Bell Curve Rolling and Threat Ranges

“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, 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 the SRD 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 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. 😀

Published in: on October 14, 2006 at 11:38 pm  Leave a Comment  

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