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| Raven Dark04-09-06, 06:20 PM | In another thread, a poster pointed out that nearly everything in D&D (or at least in the rules) is mathematically based. This poster cited that you could determine the ability modifier for any ability score using the following formula: (Score - 10) / 2 (round down) Another one the poster cited was: Total XP needed to reach a given LEVEL = Sum (LEVEL-1)*1000, with a minimum of 0 I'm no good at mathematics and have a hard time determining formulas on my own, so I wanted your help in this regard. I want you to list as many (accurate) algebraic formulas for D&D as you can think of, things that will help roleplayers when they don't have their books on hand or when the books aren't helpful--things like how to determine the good/bad saves or the base attack bonus of creatures with really high hit dice. EXAMPLE: The MM says many monsters get the base attack bonus of a cleric, but the cleric chart only goes to level 20. What pray tell is the base attack bonus of a monster with 74 HD then? Extrapolating from the chart in the PH can be painstaking and time consuming. Formulas to help solve questions like that quickly and easily are what I am looking for. May this be a productive and helpful thread. Thanks in advance everyone! EDIT: I used the formulas provided AND the lengthy brain numbing method of determining the mediocre BAB of a 74 HD creature (extropolating level by level). Both methods came up with a BAB of 55, so I gueess they are accurate. Keep up the good work everyone! Also, I have decided to write down your formulas below in smurf blood for ease of reference (and to help avoid future redundancy in this thread). Please check your formula's accuracy thoroughly before submitting it. Unless otherwise noted in the below formulas, always round the answer down to the nearest whole number. Ability Score Modifiers Ability Modifier = (Ability Score - 10) / 2 Base Attack Bonus As Fighter (full base): Base Attack Bonus = Hit Dice As Cleric (normal base): Base Attack Bonus = Hit Dice * .75 As Wizard (poor base): Base Attack Bonus = Hit Dice * .5 Base Save Bonuses Good Base Save: Base Save Bonus = (Class Level / 2) + 2 Poor Base Save: Base Save Bonus = Class Level / 3 Bonus Power Points for High Ability Scores Bonus Power Points from High Ability Scores: .5 * Ability Modifier * Class Level Bonus Spells for High Ability Scores Bonus Spells from High Ability Scores: 1 + .25 * (Ability Modifier - Spell Level), minimum 0 Carrying Capacity If your Strength score is 10 or less, your heavy load limit is 10 * Strength If your Strength score is 10 or greater, your heavy load limit is 25 * 2^(.2 * Strength) Note - Both formulas give the same result for a Strength of 10. Also, round your answer to the nearest multiple of 1.25 pounds to get the exact result as shown on the encumbrance tables. Light load limit = 1/3 your heavy load limit Medium load limit = 2/3 your heavy load limit Apply appropriate multipliers for different sizes (* .75 for small bipeds or * 2 for large bipeds), body types (* 1 for small quadrupeds, * 1.5 for medium quadrupeds, & * 3 for large quadrupeds), etc. D20 Multiplication (i.e. – critical hit + spirited charge) A * (2x) + B * (3x) + C * (4x) where A = number of doublings, B = number of triplings, C = number of quadruplings, and x represents the base numbers Dice Roll Averages (# of dice) * (sides on die + 1) / 2 Experience Awards Experience Award = 300 * Effective Character Level * 2^(.5 * [Encounter Level - Effective Character Level]) / Number of party members Note – If you are level 1, treat your level as 2 for purposes of this formula. The table is a rounded version of this formula. Experience Points to Reach Next Level Total XP needed to reach a given a Level: Experience Points = (Effective Character Level - 1) * 1,000, with a minimum of 0 Total XP needed to reach next level: Experience Points = Current Character Level * 1,000 Note – This is not the XP total you need to reach the next level, it's the difference between the XP total you need for level X and level X + 1. So you need 0 XP at level 1. Example: Level 1 x 1,000 = the amount of XP you need to gain to reach level 2. At level 2, you need 2 x 1,000 = 2,000 more XP to reach level 3, for a total of 3,000 XP. Maximum Spell Level Maximum Spell Level for Bards: Max Spell Level = (Class Level + 2) / 3, with 1st-level as an exception Maximum Spell Level for Clerics/Duids/Wizards: Max Spell Level = (Class Level + 1) / 2 Maximum Spell Level for Sorcerers: Max Spell Level = Class Level / 2 Note – The spell level cannot go higher than 9 (in the case of clerics, druids, sorcerers, and wizards; nor can it go higher than 6 (in the case of bards). Movement Speed Encumbered Speed (per move action): Encumbered Speed (in feet) = (Base Speed + Speed Enhancement Bonus) * (2 / 3) Local Speed (by minute): Local Speed (in feet) = Speed * 100 Overland Movement Speed (by day): Daily Overland Movement Rate (in miles) = (Speed / 10) * 8 Overland Movement Speed (by hour): Hourly Overland Movement Rate (in miles) = Speed / 10 Apply appropriate multipliers for walking (* 1), hustling (* 2), running while encumbered (* 3), running (* 4), or sprinting (* 5 with the Run feat). Note – For tactical movement speed, round down to the nearest 5 feet. For speed in miles, do not round at all. Optimal Power Attack Optimal points of Attack Bonus to sacrifice to Power Attack: (A – B / C) / 2, where A is your chances of hitting out of 20 (w/o Power Attack), B is your average damage (w/o Power Attack), and C is the number of points of extra damage you get from Power Attack for every point of attack bonus you give up Note – The result does not always hold true for scenarios with lots of miscellaneous factors. This formula is best used for a single standard attack. Total Feats By Level (excluding bonus feats) Total feats = (Hit Dice / 3) + 1 Total Skill Points by Level (Class Level + 3) * (class skill points + Intelligence modifier [+ 1 if human]) ...Bob Loblaw, CryoSilver, Jayr, JulesCARV, Lord Gwydion, pres man, Raven Dark, and The Hive Custodian. Honorable mention goes out to Tempest Stormwind (who inspired this thread) and to Seeker95 (whose commentary will always be valued in my threads). Thank you all for your kind contributions. |
| CryoSilver04-09-06, 06:28 PM | Base Attack bonus As fighter: HD*1 As cleric: HD*.75, rounded down As wizard: HD*.5, rounded down Feat total: HD/3 (rounded down) + 1 Multipliers: a(2x)+b(3x)+c(4x) where a=number of doublings, b=number of triplings and c=number of quadruplings, and x=base numbers. |
| Jayr04-09-06, 06:30 PM | Total Skill Points = (LEVEL+3)(Class skill points + Int mod [+1 if human]) Good Base Save = (LEVEL/2)+2 Poor Base Save = LEVEL/3 Dice Average = (# of dice)(sides on die+1)/2 Max Spell Level for Prepared Spellcasters = (LEVEL+1)/2 Max Spell Level for Spontaneous Spellcasters = LEVEL/2 Max Spell Level for Bards = (LEVEL+2)/3, with 1st-level as an exception As always, round the final result down. |
| Seeker9504-09-06, 06:47 PM | This is going to be a thread worth re-visiting. :D |
| JulesCARV04-09-06, 07:09 PM | Total XP minimum for given level = 500 * level * (level - 1) |
| The Hive Custodian04-09-06, 07:14 PM | Bonus spells from high ability score: 1 + 0.25 * (ability modifier - spell level), rounding down, minimum 0. Bonus power points from high ability score: 0.5 * ability modifier * class level, rounding down. Optimal number of points of attack bonus to sacrifice to Power Attack: (A - B/C) / 2, where A is your chances of hitting out of 20 (without Power Attack), B is your average damage (without Power Attack) and C is the number of points of extra damage you get from Power Attack for every point of attack bonus you give up. This does not hold exactly for all situations, but should be fairly accurate. |
| Lord Gwydion04-09-06, 07:48 PM | Amount of Experience Points a character needs to accrue over the course of a level to reach the next level is equal to Current Character Level x 1000 xp. (Note--this is not the XP total you need to reach the next level, it's the difference between the XP total you need for level X and level X+1. So you need 0xp at level 1, level 1 x 1000= the amount of XP you need to gain to reach level 2. At level 2, you need 2 x 1000 = 2000 MORE XP to reach level 3, for a total of 3000 XP). |
| CryoSilver04-09-06, 07:54 PM | I've been looking at carrying capacities and trying to find a pattern, but after 6 layers, I have yet to locate one. |
| Raven Dark04-09-06, 08:04 PM | I've been looking at carrying capacities and trying to find a pattern, but after 6 layers, I have yet to locate one. Good luck with that. Maybe you should check out the Rules of the Game articles. I remember they discussed carrying capacity in great detail a while ago. Maybe that will help...or maybe it will just confuse you further... :P |
| CryoSilver04-09-06, 08:10 PM | I'm at 12 layers; no pattern |
| The Hive Custodian04-09-06, 08:18 PM | Good luck with that. Maybe you should check out the Rules of the Game articles. I remember they discussed carrying capacity in great detail a while ago. Maybe that will help...or maybe it will just confuse you further... :P Ooh! Ooh! Pick me! Carrying Capacity (for a human): If your Strength score is 10 or less, your heavy load limit is 10 lbs. * Strength. If your Strength score is 10 or greater, your heavy load limit is 25 lbs. * 2^(0.2 * Strength). (Both formulas give the same result for a Strength of 10.) Your light load limit is 1/3 your heavy load limit. Your medium load limit is 2/3 your heavy load limit. Apply appropriate multipliers for different sizes, body types, etc. This does not match the table exactly. The table is a rounded version of this formula. |
| Raven Dark04-09-06, 08:25 PM | This does not match the table exactly. The table is a rounded version of this formula. *Picked* Is it rounded up or down though? That can make a big differance. Also, if the RotG article is to be believed, you don't really round anything. |
| The Hive Custodian04-09-06, 08:39 PM | Strength Table Formula Difference 10 100 100 0% 11 115 114.870 -0.113% 12 130 131.950 +1.501% 13 150 151.572 +1.048% 14 175 174.110 -0.509% +5 x2 x2 same% So it's rounded up in some cases, and down in others. The table is based on this formula; it's just rounded to look prettier. |
| Raven Dark04-09-06, 08:45 PM | So it's rounded up in some cases, and down in others. The table is based on this formula; it's just rounded to look prettier. From the table you presented, it looks as though you are supposed to round to the nearest multiple of 5. Would you do some more math for me and see if my statement holds up? |
| The Hive Custodian04-09-06, 09:10 PM | If you want to duplicate the table exactly, round to the nearest multiple of 1.25 lbs. * 2^[0.2 * Strength], where [] denotes the floor function, i.e., the greatest integer less than or equal to whatever is contained in the brackets. So you round to the nearest 5 lbs. for a Strength of 11-14, to the nearest 10 lbs. for a Strength of 16-19, to the nearest 20 lbs. for a Strength of 21-24, and so on, doubling the nearest increment you round to every time you add 5 points of Strength. |
| Tempest Stormwind04-09-06, 09:19 PM | I should just point out that I was the poster described in the thread opener here, and those are direct copies of two of the three examples I cited. It amazed me how people still thought this was like second edition, where it was faster to look on tables buried six books deep than to do the math in the first place. The other example was bonus psionic power points, which is (Manifester Level for that class * Key Ability Mod for that class * 0.5), added across all your manifesting classes. Hive Guardian already posted that one, though -- the only thing I need to clarify here is that it is, in fact, pooled from all classes. I mentioned before that I hadn't really looked at the main thing I hadn't statted out (namely, bonus spells, since I never play Vancian casters and hate the mechanics with a passion), but I'm impressed that someone worked it out. I'd reached the same result on Carrying Capacity as well. At least this isn't a "mathematical Gordian knot". And I do hope I'm not the only one who gets the reference. |
| The Hive Custodian04-09-06, 10:45 PM | Unfortunately, I can't say I get the reference. I do, however, have a formula for XP gained from an encounter: The XP you gain for an encounter is equal to 300 * your level * 2^(0.5 * (EL - your level)) / # of people in your party. If you are level 1, treat your level as 2 for purposes of this formula. Again, the table is a rounded version of this formula. |
| Seeker9504-09-06, 10:48 PM | At least this isn't a "mathematical Gordian knot". And I do hope I'm not the only one who gets the reference.Gord was that rogue in the Gygax novel series back in the old days in Greyhawk, right? :P |
| Tempest Stormwind04-09-06, 11:44 PM | The Gordian Knot is a (possibly entirely) mythical construct, in that it was a knot tied so complex that whoever could untie it was prophesized to be the king of Asia. It's said that Alexander the Great took a brief look at it and then promptly slashed it in two with his sword. It's been taken to mean "something so complex that no one but the amazing can figure it out." Or something similar; accounts vary. The line I cited was half of an 8-bit Theater quote from Thief, responding to Red Mage's preference of Third Edition: "It's just not right. Calculating THAC0 should be a mathematical Gordian knot! It's part of a secret plot to ward off newbies." This isn't on the site anymore, but used to be a random splash banner for it years ago. |
| pres_man04-10-06, 12:29 AM | Total XP minimum for given level = 500 * level * (level - 1) An equivalent formula, but one I think is easier (using 1000 instead of 500). Total XP minimum for a given level = (1/2)(level)(level-1)(1000) So the xp needed for 10th level = (1/2)(10)(9)(1000) = (5)(9)(1000) = 45(1000) = 45000 Note: either the level or the level-1 will always be even so multiplying by 1/2 will always be fairly easy. So the xp needed for 11th level = (1/2)(11)(10)(1000) = (11)(5)(1000) = 55(1000) = 55000 |
| Raven Dark04-10-06, 11:30 PM | Whoah! I just got a serious case of gooseBUMPs! :bump: |
| Bob Loblaw04-11-06, 01:11 AM | I found this posted on the boards a while ago. It's all Excel formulas: MATH FORMULAS FOR D&D A compilation of important formulas derived from d20 System sources. Copyright © 2003 Daniel R. Collins. Ability Modifers modifier = ability / 2 - 5 Division is rounded down. Ability should be 0 or greater. (Note this is equivalent to modifier = (ability – 10) / 2 , round down.) Bonus Spells bonus = (ability – (spellLevel + 1) * 2) / 8 Division is rounded down, to 0 minimum. 0-level spells receive no bonuses. If the ability is less than 10+spellLevel, no spells of that level can be cast. Ability should be 0 or greater. SpellLevel should be between 1 and 9. Base Attack Bonus goodAttacks = classLevel * 1 normAttacks = classLevel * 3 / 4 poorAttacks = classLevel * 1 / 2 Division is rounded down. Use the first category for Barbarians, Fighters, Paladins, Rangers, Warriors, etc. Use the last category for Adepts, Commoners, Sorcerers, Wizards, etc. ClassLevel should be greater than 0. Saving Throws goodSave = classLevel / 2 + 2 poorSave = classLevel / 3 Division is rounded down. ClassLevel should be greater than 0. Skill Max Ranks inClassMax = characterLevel + 3 crossClassMax = (characterLevel + 3) / 2 Division is not rounded. CharacterLevel should be greater than 0. Spell Cost cost = spellLevel * casterLevel * 10 0-level spells count as ½ spell level. SpellLevel should be between 1 and 9. CasterLevel should be greater than 0. Treasure and Character Wealth Neither the treasure tables, nor NPC or PC wealth tables, appear to follow a regular formula. Speed encumberedSpeed = baseSpeed * 2 / 3 Division is rounded to the nearest multiple of 5. BaseSpeed should be greater than 0. Encumbrance if strength <=; 10, then: maxLoad = strength * 10 if strength > 10, then: maxLoad = 1.1487 ^ (strength - 10) * 100 Rounding is done to the nearest multiple of 5, 10, 20, or 40 (in steps of 5 strength). Other modifiers may be made per the d20 System for character size, number of legs, etc. Light load is 1/3 the max load; medium load is 2/3 the max load (round down). (Note: 1.1487 approximates of the tenth root of 4.) Strength should be greater than 0. Movement movePerHour = speed / 10 movePerDay = speed / 10 * 8 Terrain modifiers may apply to these figures. Speed should be greater than 0. Here's my Excel formula for converting total XP to Level: FLOOR((1+SQRT(1+XP/125))/2,1) For example, if you have 11952 XP, what level are you at? If you plug it into the formula, you'll get around 5.4, or Level 5 after the floor. Hope these are useful. I've been enjoying them. |
| Raven Dark06-17-06, 01:28 AM | :bump: |
| Uncle Meat06-17-06, 02:39 AM | Hear hear! This thread rocks. |
| Raven Dark06-17-06, 12:34 PM | Does anybody know the formulas for determining the maximum spell level of paladins and rangers? :confused: We seem to have all of the other spellcasting classes so far. |
| Ske06-17-06, 12:37 PM | Middleage is half venerable and old is three quarters of venerable. Of the PHB-races it's rounded up, except half-elf which is rounded down. It's an easy one, but all the good ones were taken (that I could think of at least). |
| Ranger REG06-20-06, 10:40 PM | I'm surprised this thread does not warrant a sticky. :nonono: |
| PortapottyPunk06-21-06, 03:40 AM | This thread is great...now all I need to do is memorize what all the spells do... *Head explodes* |
| Magocrat01-09-07, 02:22 PM | Because Tempest Stormwind participated in this thread, I'm surprised that this one hasn't come up yet: Bonus Power Points = key ability modifier x manifester level x .5 Also, it might be a good idea to note that the carrying capacity is in pounds, especially for those of us who didn't grow up with the imperial measuring system. :rolleyes: |
| Tempest Stormwind01-09-07, 02:51 PM | Because Tempest Stormwind participated in this thread, I'm surprised that this one hasn't come up yet: Bonus Power Points = key ability modifier x manifester level x .5 Umm.... ...The other example was bonus psionic power points, which is (Manifester Level for that class * Key Ability Mod for that class * 0.5), added across all your manifesting classes. Hive Guardian already posted that one, though -- the only thing I need to clarify here is that it is, in fact, pooled from all classes.;) |
| Kevtar01-09-07, 04:42 PM | How about algebraic formulas that can be used in an encounter? (i.e. Pythagoras theorem for hitting an orc on a 20' hilltop that is 50' away). Personally, I would love to see Time/Distance formulas and formulas regarding volume (i.e. a pool leaks 1 liter/round, and is filled by a hose adding x liters/round. How long before it is drained?) I think a lot of these would be great for the game I DM since I DM for my sons and their teen-age friends. Algebraic word problems in D&D; I am the most evil DM in the world! Mua ha ha ha ha! ;) |
| Tolby02-04-07, 07:11 PM | The pool leak problem is not a a algrebraic question. It is a differential equation problem. Requires calculus to figure out. |
| Tyler Do'Urden02-04-07, 08:22 PM | Minimum Save DC = 10 + (spell level x 1.5), rounded down Hexblade/paladin/ranger spells are not consistently tied to their caster level or their class level, so there's no easy formula for it. Just use the table; it's small. |
| boozerker02-05-07, 07:03 PM | Maybe include a explanation of certain symbols (http://mathforum.org/library/drmath/view/57226.html) for us non-math geeks :) |
| questionc02-06-07, 02:46 AM | The treasure values per encounter appear to be... T(1)=300 T(2)=600 T(3)=900 T(4)=1200 T(n)=T(n - 1) * 1.3 Rounded off, of course. Starting equipment for NPCs above first level appears to be Previous Level's Starting equipment + Treasure Values Per Encounter * 3 Except, the treasure values seriously tank at level 6 and 13 for some reason. I get the feeling this table was originally according to formula, but later manually modified. |
| Azar_of_Faerun02-06-07, 02:52 AM | Logic + D&D = Lolgic |
| Sajek02-06-07, 01:06 PM | How the pythagorean theorem works: A goblin is on a tower 150 feet high and 100 feet away from you. How far is he really? You square (multiply by themself) both distances, add them together, and find the square root of your new number. 100x100=10000, 150x150=22500. 22500+10000=32500, square root of 32500 is about 180 feet. |
| CroydThoth02-23-07, 01:04 AM | D20 Multiplication (i.e. – critical hit + spirited charge) A * (2x) + B * (3x) + C * (4x) where A = number of doublings, B = number of triplings, C = number of quadruplings, and x represents the base numbers. This is wrong; try it with 2 doublings and you get 2 * (2x), or 4x, but 2 doublings is a tripling according to the SRD. The correct formula is (1+A+2B+3C)x. (If you have bigger multipliers to combine, you keep on in the obvious way.) |
| pres_man02-23-07, 01:39 AM | The pool leak problem is not a a algrebraic question. It is a differential equation problem. Requires calculus to figure out. Depends on how it is set up. There are problems like that in algebra courses. |
| Always-Late02-23-07, 03:58 AM | Logic + D&D = LolgicHave you been to the threads where people discuss theoretical [p]hysics as applys to D&D? |
| LonePaladin03-20-07, 06:24 PM | I just made a little Excel spreadsheet to handle the math regarding carrying capacities, I'll be prettying it up later and incorporating all the modifiers (like size, quadruped, etc.). Once it's done, I'll repost here and let everyone clamor for a copy. With my work on HeroForge, I had to figure out a LOT of those formulas on my own, and it just never occurred to me that you guys on the message boards might actually WANT to see the formulas behind the game. So, it all got added into the program, made to work invisibly. What're the odds? If there is anything that isn't on the first page and is obviously formulaic, point it out to me and I'll open it up to expose the gears. |
| draco111903-20-07, 06:55 PM | One more: In order to find the TOTAL XP of a level X creature (minimum for that level), the formula is [(X-1)!] x 1,000. |
| pres_man03-20-07, 08:10 PM | One more: In order to find the TOTAL XP of a level X creature (minimum for that level), the formula is [(X-1)!] x 1,000. I think that is incorrect. Using 5th level and your formula we get: (5-1)!*1000 = 4!*1000 = 24000 Yet for 5th level you only need 10000. An accurate formula would be 0.5(X)(X-1)*1000 For 5th level we would get: 0.5(5)(4)*1000 = 10*1000 = 10000 |
| draco111903-21-07, 12:48 AM | I think that is incorrect. Using 5th level and your formula we get: (5-1)!*1000 = 4!*1000 = 24000 Yet for 5th level you only need 10000. An accurate formula would be 0.5(X)(X-1)*1000 For 5th level we would get: 0.5(5)(4)*1000 = 10*1000 = 10000 Urg. You're right. I was thinking of "!=+" instead of "!=x". Unfortunately, yours doesn't work, either. Think about level 2 with your formula: 0.5x2x1x1,000=1,500 |
| Solaris03-21-07, 12:51 AM | 0.5x2x1x1,000=1,500 Stop trying to do math. |
| Kevtar03-21-07, 09:00 AM | Urg. You're right. I was thinking of "!=+" instead of "!=x". Unfortunately, yours doesn't work, either. Think about level 2 with your formula: 0.5x2x1x1,000=1,500 Um, I'm no math genius by any stretch of the imagination, but I think that .5x2x1x1000 = 1,000 .5 x2 = 1 1x1000 = 1000 Probably just a simple mistake. That is one is one of the causes of angst around my gaming table - PERFORMANCE MATH. I have a bunch of teenagers who are regularly in situations where one of them is raging, fighting defensively, with combat expertise, power attack, dodge, haste, and a +3 shocking burst dwarven waraxe and they roll a crit. (that's an example, not a real situation. I'm not sure if you can fight defensively while raging ;)) The confusion when they try to calculate their bonuses to hit or damage is hilarious. |
| draco111903-21-07, 01:20 PM | Stop trying to do math. Yessir... :allalone: |
| AT-AT Assault05-30-07, 02:44 PM | For more Algebraic Equivalency: Another formula for minimum XP required for a specific level: 500x2 - 500x , where x is the effective character level. Much simpler IMO. |
| pres_man05-30-07, 02:47 PM | For more Algebraic Equivalency: Another formula for minimum XP required for a specific level: 500x2 - 500x , where x is the effective character level. Much simpler IMO. 500x2 - 500x = 500x(x - 1) = 0.5(1000)x(x-1) = 0.5(X)(X-1)*1000 same formula just multiplied out. |
| AT-AT Assault05-30-07, 02:50 PM | 500x2 - 500x = 500x(x - 1) = 0.5(1000)x(x-1) = 0.5(X)(X-1)*1000 same formula just multiplied out.Hence my use of "Algebraic Equivalency". I just find my formula easier, less room for multiplication error (and far easier to enter into my handy dandy graphing calculator ;) ). |
| pres_man05-31-07, 02:39 PM | Hence my use of "Algebraic Equivalency". I just find my formula easier, less room for multiplication error (and far easier to enter into my handy dandy graphing calculator ;) ). Yeah, I find the other version easier when doing it by hand since either x or x-1 will have to be even thus taking half of it is easier. Example: xp for 10th level (1/2)(10)(9)(1000) = 5(9)(1000)=45(1000)=45000 xp for 13th level (1/2)(12)(13)(1000) = 6(13)(1000) = 78(1000) = 78000 |
| AT-AT Assault05-31-07, 02:54 PM | Yeah, I find the other version easier when doing it by hand since either x or x-1 will have to be even thus taking half of it is easier. Example: xp for 10th level (1/2)(10)(9)(1000) = 5(9)(1000)=45(1000)=45000 xp for 13th level (1/2)(12)(13)(1000) = 6(13)(1000) = 78(1000) = 78000I guess Im just used to quadratic equations and such. Though for hand work I guess factoring it would be easier: (500x)(x-1). |
| JulesCARV05-31-07, 06:04 PM | On carrying capacity... For strength less than or equal to 10: heavy carrying capacity = strength * 10. For strength greater than or equal to 10: heavy carrying capacity = 25*(2^(strength/5)), rounded a bit so that it ends in a pretty number. Or, if you prefer something uglier, 25*(1.148698355^strength). |
| VrecknidjX05-31-07, 09:35 PM | For a long time I used something like this to calculate each PCs experience from an encounter. In FR, there was a system to hand out different XP based on what level each PC was. I converted it all the way down to how much XP each character already had. =(300*(((SQRT(250000+2000*(previousXP))+ 500))/1000*(10/(numberofPCs))^(((CR)-(((SQRT(250000+2000*(previousXP)))+500)/1000))/(numberof PCs))*(# of creatures at that CR) After a while though, I just went back to using the DMG. Dave |
| raalynthslair06-10-07, 09:11 PM | Attribute bonuses are mathematically based too: ([Attribute Score]/2)-5 = Bonus/Penalty. And of course, you round down (for the odd number Att. Scores). Here are two examples: 16/2 = 8 - 5 = +3 6/2 = 3 - 5 = -2 |
| Millenia08-28-07, 11:03 PM | I figured out the formula for the total experience points necessary for any level, without needing the whole "sum of whatever" thing. When L equals the level wanted, one gets: 500*L^2 - 500*L Where L^2 is L to the second power. For instance: Experience needed for level 1: 500*1^2 - 500*1 = 0 Experience needed for level 2: 500*2^2 - 500*2 500*4 - 1,000 2,000 - 1,000 = 1,000 Experience needed for level 3: 500*3^2 - 500*3 500 *9 - 15,00 4,500 - 1,500 = 3000 Experience needed for level 20: 500*20^2 - 500*20 500*400 - 10,000 200,000 - 10,000 = 190,000 |
| weasel0509-04-07, 10:13 PM | :bump: |
| Knitsuge09-26-07, 02:43 AM | :bump: No wonder people think were nerds! We are! :cheer: (And I'm loving every minute of it!) |
| Slash_Z11-25-07, 03:50 PM | :bow: |
| eamon11-26-07, 10:06 AM | Unfortunately, the Character wealth per level table isn't an exact formula, but it can be approximated by wealth ~= 915* (level-1) * 1.22^(level-1) (this overestimates the 1st level gold by quite a bit, but is otherwise quite OK) Of course, characters start out with 0 gold (pretty much), 0 XP but .... 1 level? That's just unhandy, so let's consider your level zero-based Z: Z = D&D Level - 1 Then wealth ~=915 * Z * 1.22^Z This can be interesting when combined with xp = 500*level*(level-1) = 500 *Z*(Z+1) i.e. Z = (sqrt(xp/125 + 1) - 1)/2 We can just the XP->level formula into the level -> wealth formula... wealth ~= 915 * (sqrt(xp/125 + 1) - 1)/2 * 1.22 ^ ((sqrt(xp/125 + 1) - 1)/2) = 457.5 / sqrt(1.22) * (sqrt(xp/125 + 1) - 1) * sqrt(1.22) ^ sqrt(xp/125 + 1) And now you know about how much character wealth you should have, based on your current XP total ;-) |
| azirafel11-26-07, 07:07 PM | ok, * its multiplication, / its division.. what its ^ ?? |
| RavingDork11-26-07, 09:35 PM | ok, * its multiplication, / its division.. what its ^ ?? "Exponentials." "To the power of..." Thus, 5^5 = 5*5*5*5*5 = 3,125. |
| Ariakus11-29-07, 11:02 AM | Wow, I'm a huge math freak and this is the first time I've looked into this thread. I hadn't given consideration to why I would need equations for D&D, but it's awesome for creating spreadsheets. I didn't see LonePaladin's spreadsheet on here, but that's cool...I can make my own. Keep 'em coming guys and gals...I love this... |
| Tempest Stormwind11-29-07, 01:44 PM | Wow, I'm a huge math freak and this is the first time I've looked into this thread. I hadn't given consideration to why I would need equations for D&D, but it's awesome for creating spreadsheets. I didn't see LonePaladin's spreadsheet on here, but that's cool...I can make my own. Keep 'em coming guys and gals...I love this... I mostly use them for OpenRPG macroes. Ever pressed ONE button and Turn Undead works instantly, without having to cross-reference four tables? I have. That formula, by the way, accounting for those tables is: Turning check: (1d20+Cha-10+{Miscellaneous mods, i.e. mwk. holy symbol})*1/3+(Effective cleric level) = Hit dice effected (min Level-4, max Level+4). There. No table required. OpenRPG macro: <i><b>Turning Check:</b> Affect undead up to [q(1d20+!@CS_CHA@!-10+?{MiscMods})*1/3+!@CS_TURN_LEVEL@!] Hit Dice (Max [q!@CS_TURN_LEVEL@!+4]).</i><br><i><b>Turning Damage:</b> [q2d6+!@CS_CHA@!+!@CS_TURN_LEVEL@!] total Hit Dice affected.</i> This is designed to run on my custom character sheets in OpenRPG, and thus draw all the required numbers automatically except the miscellaneous modifiers. ONE click! I also used variants on these to work with the rubric method I used to compare the warblade to the barbarian. Look for yourself (http://telusplanet.net/~sdupuis/Tempest/warbladevsbarbarian.xls). |
| LordPendragon03-24-08, 09:20 AM | For your dorkitude, I humbly submit... Experience total required for X level = X * (X-1) * 500 Note that this is subtly different than the current experience formula listed on page 1. |
| Cryonax03-24-08, 09:50 AM | Note that this is subtly different than the current experience formula listed on page 1. But mathematically is identical to that formula (per the commutative (http://en.wikipedia.org/wiki/Commutativity) law of mathematics). What's the point of posting it? |
| UAMDB03-24-08, 11:01 AM | All female characters are evil, since girls are evil Given Girls take both time and money or Girls = Time * money Also given Time = Money So Girls = Money * Money or Girls = Money^2 Also Money is the root of all evil or Money = Squareroot(Evil) So Girls = Squareroot(evil)^2 Girls = Evil Just remind players this the next time they try to play a Female Paladin :) |
| LordPendragon03-24-08, 12:08 PM | But mathematically is identical to that formula (per the commutative (http://en.wikipedia.org/wiki/Commutativity) law of mathematics). What's the point of posting it? Thank you for the informative link, but I do know what commutativity is :rolleyes: The point is that the current exp formula listed on the front page only calculates the amount needed to go from one level to the next, assuming that you reset to 0 after each level and count up from there. My formula allows you to keep a running total of your exp and compare to specific benchmarks to see what level that puts you at. Admittedly, the differences in practical use aren't very much, but if we want formulas for everything in D&D then it's different enough to warrant posting. If you want to look at it another way, my formula is the summation of all the levels that can be represented by the currently posted formula. Newton told us that this is equal to n * (n+1) / 2. Using the other formula, we have (ECL - 1) * (ECL - 1 + 1) * 1000 / 2, or just (ECL) * (ECL - 1) * 500. Also, UAMDB's lemma on the relative evilness of girls is both sound and concise. |
| Nathreet03-24-08, 03:45 PM | 2 * 2 = 3 |
| pres_man03-24-08, 04:02 PM | For your dorkitude, I humbly submit... Experience total required for X level = X * (X-1) * 500 Note that this is subtly different than the current experience formula listed on page 1. Personally I prefer the version: total xp for level X = X(X-1)/2*1000 but that is because I rarely use a calculator and either X or X-1 will always be even, so easily divisible by 2, and then multiplying by 1000 is just adding three zeros. So to find the xp for 13th level: 13(12)/2*1000 13(6)*1000 = 78*1000= 78,000 To find how much xp to gain from level X-1 to X, the formula is simple: = (X-1)*1000 |
| Cryonax03-25-08, 11:20 AM | Thank you for the informative link, but I do know what commutativity is :rolleyes: You're not the only one on this list. There are probably plenty of people who don't know (or don't remember) the law. Providing cites to obscure or seldom-discussed principles is a good idea, and Wikipedia, as unreliable as it is, is a site with which everyone is familiar. Another point: one thing that annoys me is when people use knowledge as social leverage to make themselves feel smarter. It's pathetic, and I don't do that. If I reference something, I provide a cite if there's any possibility of someone getting lost. Either your ego is so great that you think everything's about you, or your ego is so frail that you interpret any attempt at education as an insult to your intelligence. Either way, I sarcastically apologize. The point is that the current exp formula listed on the front page only calculates the amount needed to go from one level to the next, assuming that you reset to 0 after each level and count up from there. My formula allows you to keep a running total of your exp and compare to specific benchmarks to see what level that puts you at. <snip> Then the formula is identical. What's changed is that you've shown it has a broader application. Fair enough. Also, UAMDB's lemma on the relative evilness of girls is both sound and concise. Agreed. I've already sent it to my regular home game group and expect to be in deep trouble when we meet this weekend. :) |
| Ariakus03-25-08, 11:28 AM | I agree, I'm not the brightest guy in the world, but far from the dumbest either. I have not received anything more than high school trig in training, but most math makes sense to me even if I've not been taught it's intricacies in college. But I do tend to lose patience with people that don't understand at least the basics and want to argue their point when they have an off the wall (or as I call it "New Math") answer. I have to say I didn't know about commutative, but when it's definition was pulled in, (even if from Wiki) it made sense, thanks for the info ;) And it's nice to see you smart folks give us dumb folks a chance :D |
| Cryonax03-25-08, 11:32 AM | And it's nice to see you smart folks give us dumb folks a chance :D Fine, just don't talk to us in public, okay? :) (BTW, knowledge <> intelligence. Do you know my middle name? No? That doesn't make you stupid, just ignorant as to that one piece of information.) |
| Ariakus03-25-08, 11:33 AM | :rofl: That's all I have to say about thaat. |
| Etarnon03-25-08, 02:47 PM | Bah. I'm all for remembering to bring my books. That way, it's a process of: things to remember: 1. Bring books. Simple. |
| LordPendragon03-25-08, 11:20 PM | Either your ego is so great that you think everything's about you, or your ego is so frail that you interpret any attempt at education as an insult to your intelligence. Either way, I sarcastically apologize. Or possibly you can't conceive of a situation in which someone thanks you for something they didn't need. I egotistically accept your sarcastic apology. Then the formula is identical. What's changed is that you've shown it has a broader application. Fair enough. Either I'm missing something, or you're making a mistake. I don't see anything identical to what I've posted, so can you quote the formula from the first post that you're talking about?? If I'm not mistaken, then this formula definitely should go in the first post, since finding the sum of a series isn't something everyone knows how to do with one formula. Also, for the reading pleasure of those who wish to know more about summations, the link is here (http://en.wikipedia.org/wiki/Evaluating_sums). Though the link is a little complicated in terms of notation, all I really wanted to show with it is that adding up all the numbers from 1 to n gives a number equal to n * (n+1) / 2. 1. Bring books. Simple. You forgot something. 2. Remember page numbers. Difficult. |
| Tempest Stormwind03-26-08, 01:03 AM | Also, for the reading pleasure of those who wish to know more about summations, the link is here (http://en.wikipedia.org/wiki/Evaluating_sums). Though the link is a little complicated in terms of notation, all I really wanted to show with it is that adding up all the numbers from 1 to n gives a number equal to n * (n+1) / 2. This, interestingly, was taught in the courts of Europe *before* algebra made its way to the west. The solution there is less generalized, of course, but it can be related very quickly in text, and the method is very similar to the derivation of that theorem. (That's why I would have described it in text: "Note that 1+the last number = 2+the second-last number = 3+the third-last number and so on. This means there are half as many pairs of numbers, that sum up to the total number of numbers +1. Expressed algebraically, this is (N/2)*(N+1), or N * (N+1) / 2." Gets your point across explicitly.) For the record, I use the formulae instead of looking through books in nearly every circumstance. As I said on page 1, this isn't second edition -- everything can be derived from very simple basic principles, and if you're good at even basic arithmetic, you can get most of it without cracking a book. Crack books for things you aren't fast at, crunch numbers on things you'd rather not cross-reference, and congratulations. Since I game using fractional base attack, it's even easier (i.e. total base attack bonus = [levels in full base attack] + [3/4 levels in 3/4 base attack] + 1/2 levels in 1/2 base attack], even if there's unusual multiclassing, such as rogue 1 / cleric 1). I also game online, using OpenRPG. I was able to set up a character node there that used autocalculation based on the formulae I'd derived -- so the player does nothing more than enter, say, what his Strength score is, and when he presses the Attack button, it calculates the total numbers for him without him having to remember anything except, say, conditional modifiers (i.e. +2 from flanking). Even if we gamed using books over OpenRPG, these formulae would come in handy there. |
| Etarnon03-26-08, 12:54 PM | I've been doing this for 31 years, so I got the page numbers memorized. When I had been doing it for a single year, I read, and re-read the DMG, and consulted the index at need, and wrote notes in my adventure on what creatures needed what Thac0, etc. There's no excuse for DMing without a book, unless you're so good you don't need it, or all your rulings are final. In those cases, you didn't need the book, which in the end is a guide, anyway. Or should be. |
| Ariakus03-26-08, 01:19 PM | I've been doing this for 31 years, so I got the page numbers memorized. When I had been doing it for a single year, I read, and re-read the DMG, and consulted the index at need, and wrote notes in my adventure on what creatures needed what Thac0, etc. There's no excuse for DMing without a book, unless you're so good you don't need it, or all your rulings are final. In those cases, you didn't need the book, which in the end is a guide, anyway. Or should be. But the 3.5 books are not 31 years old :) |
| Tempest Stormwind03-26-08, 02:19 PM | And some of us have been practicing math for so long that, rather than spend 31 years doing indexing, we find it easier to remember a handful of first principles and apply them when needed. |
| Cryonax03-26-08, 03:34 PM | Or possibly you can't conceive of a situation in which someone thanks you for something they didn't need. I egotistically accept your sarcastic apology. If he also inserts a :rolleyes:, which is labeled "roll eyes (sarcastic)," then yes, that concept is beyond me. Either I'm missing something, or you're making a mistake. I don't see anything identical to what I've posted, so can you quote the formula from the first post that you're talking about?? :banghead: For your dorkitude, I humbly submit... Experience total required for X level = X * (X-1) * 500 Note that this is subtly different than the current experience formula listed on page 1. Looking at that post from page 1 that you cited: Total XP minimum for given level = 500 * level * (level - 1) Substitute "X" for "level" and you get: X * (X-1) * 500 vs. 500 * X * (X-1) :teach: Commutativity. Identical, just with broader application (as I conceded). W^5.* QED. * "Which was what we wanted." |
| Etarnon03-26-08, 04:27 PM | But the 3.5 books are not 31 years old Quite true. Yet the game existed, Imagine. |
| Frozen Yakman03-26-08, 05:18 PM | Average Weapon Damage This is actually a very complicated formula and most people get it wrong, actually they're usually correct but they fail to state all the assumptions they make. So anyway on a given swing a weapon can do any of three damage categories: Critical Hit Damage (cd), Hit Damage (hd), and Miss Damage (md). These three categories interact with the Base Weapon Damage (bwd) in different ways based on the different kinds of damage that make up bwd which are as follows: Weapon Damage (wd) - Being the average damage of the weapons base dice plus any bonus damage not expressed in dice terms (such as Strength or weapon specialization). Bonus Damage (bd) - Being the average damage of bonus damage expressed in the terms of extra dice (such as Sneak Attack or Flaming). Burst Damage (ud) - Being the average damage of damage that only appears in a critical hit. So we have three damage constants cd = m * wd + 1 * bd + 1 * ud = m * wd + bd + ud where m = the weapon's critical multiplier hd = 1 * wd + 1 * bd + 0 * ud = wd + bd md = 0 * wd + 0 * bd + 0 * ud = 0 Next we need to define a function to tie the damage functions together which is based upon the following out comes on a hit roll: 1) Roll a miss 2) Roll a hit 3) Roll a threat but do not confirm 4) Roll a threat and confirm To figure the chance of these happening I'm going to create a term called normalized AC (NAC) where NAC = AC - attack bonus NAC has a maximum value of 20 and a minimum value of 2 thus NAC is the number you need to roll on a d20 to hit the target. So expressing the four events in terms of NAC we get 1) Roll less than NAC 2) Roll greater than NAC but less than t (where t is the minimum threat range value of the weapon, 18 for a scimitar, 19 for a longsword, 20 for an axe, etc.). 3) Roll greater than T(NAC)* and then roll less than NAC 4) Roll greater than T(NAC) and then greater than NAC * T(NAC) = Max(NAC, t) and is needed for the case when you need to roll higher on the d20 to hit the creature than the weapons threat range (i.e. needing a 19 to hit when using a Scimitar) So for two d20 rolls, d1, d2 we get the following probabilities for the given outcomes. 1) P(d1 < NAC) 2) P(t > d1 > NAC) (this is 0 when NAC > t) 3) P(T(NAC) < d1, d2 < NAC) 4) P(T(NAC) < d1, d2 > NAC) All of these probabilities are independent. Combining these probabilities with the weapon damage we get Avg Damage (NAC) = P(d1 < NAC) * md + P(t > d1 > NAC) * hd + P(T(NAC) < d1, d2 < NAC) * hd + P(T(NAC) < d1, d2 > NAC) * cd Simplifying Avg(NAC) = (P(t > d1 > NAC) + P(T(NAC) < d1, d2 < NAC)) * hd + P(T(NAC) < d1, d2 > NAC) * cd This equation gives you the average damage needed for a given number needed to hit. This is about as far as you can go unfortunately. The only way to remove NAC is to do the following: True Average = (P(NAC = 2)*Avg(2) + P(NAC = 3) * Avg(3) + ... + P(NAC = 20) * Avg(20))/19 Unfortunately P(NAC = 2) - P(NAC = 20) are unknown and not computable. |
| LordPendragon03-26-08, 08:28 PM | If he also inserts a :rolleyes:, which is labeled "roll eyes (sarcastic)," then yes, that concept is beyond me. Pshaw. I roll my eyes all the time, with no harm intended. Looking at that post from page 1 that you cited: Ah, now I see the problem. The post that I cited was the first post. The post where all the equations are supposedly listed. The equation in the post you just referred me to isn't actually in the first post (which contains all the equations). I didn't bother reading through the thread, since I assumed everything was already in that first post, and so missed the one you referred to. As a side note, wouldn't it have been easier just to link that post the first time than to actually have this argument?? |
| Ariakus03-26-08, 09:56 PM | People seem more want to prove you wrong publicly than to aid you...or so it seems on these threads. The only time anyone helps anyone else on these forums is if they outright ask for it, otherwise they take personal offense at your ignorance and feel a need to argue or insult instead of remedying the initial problem by HELPING... makes you wonder who died and left them god...I know GG died, but it doesn't leave the position open... My question is why cant you just point something out instead of attacking? Do you really feel that insecure about yourself that you need to publicly berate or attempt to belittle instead of just assisting in something you may already know? Ignorance does not=stupidity, but stupidity will certainly beget the former! |
| Cryonax03-27-08, 09:51 AM | I didn't bother reading through the thread. For a thread like this, I'd say that you should before posting. Of course, the reason for that is to avoid wasting space with useless posts, but . . . As a side note, wouldn't it have been easier just to link that post the first time than to actually have this argument?? Probably, but as Adam West says, "Stupid? Yes. Idiotic? Yes." |
| RavingDork03-27-08, 01:22 PM | Of course, the reason for that is to avoid wasting space with useless posts, but . . . Pishaw! This is the internet! There is no such thing as "finite space." :P |
| LordPendragon03-27-08, 03:57 PM | Pishaw! This is the internet! There is no such thing as "finite space." :P But the people reading this have finite brainspace, and we're wasting it with useless things. Next time they're writing an exam they'll only be able to think about the epic confrontation between the evil Cryonax and the valiant LordPendragon. Think of how many failing grades we may have just caused. |
| Decivre04-21-08, 02:09 AM | I like your Formula, Frozen Yakman, but way too much averaging. I have a much simpler formula that gets the same effect... average damage per attack. DECIVRE'S ALGEBRAIC ATTACK FORMULA First, we calculate average damage... which is... (a + ab) / 2 a = number of dice rolled per attack b = die used for attack (d6 = 6) Next, we figure basic damage (discounting criticals for now) for the attack. (a + ab) / 2 21 - c c = minimum die result to hit target for purpose of this, we will assume that a 10 will hit the target, so I shall simplify 21 - c to 11... if you wish to recalculate average damage based on a creature who is easier or harder to hit than this, then change 11 to 21 - c (a + ab) / 2 11 Now time to do crits. Since crits have a specific range, but it's always some number to 20, we shall calculate it thusly 21 - d d = lowest number in critical hit range So total average damage for a critical hit is. e(21 - d)((a + ab) / 2) 20(21 - c) e = crit multiplier This of course only calculates damage on critical hits, completely ignoring any other damage. Combining total damage the complete formula will be... ((a + ab) / 42 - 2c)) + ((e - 1)(21 - d)(a + ab) / (840 - 40c)) a = number of dice rolled in damage roll b = type of damage die c = minimum die roll on d20 to hit d = minimum die roll on d20 to crit e = crit multiplier This is my favorite version of the formula. If you like to cross multiply because you think it'll make things simpler, here's what it'll look like if you do so. ((a + ab) / 42 - 2c)) + ((ad+abd+21abe+21ae-21a-21ab-abde-ade) / (840 - 40c)) Yeah, I think this one sucks too.... |
| Cryonax04-21-08, 03:54 PM | But the people reading this have finite brainspace, and we're wasting it with useless things. Next time they're writing an exam they'll only be able to think about the epic confrontation between the evil Cryonax and the valiant LordPendragon. Think of how many failing grades we may have just caused. As the "evil" one, that makes me happy. :) |
| Crashy7505-12-08, 12:05 AM | The Gordian Knot is a (possibly entirely) mythical construct, in that it was a knot tied so complex that whoever could untie it was prophesized to be the king of Asia. It's said that Alexander the Great took a brief look at it and then promptly slashed it in two with his sword. It's been taken to mean "something so complex that no one but the amazing can figure it out." Or something similar; accounts vary. ... I had assumed that it meant something like, "something that seems complex but is really pretty simple." (yeah, from two years ago, but I just found this thread) |
| Varble05-31-08, 05:17 PM | I have been tinkering with a complete formula for max ranks per skill for a while, and I finally figured it out: All levels + 3 - (all cross-class levels)/2 EDIT: Is what I would say if it was correct. See 5 posts down for explanation. |
| RavingDork05-31-08, 07:52 PM | I have been tinkering with a complete formula for max ranks per skill for a while, and I finally figured it out: All levels + 3 - (all cross-class levels)/2 Thanks for the contribution. I couldn't get the formula to work for me though. I'm thinking I just misinterpeted your post though. :embarrass Could you please show us some examples of the formula in action? :confused: |
| Varble05-31-08, 08:36 PM | Sorry, I read the book and found out I was incorrect. Hiding my mishap in a spoiler box. What basically happens with this formula is count all levels as normal class levels, i.e. the standard "Level+3" formula. Then it subtracts half of each cross-class level from the total, so in the end each cross-class level only counts for half(counted as a full level initially, then half is subtracted in the latter part). Take a 7th level Rogue/5th level Fighter/2nd level Bard. Besides the fact that the character is rather silly, let's run a few skills through the formula: Skill: Disable Device Rogue: Class Fighter: Cross-class Bard: Cross-class So Fighter and Bard are cross-class, meaning 5+2=7 cross-class levels. (7Rogue+5Fighter+2Bard) +3 - (5Fighter+2Bard)/2 7+5+2+3 - (7)/2 17-3.5 13.5 max ranks This works if all skills are cross-class: Skill: Heal Rogue: cross-class Fighter: cross-class Bard: cross-class (7Rogue+5Fighter+2Bard) +3 -(7Rogue+5Fighter+2Bard)/2 7+5+2+3 -(7+5+2)/2 17-8.5 8.5 max ranks Or if all skills are class: Skill: Climb Rogue: class Fighter: class Bard: class (7Rogue+5Fighter+2Bard) +3 -(0)/2 7+5+2+3 - 0 17 max ranks I hope this clears it up for ya. On a separate note, I had an idea. We all (seem) to like excel. Some formulas here only work in excel, or are way too complicated to work out by hand. I was thinking someone could attach an excel sheet with their formulas all worked out and prettified to this thread. Then anyone wanting to add onto that worksheet downloads it, adds worksheet page(s) to it, then PMs it to the original poster who then adds credits to a title page in the file and re-posts it here. For those who want to avoid headaches, I have Xp per level and Encumbrance already worked out in excel. |
| duboisjf06-05-08, 04:46 PM | Sometime ago I've come up with a formule for the DC of a jump that have a vertical and a horizontal component (with a running start) It only correct for jump with horizontal distance that are twice the vertical distance or more X is the horizontal distance Y is the vertical distance Formula is : DC = (x*x) / (x-y) Example : - Standard long jump of 40ft : (40*40) / (40-0) = 40 (same as rule for long jump) - A jump that is 20 ft long and 10 ft high (in fact, this jump is the middle point of a 40 ft long jump because maximum height is 1/4 the distance) : (20*20)/(20-10) = DC40 ... It's ok because it's the same jump used in the first example but stopped at middle point. - A jump that is 40 ft and 5 ft high : (40*40)/(40-5) = 45.7 rounded to DC46 Where it becomes interresting is for stuff like jumping down a cliff. Let's see ... My character is at the top of a cliff of 20 ft and want to jump a horizontal distance of 40 ft DC = (40*40) / (40 - -20) = 26.6 rounded to 27 * Please note that 20ft in this case is negative because the character ends up lower than it started. Everything woks fine : It is easier to jump 40 ft long when you start from a place that is 20ft higher. Interresting stuff too ... When you divide the DC by 4 and you add the strating height you obtain the maximum vertical distance reached by the jump In the latest example: starting point at 20 ft high DC of 27 Maximum height is 20 + 27/4 = 27 ft high. |
| Amon_V06-05-08, 07:22 PM | Here are some I play with: I'm not sure they appear in any books, but here they are. Leveling Up is supposed to represent a 41% increase in power. Basically: (1.41)^Level - 1 This means that a 3rd Level Character is roughly twice as powerful as a 1st level one, matching the description of CR as intended. Maximum Skill Check: Maximum Skill Check=10 + 3 + 2(Level) This is the highest I can ever expect a PC or NPC to make as a function of Level. At 10th Level, the most someone should be able to do, with stats, feats, skills and skill boosting items would therefore be about DC 33 on average. Minimum HP for Monsters: Minimum HP =5 x PC's Average ECL + 1/2 (Average ECL^2): Monsters without this much HP can be expected to be taken down with a single round of fighting, assuming they have no special defenses like High AC or High SR for their level. This gives 6 HP for 1st level, 100 HP for 10th Level, and 300 HP for 20th Level. ECL Calibration: By definition, an at CR encounter should consume 20% of the Party's resources. And a Match CR +2 above the party should consume 80% of the party's resources. You can calibrate ECL by determining how many resources were consumed by the Party (Spells, Magic Items, Potions, HP, Etc) and out of their possible amount expendable. If you had a CR 8 battle but the Party expended 20% of its resources even though they are 4 7th level characters, your Party is probably in excess of its power by level. |
| Varble07-04-08, 03:03 AM | After reading the book thoroughly once more last night I found the very important paragraph in the Skills chapter that nixes my "All levels + 3 - (all cross-class levels)/2" formula. That paragraph illuminated to me that, per skill, if you have one Class that is class skilled, all your CL's are counted as a full skill-classed Class. (I wish they'd come up with a different name for class-skill. It's very confusing when explaining.) The developers probably put that paragraph in there to avoid the headache that I put myself through. :P |