.

    Lastly, snare movement speed should be adjusted similarly to the general CC formula but instead of adjusting snare duration, it should adjust snare movement speed reduction. This would enable a player standing in caltrops to move at full speed after a few seconds of standing in it; however, once leaving the caltrops, they could again be snared as their snare resistance diminishes at a fixed rate while not snared.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    LS Scaling

    There are many ways for a player to restore lost health but the most common are: Life Regeneration, Life on Hit, Life Steal, Life from Health Globes, Life from Potions, and Life from Skills (either % max HP and fixed amount). I will address these one at a time:

  • Life Regeneration should be multiplied by the escale parameter to ensure a hardy player cannot just sit idly in the face of attackers.
  • Life on Hit should also be multiplied by the escale parameter to similarly avoid never-ending battles and prevent mindless tanking.
  • Life Steal should remain unaltered since DPS is already adjusted; however, the inferno amount of 80% reduction to Life Steal should still be used.
  • Life from Health Globes should be multiplied by the escale amount. This is especially important if many sources of Health Globes will exist in PVP.
  • Life from Potions should also be multiplied by the escale amount. This isn't as important since potions can only be consumed every 30 seconds.
  • Life from skills need to be adjusted by the escale amount as well in the same way as Life on Hit and Life Regeneration.

  • This should provide ample scaling to sources of Life to discourage immortality builds.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Closing Comments

    In closing, I would like to add that none of the formulas listed here are certain, nor might they be remotely close to the final release of PVP. I provided formulas here that I think are balanced and would allow most players some footing on a playing field since the current spread of player's statistics is very very large.

    Also, further adjustments can be made to individual skills that may prove troublesome to balance the game. Examples of these skills are: Threatening Shout - Demoralizing Roar taunt mechanics, Mantra of Retribution mechanics, Smokescreen, etc.

    I hope you all enjoyed reading my theory-crafted ideas for PVP!

    TL;DR: This post explains a possible PVP system which could be implemented to promote balance.

    Edit: fixed some typos.
    Edited by Iria#1342 on 2/4/2013 12:29 PM PST
    Reply Quote
    ^ bump for justice

    An awesome thread with great details.

    I think some of these ideas are great for balancing PVP which is definately needed to keep the game playable for everyone.

    Hopefully blizzard will read this and hurry up and finish PVP dammit.

    Many other games use the same formulas as you were suggesting above and they work perfectly well, I wonder what's taking them so long.

    Even in WoW the balance in PVP is pretty amazing considering each class/character has over 50+ spells at a time on their action bars
    Reply Quote
    Thanks for your support!

    Please feel free to comment on my ideas here so more people can view this thread (although reading it may be too much to ask for lol).
    Reply Quote
    Diablo III PvP is vaporware.
    Reply Quote
    Considering how simplified the skill system and item system is ... to balance the characters for PVP will not be an easy task.

    Heh, we will see what comes out of that.

    All I hope is that they dont decide to change skills which work right now well in PVE on the characters based on PVP
    Reply Quote
    The skill adjustments I mentioned were only for PVP. The PVE skills should remain unchanged (aside from normal class balance updates).
    Reply Quote
    Posts: 114
    Hi, I would like to inform the general community of my ideas on how the PVP system could be balanced and possibly expedite its release (if the ideas are accepted by Blizzard)! First of all, I am an applied mathematician and I have used my talents to aid others in calculating effective strategies in various games in my free time. While the mathematical analysis of games isn't a topic I specialize in (I specialize in computational physics), the formulas used in these games aren't too mathematically complex.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Introduction

    Now to begin the talk of PVP! I believe an effective PVP system should be accessible to all players on roughly an even footing; however, in doing so I do believe there should be customization of the characters to promote diversity (it would be boring to directly overwrite everyone's stats to some fixed template for PVP).

    Currently, with the PVE system, player damage is on average very high and as such would lead to very short battles. On the other hand, some players have very high health and can survive a very long time. I believe that roughly 99% of the matches would consist of 1 of 4 cases:
  • (i) Player 1 can kill player 2 in seconds.
  • (ii) Players 1 and 2 can kill each other in seconds.
  • (iii) Player 1 cannot kill player 2 due to life sustainability and damage mitigation.
  • (iv) Players 1 and 2 cannot kill each other due to life sustainability and damage mitigation.

  • To counteract this I believe several adjustments must be made on various parameters to try to prevent these 4 cases most of the time. The adjustments must be made to Damage Per Second (DPS), Effective Health (EHP), Crowd Control (CC), and Life Sustainability (LS). Here I propose formulas for the following by using a standard value and logarithmic diminishing returns after that standard value is attained.

    Consider the following formulas and explanations:

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    DPS Scaling

    Set a standard reference for DPS and denote it by sDPS. This will be the scale that player damage will be adjusted on. Next, set a diminishing returns factor and denote it by dmfD. This will affect how quickly additionally DPS will be attenuated beyond the standard reference. Introduce a multiplicative factor which will attenuate DPS and denote it by dscale. Lastly define PVPDPS as the adjusted DPS used for PVP.

    Now the formulas become:
  • If (DPS <= sDPS), then dscale = 1.00
  • If (DPS > sDPS), then dscale = (1 + dmfD* log(DPS / sDPS)) * sDPS / DPS
  • PVPDPS = DPS * dscale

  • This equation allows for some flexibility by adjusting sDPS and dmfD. By decreasing dmfD, it is possible to make diminishing returns steeper and by setting dmfD to 0, everyone's PVPDPS will be hard capped at the sDPS.

    As an example, if a player has 200,000 DPS and sDPS is 50000 and dmfD = 1.00 then the dscale becomes roughly 0.4 and the player's PVPDPS becomes roughly 80000.

    The PVPDPS will be adjusted by multiplying the damage-per-hit by the dscale multiplier as defined above. This will allow players to maintain high critical chance and attack speed but will lower the damage-per-hit in doing so.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    EHP Scaling

    Start by calculating a player's EHP amounts, these amounts may be different depending on they type of damage (e.g. melee, ranged, poison, etc.) and they player's resistances to those types as well as overall mitigation from armor, skill, passives, etc. This EHP calculation should include dodge and block chance. And for the block amount calculation, use an attacker that hits for the sDPS amount. Without loss of generality, let EHP denote the EHP of any particular type of damage as the formulas will be the same.

    Now set a standard reference EHP and denote it by sEHP similar to sDPS for DPS. Again, also set a diminishing returns factor dmfE similar to dmfD for DPS. Introduce a multiplicative factor which will attenuate EHP and denote it by escale. Lastly, PVPEHP will denote the adjusted EHP used for PVP.

    Now the formulas become:
  • If (EHP <= sEHP), then escale = 1.00
  • If (EHP> sEHP), then escale = (1 + dmfE* log(EHP / sEHP)) * sEHP / EHP
  • PVPEHP = EHP * escale

  • The flexibility of the equation is the same as for DPS. The way PVPEHP will be implemented won't be by decreasing a player's EHP but instead by increasing the damage taken by the player by a factor of 1/escale. This effectively allows players to penetrate absurd defenses by increasing the damage they do to those targets.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    CC Scaling

    This system can be simply the current CC system used for elites except with the CC cap at 100% instead of 65% as used in PVE. This will enable players to only temporarily lock their opponent down (stun/freeze/etc.) without the ability to permanently prevent a player from doing anything.

    In addition, a knockback adjustment should be made similarly to CC by reducing the amount knocked back with subsequent attacks which inflict knockback.

    Lastly, snare movement speed should be adjusted similarly to the general CC formula but instead of adjusting snare duration, it should adjust snare movement speed reduction. This would enable a player standing in caltrops to move at full speed after a few seconds of standing in it; however, once leaving the caltrops, they could again be snared as their snare resistance diminishes at a fixed rate while not snared.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    LS Scaling

    There are many ways for a player to restore lost health but the most common are: Life Regeneration, Life on Hit, Life Steal, Life from Health Globes, Life from Potions, and Life from Skills (either % max HP and fixed amount). I will address these one at a time:

  • Life Regeneration should be multiplied by the escale parameter to ensure a hardy player cannot just sit idly in the face of attackers.
  • Life on Hit should also be multiplied by the escale parameter to similarly avoid never-ending battles and prevent mindless tanking.
  • Life Steal should remain unaltered since DPS is already adjusted; however, the inferno amount of 80% reduction to Life Steal should still be used.
  • Life from Health Globes should be multiplied by the escale amount. This is especially important if many sources of Health Globes will exist in PVP.
  • Life from Potions should also be multiplied by the escale amount. This isn't as important since potions can only be consumed every 30 seconds.
  • Life from skills need to be adjusted by the escale amount as well in the same way as Life on Hit and Life Regeneration.

  • This should provide ample scaling to sources of Life to discourage immortality builds.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Closing Comments

    In closing, I would like to add that none of the formulas listed here are certain, nor might they be remotely close to the final release of PVP. I provided formulas here that I think are balanced and would allow most players some footing on a playing field since the current spread of player's statistics is very very large.

    Also, further adjustments can be made to individual skills that may prove troublesome to balance the game. Examples of these skills are: Threatening Shout - Demoralizing Roar taunt mechanics, Mantra of Retribution mechanics, Smokescreen, etc.

    I hope you all enjoyed reading my theory-crafted ideas for PVP!

    TL;DR: This post explains a possible PVP system which could be implemented to promote balance.

    Edit: fixed some typos.


    I'm not a math wiz, and I didn't understand anything you said.

    Do you mean there should be diminishing returns to PvP damage, PvP EHP, and PvP Life Regeneration?

    If Yes, then I agree with you on the PvP Damage. But I don't think EHP or Life Regen should have diminishing returns.
    Edited by Acolytesftw#1665 on 12/20/2012 12:46 PM PST
    Reply Quote
    I'm not a math wiz, and I didn't understand anything you said.

    Do you mean there should be diminishing returns to PvP damage, and PvP EHP?

    If Yes, then I agree with you on the PvP Damage. But I don't think EHP should have diminishing returns.


    Yes there are diminishing returns, and if EHP isn't diminished too then you will end up with immortal characters. Consider my Barbarian in my profile (currently #1 character for EHP in Americas region), how on earth would you kill him unless he had nerfed EHP? I can literally face-tank enraged ubers on high MP settings or 50-60 enemies with 2-3 elite packs in MP10 and survive indefinitely standing on desecrator fires and arcane beams!
    Reply Quote
    Unfortunately, I don't have any graphs I can post here. However, what the damage scale multiplier dscale would look like is a straight line at 1.00 until you reached the standard DPS at which point the dscale starts to drop but never to the point it reaches zero. You can always increase your PVPDPS by increasing your DPS and there is no hard cap, but the returns are diminished very quickly after you reach the standard amount.
    Reply Quote
    Posts: 114
    If there is diminishing returns to Everything, then it will make everybody equal (more or less).

    I don't think that's a good idea in a game that promotes spending real money to buy gear. Because no matter how much money people spend on their gear, there won't be a feeling of "Godliness" or being superior to others. Therefore RMAH sales will drop.
    Edited by Acolytesftw#1665 on 12/20/2012 2:32 PM PST
    Reply Quote
    Even with the diminishing returns, a better geared player will still have the edge. In my example a 200k dps vs 50k dps player would scale to 80k dps vs 50k dps which is still highly in favor of the better-equipped player. The diminishing returns are there to close the gap somewhat as some players are several orders of magnitude more powerful than average newcomers.
    Reply Quote
    You might have a point. Perhaps.

    I was hoping for something different. In order to remove the imbalance between players who have 100s of mil of gold to spend on gear before PVP even starts, the odds could be evened out significantly by only allowing crafted gear in PVP fights. Hopefully some new designs can be introduced to make use of the brimstones we have.

    That way even a player who just got to level 60 can compete after crafting the initial set of gear and though the player is new the gear could actually end up being he best in game, given some luck.

    It's not fair to apply diminishing returns to all DPS as that would take away from players who have reached high paragon levels. The extra 300 of main stat after reaching paragon 100 should mean something and should not be diminished in any way, though I can see why you think that some adjustment is needed after looking at your barb :)

    Its OK if it was only applied to gear, but in no way do I want the extra damage earned through higher paragon to be diminished, even if its only a couple thousand DPS.

    I think crafted gear for PVP is the answer.
    Reply Quote
    Hmmm... now, all blizz need to do is copy-paste it into a webpage with the title: PvP Blog.
    Reply Quote
    Let the loot decide who wins or dies. Just like the previous titles.

    I am playing a loot based pve game, right?

    There is a ratings system for people who want to fight "fair".


    The loot based in D3 has failed in a sense where design component: random has been given way too much weight.

    It will result into: Lucky 2 Win, rather than Play 2 Win.

    Imagine, one player at level 60, farm MP 0 for 5 minutes and get a Echoing Fury with CD 100% plus open socket vs you farmed 1000 hours and the best you got is blue open socket ring only.

    Well, then you could cry the "unfair" here, and we will flame you on "random is random", "stop QQ", etc...

    So, in a sense, I think some kind of nerf is needed on the random is random in relation to played hours.

    Afterall, the game should reward players who play more and not 90% based on luck.
    Reply Quote
    Yeah my idea was to balance it slightly but not completely level the playing field as placing a hard cap on ehp and dps would do.
    Reply Quote

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