Post/Author/DateTime	Post
tsuyoshikentsu 10-15-06, 02:38 AM	(Cross-posted from my blog.) "Consider - One: Probability is a factor which operates within natural forces. Two: Probability is not operating as a factor. Three: We are now held within un-, sub-, or supernatural forces." --Guildenstern, Rosencrantz & Guildenstern are Dead So I was reading the bell-curve rolling rules (here) (http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm), and I had a thought: How good would range multipliers be under them? For instance, let's take everyone's favorite, the Disciple of Dispater with attached Improved Critical. The table in UA seems to imply that you multiply the old threat range and then calculate the new one. All right, let's try the quadrupled threat range of a scimitar: 9-20/x2, a 60% probability. We then run the handy Harlequin Jones Dice Probability Calculator (http://www.anwu.org/games/dice_calc.html) for 3d6. Then, we start adding results until we hit .6 or more. The exact chance of hitting a 14-18 is .16204, which means that 18-20 weapons got a boost and 17-20 weapons got a hit, as they say. 20 by itself takes the hit they indicate as well... but what they DON'T say is that 19-20 is only .0925, or 9.25% -- a hit of .75%, which in bell curve rolling is a heck of a lot. Shafting 19-20 even further is the fact that taking Improved Critical only adds less than 7% to your threat range, as opposed to the previous 10%. Weapons with a range of 20 (Greataxe, for example) are actually .0463, meaning that they too take a hit to IC strength -- down from +5% to +.0462, or 4.6%. This is a better increase than 19-20 gets. The percentage increase for 18-20 goes down as well, by a little over 5%. (.05279, to be exact.) But here's the thing: even with this drop, you're still at a net advantage over normal rolling. This isn't true of any other range... and, as we get closer and closer to the top of the bell curve, this is more and more and more of an advantage. Now, let's get back to the DoD. He has a threat percentile of 60. His cap is either going to be 11-18 (.5) or 10-18 (.625). Which one do we choose? Well, the obvious analouges here are 18-20 and 17-20. 18-20 has a threat percentile of 15%, whereas 17-20 has a threat percentile of 20%. A 14-20 has a .16204 chance of occuring, while a 13-20 has a .25926. A 15-18 occurs .0925. So, we find the deviation from each to find how WotC rounded. .0925 - .15 = -.0575 .16204 - .15 = .01204 .16204 - .20 = -.03796 .25926 - .20 = .05926 So in both cases the plan was to go with the least deviation from the norm. This means that a converted 9-20 threat range is .625, or 10-18. Now, stop a minute. Think about that. In terms of probability, that's a bit of an upgrade -- 2.5%. But in practical terms, as mentioned, rolls will cluster around 10 and 11. This means that you're going to be threatening a good deal more than under the other system -- meaning that a Disciple with a large STR score, a greatpick and someone willing to give him lots of burst enhancements is going to cause a great deal of trouble. It also means that he'll be critting more than "equivalent builds" under the old system. For example, a Dervish with a threat range of 15-20 will critical for about the same amount as a DoD, since his Dervish Dance gives him twice as many attacks. (Usually more due to TWF and all, but let's say twice as many for the sake of comparison.) However, in bell urve rolling the DoD takes a jump in power, as you'll probably roll a lot closer 10 and 11 -- inside the DoD's threat range, but not the Dervish's. (This is reflected in terms of their probability; in bell curve, a Dervish has about a 25% chance of critting, but the Disciple has 62.5% -- a diference of 37.% as compared to the original difference of 30%.) What does all this mean, though? Well, in the bigger picture, it makes bell curve rolling a much better choice for crit range specialists. That's nice, because it also decreases CL checks and increases general sucess rates on saving throws -- meaning that the environment is more melee-friendly. The end result for me is that I think I'm going to be trying it sometime soon -- if for no other reason than my local Walgreens sells lighters with 3d6 in 'em. :D
Rass Frostwhisper 10-15-06, 02:45 AM	Threats don't always result in criticals, or, even hits for that matter. What good is a 9-20 threat range if you only hit on a 18, 19, or 20? ... just saying.
X-Codes 10-15-06, 02:50 AM	In terms of probability, that's a bit of an upgrade -- 2.5%. But in practical terms, as mentioned, rolls will cluster around 10 and 11. This means that you're going to be threatening a good deal more than under the other system -- meaning that a Disciple with a large STR score, a greatpick and someone willing to give him lots of burst enhancements is going to cause a great deal of trouble. It also means that he'll be critting more than "equivalent builds" under the old system. You're thinking too much. Yes, rolls cluster around 10 and 11 and, at the same time, in terms of probability theres still only a 62.5% chance of rolling a 10 or higher with 3d6. This is already taking into consdieration the clustering of rolls.
tsuyoshikentsu 10-15-06, 03:11 AM	You're thinking too much. Yes, rolls cluster around 10 and 11 and, at the same time, in terms of probability theres still only a 62.5% chance of rolling a 10 or higher with 3d6. This is already taking into consdieration the clustering of rolls.eh. Even so, I think the fact that 18-20 weapons (and multiples thereof) gain in a system where everything else loses is still worth noting.
oontyex 10-15-06, 04:13 AM	Threats don't always result in criticals, or, even hits for that matter. What good is a 9-20 threat range if you only hit on a 18, 19, or 20? ... just saying. true i did a similar thing when i was picking between the 19-20/x2 and the 20/x3 weapon (compared the probabiility curves of damage from a heavy crossbow, composite longbow and great crossbow), as the chance to hit is totally situational, damage,average damage etc become functions of your chance to hit: based on: average damage = average damage from confirmed crit x chance to successfully score and confirma crit + average damage from a normal hit x chance to do a normal hit (chance to do a nomral hit is either a hit- noncrit or a nonconfirmed crit) let CH = chance to hit for the given situation CC = chance to crit D = average base damage M = crit multiplyer Average damage = av damage from non crit = roll between CH and CC = CH- CC x D |1| ------ CH ---[ here]--- CC ---|20| + nonconfirmed crit = CC . (1-CH) . D |1| --- [roll here when trying to confirm]---CH-----|20| = (CH -CC)D + CC.(1-CH).D = CH.D -CC.D +CC.D -CC.CH.D av damage from confirmed crit = CC.CH.M.D so, av damage= CH.D -CC.D +CC.D -CC.CH.D +CC.CH.M.D =CH.D -CC.CH.D +CC.CH.M.D = CH.D + CC.CH.D.(M-1) = CH [D +CC.D.(M-1)] = f(CH) as everything else is a constant for the given weapon
tsuyoshikentsu 10-15-06, 11:54 AM	Threats don't always result in criticals, or, even hits for that matter. What good is a 9-20 threat range if you only hit on a 18, 19, or 20? ... just saying.Because every DM I've ever played with has treated a threat as an autohit, and merely normal damage if it fails. Not even as a houserule -- most of them honestl thought it worked that way.
Rathmun 10-16-06, 04:27 PM	If that were the way that things actually worked, weapons with wide crit ranges would be so far beyond broken it wouldn't even be funny. there is a weapon somewhere (can't remember exactly where) that has a 17-20x2, slap keen on that and it has 13-20x2. If a threat were an autohit... Well, I'll leave that to your imagination.:uh-huh: Though, come to think of it, what would be the threat range of that thing on the 3d6 system anyway?
oontyex 10-16-06, 10:54 PM	IF that's how it worked: great falchion 18-20, improved crit, 15-20, disciple of dispater 8, 9-20, weapon master 7, 7-20 and 5 for fighter to meet the prereqs :P lol luckily its nothing like that hehe
tsuyoshikentsu 10-17-06, 12:29 AM	If that were the way that things actually worked, weapons with wide crit ranges would be so far beyond broken it wouldn't even be funny. there is a weapon somewhere (can't remember exactly where) that has a 17-20x2, slap keen on that and it has 13-20x2. If a threat were an autohit... Well, I'll leave that to your imagination.:uh-huh:Well, here's the thing: like I said above, every DM I've ever played with (and all the ones I currently do) rule just that. That weapon was errata'd, btw. IF that's how it worked: great falchion 18-20, improved crit, 15-20, disciple of dispater 8, 9-20, weapon master 7, 7-20 and 5 for fighter to meet the prereqs :P lol luckily its nothing like that heheThat IS how it works, minus Weapon Master. And Fighter 5. No one EVER takes Fighter 5.
Animefunkmaster 10-17-06, 01:00 AM	four fighter and fighter feat rogue... or fighter4 barb1... and isn't psychic weapon master 3.5?
Subedei 10-17-06, 01:15 AM	Threats don't always result in criticals, or, even hits for that matter. What good is a 9-20 threat range if you only hit on a 18, 19, or 20? ... just saying. Yeah, it really depends. The character I'm currently designing for instance gets his Int bonus to confirm critical hits. He's just not going to miss unless he rolls a 1. Although not exact I think I can pretty much just assume he'll crit 25% of the time.
catharz 10-17-06, 01:48 AM	Threats don't always result in criticals, or, even hits for that matter. What good is a 9-20 threat range if you only hit on a 18, 19, or 20? ... just saying. If you only hit on an 18, 19, or 20, you'll never hit anyway. You can't roll a 19 or 20 on 3d6. The probability of getting an 18 is 1/6x6x6 = 1/216 = .46%, that is you could expect to make about 200 attacks before hitting.
DarkRhystar 10-17-06, 01:53 AM	I made an excel sheet to calculate all this stuff out a year or so ago. It took everything into account from critical threat range to effective critical threat range to base weapon damage and added weapon damage as well as critical threat range modifiers...etc. The results were interesting. Assuming a 95% chance to hit, a mundane Greatsword is statistically (barely) better than a mundane Scythe or Falchion until it has 39 points of bonus damage. At which point, they are equal. Adding keen to the Greatsword and Scythe/Falchion makes them equivalent with 19 points of extra damage. Expanding a critical threat range by an arbitrary amount will favor weapons with larger multipliers. Expanding a critical threat range by a fixed percentage (100%) will result in no changes compared to other weapons. Weapons like the Falchion and Scythe are statistically identical as long as the weapon with the larger threat range (Falchion) may use the entire range. Despite this, I came to the conclusion that larger threat ranges were better as there is less "waste of damage" where "waste of damage" is considered to be damage beyond a creature's remaining HP. However, if you run into a situation where you may expand your weapon's threat range a great deal to the point of lowering its effective critical threat range... a higher multiplier is more beneficial statistically.
Surreal 10-17-06, 02:03 AM	I've never noticed this variant before, but I like it. Let's ignore the whole crit range thing for a second; would Weapon Focus be statistically better under this system?
catharz 10-17-06, 04:48 AM	I've never noticed this variant before, but I like it. Let's ignore the whole crit range thing for a second; would Weapon Focus be statistically better under this system? Just as an aside: This system is really awful. All it does it add an extra two dimensions to the probability distribution. It doesn't acually represent a more 'realistic' method of die rolling, because d20 failure & success are purely binary. That is, if you want a player to fail 25% of the time you make it so he has to roll a 6 or higher. you do this with the simple calculation 20 - (0.25*20). If you want to make a player fail 25% of the time in the 'bell curve' system, how do you do it? A simpler case is 2d6: 1 2 3 4 5 6 ----------- 1| 2 3 4 5 6 7 2| 3 4 5 6 7 8 3| 4 5 6 7 8 9 4| 5 6 7 8 9 10 5| 6 7 8 9 10 11 6| 7 8 9 10 11 12 You end up with an array of 6*6 = 36 cells. Now select 1/4 = 25% of them = 9, starting from (1,1). So a character should have to roll approximately 6 or higher. Now try doing that with a three dimensional array of 216 cells. Maybe I didn't make this clear enough. In both cases, the character will fail 25% of the time. In other words, the fact that you're rolling 3d6 doesn't even matter. This is because DCs are binary: You either fail, or you succeed. If there were results for 'partial success' or 'partial failure,' using the bell curve system would have meaning. As-is, it just makes for more work.