# Community

 Dungeons & Dra.. Previous Editions .. Optimization By The Numbers
Jump Menu:
Post Reply
Page 4 of 9  •
Switch to Forum Live View Optimization By The Numbers
 6 years ago  ::  Jun 07, 2007 - 2:50AM #31 zombiegleemax Date Joined: Aug 10, 2009 Posts: 470,906 I'm actually curious as to more of the statistics involved here. Any chance that you can post the original data, or a link to it? Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 4:16AM #32 maurezen Date Joined: Apr 5, 2006 Posts: 12 Ok, let's see..Step 4: Weighted Damage (if applicable): If your character deals damage, then it needs to be weighted by its probability of success to determine just how good it is. One can say, "assuming all hits" and come up with a huge damage figure, but it means nothing if you have only a 1% chance of landing all hits. Calculating weighted damage is as simple as multiplying the probability of each attack by the damage that it deals.Just for clarity.. Calculating weighted damage is as simple as multiplying the propability of each attack by the average damage that it deals and adding the results together.The probability that N - m, where m < N, will hit you is equal to the product your probability of success for the m that miss you, multiplied by the product of your AC's probability of failure for the N- m monsters that hit you. Your probability of failure = 100% - Probability of Success.This is a little unclear. First part of the first sentence states the calculating of propability of m out of N unmarked hits, while second part of the first sentence calculates the propability of m marked hits; these propabilities differ.*sure nobody wants the formula for the propability of m unmarked hits - it's just too impractical. Just note if anyone wants, I'll post it* Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 6:26AM #33 CubeKnight Date Joined: Dec 19, 2003 Posts: 333 Tempest, how are you doing the data mining? Also, are you done with it?I ask because I have a lot of data in a database that I use for my random generators (see sig), and it's quite easy to build queries that give the desired results, instead of having to do it by hand. It's also quite easy to segment the results based on books allowed, and the like. So, if your DM only uses Core+MM2-4, you can choose not to include the Weather books and get more accurate results regarding your specific situation.Maybe I could set up a small website to query for that kind of info, but at the earliest I'd start to work on that next week. I've got a final in a couple of hours, another one tommorrow, and have to defend my thesis on monday. All of that added to my job. I think after that, I'd have some free time. Or so I hope.Anyway, I'll volunteer for doing most of the data mining, if you guys can wait for a bit. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 6:53AM #34 maurezen Date Joined: Apr 5, 2006 Posts: 12 A little bit more, for the "Explanation/Derivation" sections.Had to hide it, because there's plenty of text.*I also checked your calculations*Opposite checks. Show Whoever is taking the offensive action wins on a tie.Not always. Consider initiative checks, for example. There is a reroll for a tie.N[sup]-1[/sup]∑Pr(X+nSure.We restrict outselves to the case where X-Z = N+1, then we always lose.Er.. First, who is taking offensive action? This is important; I assume that monster taes offensive, since in your calculations all inequalities are strict.Second, to have any chance that Z+1dNto have any chance that Z+1dN<=X+1dN we should have Z-XAnyway, we always lose when Z-X>=N, not N+1.N[sup]-2[/sup]∑(N+[Z-(X+n)]) + N[sup]-1[/sup](Z-X), where n ranges from (Z-X+1) to N.Sure.Now lets evaluate the sum...I don't quite get it... Why evaluate, when you can just calculate it?N[sup]-2[/sup]∑(N+[Z-(X+n)]) = N[sup]-2[/sup]∑(N+Z-X)-N[sup]-2[/sup]∑(n), both sums over the original range.N[sup]-2[/sup](N+Z-X)(N-(Z-X))-N[sup]-2[/sup]N(N+1)/2 + N[sup]-2[/sup](Z-X)(Z-X+1)/2Bringing the total to:N[sup]-2[/sup](N+Z-X)(N-(Z-X))-N[sup]-2[/sup]N(N+1)/2 + N[sup]-2[/sup](Z-X)(Z-X+1)/2+N-1(Z-X)Sorry, by the time I read this I knew you were calculating the sum.And even though your calculations are correct, I suggest a little simplification of the result:N[sup]-2[/sup]∑(N+[Z-(X+n)]) = N[sup]-2[/sup]∑(N+Z-X)-N[sup]-2[/sup]∑(n), both sums over the original range.N[sup]-2[/sup](N+Z-X)(N-(Z-X))-N[sup]-2[/sup]((Z-X)(N-(Z-X))+(N-(Z-X))(N-(Z-X)+1)/2)Adding together:N[sup]-2[/sup](N[sup]2[/sup]-(Z-X)[sup]2[/sup]+N(Z-X))-N[sup]-2[/sup](N(Z-X)-(Z-X)[sup]2[/sup]+(N-(Z-X))(N-(Z-X)+1)/2)[b]Which results in a simple:1-(1/2)N[sup]-2[/sup]((N-(Z-X))(N-(Z-X)+1))[/b]The second case is calculated perfectly. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 8:14AM #35 Tempest_Stormwind Date Joined: Jun 20, 2004 Posts: 4,784 CubeKnight wrote:Tempest, how are you doing the data mining? Also, are you done with it?I ask because I have a lot of data in a database that I use for my random generators (see sig), and it's quite easy to build queries that give the desired results, instead of having to do it by hand. It's also quite easy to segment the results based on books allowed, and the like. So, if your DM only uses Core+MM2-4, you can choose not to include the Weather books and get more accurate results regarding your specific situation.Maybe I could set up a small website to query for that kind of info, but at the earliest I'd start to work on that next week. I've got a final in a couple of hours, another one tommorrow, and have to defend my thesis on monday. All of that added to my job. I think after that, I'd have some free time. Or so I hope.Anyway, I'll volunteer for doing most of the data mining, if you guys can wait for a bit.Far from it -- I got about halfway done the old-fashioned way (manually), since my SQL training is horribly lacking. Yes, I'm that friggin' nuts.I'll have the information done in a day or two, I hope (assuming my family doesn't put any more demands on my time), but working from a database would be easier, saner, and all-around better.Good luck on the exams and thesis defense; let's hope the number of new ones they try to rip you is at least a single-digit number.Edit: There's another case on opposed checks that has been left out. SRD]An opposed check is a check whose success or failure is determined by comparing the check result to another character’ wrote:An opposed check is a check whose success or failure is determined by comparing the check result to another character’s check result. In an opposed check, the higher result succeeds, while the lower result fails. In case of a tie, the higher skill modifier wins. If these scores are the same, roll again to break the tie....In case of a tie, the combatant with the higher grapple check modifier wins. If this is a tie, roll again to break the tie.Skill and grapple checks involve compared modifiers, with a reroll if those are identical. I have to leave for work like five minutes ago, so I couldn't find the opposed ability check rules, but I'm pretty sure it works this way as well.In fact, off the top of my head, I can't actually think of a single opposed check that doesn't work this way. Cancer prognosis: I am now cancer-free.Weekly Optimization Series: Show These are NOT all my creations! The lead authors are identified as follows:[TS] Tempest Stormwind, [AR] Andarious Rosethorn, [RT] Radical Taoist, [SN] Sionnis, [DH] DisposableHero_, [SH] Seishi.[TS] The Pinball Brothers: Large And In Charge (Melee, Lockdown, Charge, Juggling)[TS] Ashardalon Reborn: I Will Swallow Your Soul (Melee, Fear, Negative Levels, AoE, Theme)[AR] "A"-Game Paladin: Play That Funky Music, Knight Boy! (Team Support, Melee, Theme, Single-Class)[RT] Uncanny Trapsmith: Get in, make it look like an accident, get out. (Skillmonkey, Stealth/Scout/Infiltration, Unorthodox Methods, Theme)[AR] Wizsassin: *Everything* is permitted. (Spellcaster, Support, Sneak Attack, Utility)[TS] Phantom Rush: General Gish Gouda. (Gish, Theme, Setting-Specific(Eberron), Early-Entry PrC)[TS] Storm Knight: Another kind of gish. (Melee/"Gish", Theme, Setting-Specific(Eberron), Unorthodox Methods)[TS] Inevitable Nightmare: The weapon you only have to fire once. (Melee, "Unorthodox" Methods (no charging), Reliability)[AR] Captain Constitution: The number one threat to America. (Melee, TOUGHTOUGHTOUGH, Defense, Theme)[AR] Nuker: I casts the spells that makes the peoples fall down! (Spellcaster, damage, blasting, damage)[TS] Dread Lord of the Dead: Let the Reaping Begin! (NPC-only, Variable (combat/casting/leadership), Iconic Villain, Theme)[AR] Heavy Crusader: No Rest. No Mercy. No Matter What. (Melee, Damage (No charging), Variable, Theme).[TS] Gun Fu: It's bullet time (Ranged, THEORETICAL, Twin weapons, Theme)[RT] Face First: We should talk. (Psionic, social, mind-control, info-management)[SN] Chaingun Porcupine: Never Enuff Dakka. (Ranged, Skirmishing, Spike Damage, Incarnum)[RT] Always On Edge: The Mortal Draw deals death. (Melee, Generalist, Dungeoneering, Stunt)[AR] Feral Druid: Real feral taste. Zero druid calories. (Melee, offense, damage, murder)[RT] Rusty!: Man's Best Friend (Sentry, Support, Backup, Rearguard)[RT] The T3 (Tashalatora Triple Threat): My Kung Fu is More Powerful (Hybrid, Flex-Function, Melee, Caster)[RT] The #1 Snoipah: Boom. 'Eadshot. (Caster, Theme, Spike, Trapscout)[AR] Dreamblade: Rest in Pieces. (Melee, Damage, Single-Class, Combo/Momentum)[AR] Evasion Tank: “When fighting angry blind men, is best to stay out of the way.” (Melee, Tank, Unorthodox Methods (attack negation), Theme)[DH] Psycarnum Warrior: ↑↑↓↓←→←→BA Start (Melee, Tank, Psionics, Incarnum, 1337 h4x)[AR] Heavy Weapons Elf: WHO TOUCHED MY BOW? (Ranged, Cohort, Damage, Unorthodox Methods (ranged ToB))[RT] Gnowhere Gnome: A little man who wasn't there (Caster, Stealth, Single-Class, Elusive)[AR] Uberflank: I got your back. (Melee, support, stunt, teamwork)[TS] Flip the Bird: Everyday I'm shuffling (Ranged, harrier, unorthodox methods (ranged ToB / off-turn movement), support)[DH] Eat Sleep Gank: Real Ultimate Power (Stealth, Assassination, Spike, Magic Versatility)[AR] Slash and Burn: Mind, Body, Blade, Flame / Aspects of a greater whole / which delivers death. (Melee, Theme (flex-style), Damage, Stunt)[RT] Edge of the Light: Cut, Fade to Black (Melee, Defense/Offense, Momentum, Tactical)[RT] Quiet Murder: Cut throats, not corners. (Melee, Stealth, Harrier, Tactical)[TS] Wand Overdrive: Say Hello to my little friends. (Caster, support/artillery/variable, wand specialist)[RT] God Hand: What did the five fingers say to the face? (Melee/Gish, Unarmed, SAD, Theme)[AR] Zero Buff Time Gish: Try to keep up! (Gish, Speed, Movement, Opportunity)[TS] Robo Tackle: I Am Iron Man. (Melee, setting-specific (Eberron), positioning, theme, stunt)Want to see how the entire group rolls?[All] Party Optimization Showcase: Dead for Nothing[TS/RT/AR] Optimization Article: The Flash Step[RT] Optimization Article: Kung Fu Witchcraft Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 8:51AM #36 Tleilaxu_Ghola Date Joined: Sep 28, 2005 Posts: 980 Oh See, for some reason I got it in my head that no opposed check required a modifier check to break the tie. In my experience we alway did it so that the offender won ties (bluffer wins versus sense motive, tripper wins trip check ties, etc, etc). That all make sense to me since the core mechanic is: SRD]If the result equals or exceeds the target number, your character succeeds. If the result is lower than the target number, you fail.But, apparently, I've been playing the game wrong all this time. :embarrass Sooo, ah, yeah, all I need to do is separate out the tie probability, subtract it from my "win" probability and then state that a modifier check is needed here -- with the tie probability being the chance that one would need to perform a modifier check.@maurezen: Thanks for the corrections. I'll make 'em as soon as possible, along with fixing this other wrote:If the result equals or exceeds the target number, your character succeeds. If the result is lower than the target number, you fail.[/quote]But, apparently, I've been playing the game wrong all this time. :embarrass Sooo, ah, yeah, all I need to do is separate out the tie probability, subtract it from my "win" probability and then state that a modifier check is needed here -- with the tie probability being the chance that one would need to perform a modifier check.@maurezen: Thanks for the corrections. I'll make 'em as soon as possible, along with fixing this other fiasco. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 9:03AM #37 Optimator Date Joined: Jul 13, 2006 Posts: 393 This is all very fascinating. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 9:34AM #38 archerpwr Date Joined: Aug 2, 2006 Posts: 2,515 Just have to say this is brilliant once again. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 9:48AM #39 maurezen Date Joined: Apr 5, 2006 Posts: 12 2Tleilaxu_Ghola: hope that helped. Quick Reply Cancel Quote message in reply? 6 years ago  ::  Jun 07, 2007 - 10:17AM #40 Tempest_Stormwind Date Joined: Jun 20, 2004 Posts: 4,784 Tleilaxu_Ghola wrote:Oh See, for some reason I got it in my head that no opposed check required a modifier check to break the tie. In my experience we alway did it so that the offender won ties (bluffer wins versus sense motive, tripper wins trip check ties, etc, etc). That all make sense to me since the core mechanic is:But, apparently, I've been playing the game wrong all this time. :embarrassNo, you've just been playing it your way.Ideally, if the system was completely logical, it would work your way. My guess is that it works the way it does so that instead of favoring the offender, it favors the more skilled of the two participants (or the better grappler, or the stronger one, or what have you).EDIT: Since the opposed modifier isn't so much a "check" as a direct comparison (i.e. my Strength mod is +3, his is +6, he wins), and we have average values for nearly every relevant modifier... it shouldn't be hard to adjust the rubric ever so slightly to account for the probability of success on a tie. However, without standard deviations, I don't see an easy way to completely account for your odds of success on a tie. Cancer prognosis: I am now cancer-free.Weekly Optimization Series: Show These are NOT all my creations! The lead authors are identified as follows:[TS] Tempest Stormwind, [AR] Andarious Rosethorn, [RT] Radical Taoist, [SN] Sionnis, [DH] DisposableHero_, [SH] Seishi.[TS] The Pinball Brothers: Large And In Charge (Melee, Lockdown, Charge, Juggling)[TS] Ashardalon Reborn: I Will Swallow Your Soul (Melee, Fear, Negative Levels, AoE, Theme)[AR] "A"-Game Paladin: Play That Funky Music, Knight Boy! (Team Support, Melee, Theme, Single-Class)[RT] Uncanny Trapsmith: Get in, make it look like an accident, get out. (Skillmonkey, Stealth/Scout/Infiltration, Unorthodox Methods, Theme)[AR] Wizsassin: *Everything* is permitted. (Spellcaster, Support, Sneak Attack, Utility)[TS] Phantom Rush: General Gish Gouda. (Gish, Theme, Setting-Specific(Eberron), Early-Entry PrC)[TS] Storm Knight: Another kind of gish. (Melee/"Gish", Theme, Setting-Specific(Eberron), Unorthodox Methods)[TS] Inevitable Nightmare: The weapon you only have to fire once. (Melee, "Unorthodox" Methods (no charging), Reliability)[AR] Captain Constitution: The number one threat to America. (Melee, TOUGHTOUGHTOUGH, Defense, Theme)[AR] Nuker: I casts the spells that makes the peoples fall down! (Spellcaster, damage, blasting, damage)[TS] Dread Lord of the Dead: Let the Reaping Begin! (NPC-only, Variable (combat/casting/leadership), Iconic Villain, Theme)[AR] Heavy Crusader: No Rest. No Mercy. No Matter What. (Melee, Damage (No charging), Variable, Theme).[TS] Gun Fu: It's bullet time (Ranged, THEORETICAL, Twin weapons, Theme)[RT] Face First: We should talk. (Psionic, social, mind-control, info-management)[SN] Chaingun Porcupine: Never Enuff Dakka. (Ranged, Skirmishing, Spike Damage, Incarnum)[RT] Always On Edge: The Mortal Draw deals death. (Melee, Generalist, Dungeoneering, Stunt)[AR] Feral Druid: Real feral taste. Zero druid calories. (Melee, offense, damage, murder)[RT] Rusty!: Man's Best Friend (Sentry, Support, Backup, Rearguard)[RT] The T3 (Tashalatora Triple Threat): My Kung Fu is More Powerful (Hybrid, Flex-Function, Melee, Caster)[RT] The #1 Snoipah: Boom. 'Eadshot. (Caster, Theme, Spike, Trapscout)[AR] Dreamblade: Rest in Pieces. (Melee, Damage, Single-Class, Combo/Momentum)[AR] Evasion Tank: “When fighting angry blind men, is best to stay out of the way.” (Melee, Tank, Unorthodox Methods (attack negation), Theme)[DH] Psycarnum Warrior: ↑↑↓↓←→←→BA Start (Melee, Tank, Psionics, Incarnum, 1337 h4x)[AR] Heavy Weapons Elf: WHO TOUCHED MY BOW? (Ranged, Cohort, Damage, Unorthodox Methods (ranged ToB))[RT] Gnowhere Gnome: A little man who wasn't there (Caster, Stealth, Single-Class, Elusive)[AR] Uberflank: I got your back. (Melee, support, stunt, teamwork)[TS] Flip the Bird: Everyday I'm shuffling (Ranged, harrier, unorthodox methods (ranged ToB / off-turn movement), support)[DH] Eat Sleep Gank: Real Ultimate Power (Stealth, Assassination, Spike, Magic Versatility)[AR] Slash and Burn: Mind, Body, Blade, Flame / Aspects of a greater whole / which delivers death. (Melee, Theme (flex-style), Damage, Stunt)[RT] Edge of the Light: Cut, Fade to Black (Melee, Defense/Offense, Momentum, Tactical)[RT] Quiet Murder: Cut throats, not corners. (Melee, Stealth, Harrier, Tactical)[TS] Wand Overdrive: Say Hello to my little friends. (Caster, support/artillery/variable, wand specialist)[RT] God Hand: What did the five fingers say to the face? (Melee/Gish, Unarmed, SAD, Theme)[AR] Zero Buff Time Gish: Try to keep up! (Gish, Speed, Movement, Opportunity)[TS] Robo Tackle: I Am Iron Man. (Melee, setting-specific (Eberron), positioning, theme, stunt)Want to see how the entire group rolls?[All] Party Optimization Showcase: Dead for Nothing[TS/RT/AR] Optimization Article: The Flash Step[RT] Optimization Article: Kung Fu Witchcraft Quick Reply Cancel Quote message in reply?
Page 4 of 9  •
Jump Menu:

 Dungeons & Dra.. Previous Editions .. Optimization By The Numbers
Viewing this thread :: 0 registered and 1 guest
No registered users viewing