First off, thank you for taking the time and having the patience to help me with this. I would really love for this to be more sound on the probabilities.
1) Looking at your original table, I think you can see my intent. Without adding another level of complexity, the average expected damage boost is somewhat comparable both pre-and-post keen to the d20 values. However, you have made a point about how it breaks down at the 20/x3 and 20/x4 values. The 3.5x mod on the 20/x2 is because monsters often have that for their crit chance, and their burst damage potential is the most problematic.
2) What if you took into account keen and improved crit stacking? That is why the 18-20/x2 is not increased, because I was thinking that 12 is a lot closer to the 'pyramid' then, say, 15 is.
Actually, the "accepting" factor comes from a lack of ability to better account for probability, not a lack of caring. I accepted that I couldn't do better, essentially.In effect: you should first figure out what effects you want to change in your system. Decide "I want crits to be less important" or "I want the difference between crit multipliers to increase with non-keen weapons, and stay about the same when they are keen", and then tweak the mechanics.
It appears you are simply tweaking mechanics, and then accepting whatever random side effects fall out. That is a bad way to tweak a game system.
Find out what properties of the game system you want to change, and then figure out how to change the rules of the game system to get those property changes. Don't change the rules for the sake of changing the rules.
First, the main point is to cause the general distribution change, favoring mid values over extremes. This has been addressed and we agree on it (I think).
Second, I want to make criticals and threat ranges to be somewhat like they were before, but favoring those that take pains to improve their threat range and perhaps marginalizing others. Essentially, what you suggested is more-or-less accurate.
1) Yes, to an extent.So, honestly, before: did you intend to decrease the impact of crits? Did you intend to make a long sword average boost to damage from crits be indistinguishable from the scimitar after you keen both? Did you intend to nerf the 20x3, 20x4 weapons significantly in average damage delt? Did you consider the keen scimitar to be too good?
All of these things you have done -- and it appears they are just happening as side effects of rule changes, as opposed to pre-meditated goals that you aimed to change rules in order to produce.
2) No, I was attempting to take into account the stacking effect of keen and improved crit giving the scimitar a much greater chance to crit.
3) No, but I am wary of making the modifier on them so obscene that if they ever crit its an auto-kill. Also, with x3 vs x4, if they have like x16 or x20 mods, it doesn't matter, its going to kill anything outright. Furthermore, that is seriously silly (as you stated).
4) See above thoughts on the scimitar. In essence, sort of, but I was seeing something you weren't taking into account.
5) I hope you understand my goals and the reasoning behind my changes now. I may not have done such perfectly, but I assure you it was with the intention of creating a dynamic and effective change.
So, would you consider remaking that suggestion with the concept of keen and improved crit stacking in mind? Also, I want to avoid any additional layers of complexity if I can. It's a fundamental rolling mechanic, I don't want to make it convoluted.So what is the table at the end of my post? It is an attempt to produce a critical table that gives the same average boost to damage as the d20 critical tables. Ie: if your goal is to not change the relative quality of weapons, then that is the sort of table you want to use.
I'm advising you to take that approach -- compensate for changes done by default, and only after consideration change them.
Too much math for me to really get what you are saying, but good to know! I certinally would like my system (your remake of my system, whatever :) ) to be sound enough to be used in this fashion, especially since opposed rolls (such as skill checks) do this.Oh, as a rather neat side: if you also change D&D to a contest based game (ie, each side rolls 2d10 plus modifiers, instead of one side rolling and the other side providing the target), then this exactly compensates for the decrease in SD!
1d20+ATK vs 10+DEF
is nearly identical to
2d10+ATK vs 2d10+DEF
in terms of the probability impact of having a +1 or -1 edge against the opponent. :)
The only significant differences are in the low-probability zone -- ie, out among the +/- 10 edge to one side or the other area, in which d20 often just gives up and says "you have a 5% chance to win".
That is one of the primary intentions of the 2d10 change, as I say in my OP.Doing
1d20+ATK vs 1d20+DEF
has effect of making modifiers 1.4 times less important (or 70% as important), if you want to go the other way. This "flattens" the level curve somewhat, and might single-handedly reign in "save or die" spells.