AC: A simplified suggestion

[sirgog]

Thanks . . . But with an average to-hit roll of 83.5 (right?) I'm still right on this meaning a 90 AC tank will still take significantly less damage than he does now since he's not getting crazes for 50-80 on a 13-19.

Mobs would need individual reassessment of to-hit under this system as the OP's suggestion as it stands would make elite Horoth a lot more damaging than he is now to all tanks with AC. (The average might be 83.5 but the standard deviation would be much higher than at present, meaning numbers far from 83.5 would come up much more frequently).

Horoth's grazes aren't too bad, even on Elite. Yeah they add up, but they aren't over the top as most defenders have DR 25% and DR 5/- (on gear) or 6/- (inherent to fighter defenders). 60-ish damage grazes hit for a lot less through that DR. This system as written would result in players with 90-ish AC getting utterly ripped to shreds by big H, probably finding they are hit as often as the present big H grazes them.

Still I do like this idea in general.

[LeLoric]

Your 5% absolute miss, and 5-15% critical range would need to cover, not the values along the X axis, but 5% of the area of the bell curve. 5% of the distribution of 4d20 covers all rolls from 4-22 (totaling 4.57188% probability, but including all 23s as well would put us at 5.53438%).

To alleviate confusion just have the first of the four d20 rolls determine crits just like it does now.

[sirgog]

To alleviate confusion just have the first of the four d20 rolls determine crits just like it does now.

Yeah that was my suggestion in the other thread. IMO it's more intuitive than "2d20 rolls of 35-40 are treated as natural 20s for crits" (top 5.25%) and extending this pattern. In my suggestion the first roll also determined grazes, although I agree that in the OP's suggestion grazes would no longer be needed except (maybe) for players attacking monsters.

[wax_on_wax_off]

The AC system falls apart fairly quickly in game. Basically lower AC's are pointless and while leveling very high AC's are equally pointless.

So the goals here are simple to any rework...

• Lower AC's should make a difference against all mobs at all levels of play.
• Very High AC's should make a difference against all mobs at almost all levels of play (the extreme twinkage possible at the lowest levels of play is going to be deemed not important enough to worry about).
• Create a system where grazing hits are no longer needed to insure some incoming damage in raid type fights.
• Insure that AC still does not protect against 'spike' damage...ie no static type dr stuff for AC since spike damage helps retain the danger element in game.
• Create a system where there is less concern over that last point of AC being achieved which likewise frees the developers to be less wary when making new AC gear or other buffs.
• Insure that any future increases to mob to hits or player ACs will not break this system. IE make the AC system work well within the framework of an expanding game.
• Eliminate the needs for any 'special' AC related rules as band aid fixes on a broken system.

So what do I propose?

• Eliminate grazing hits.
• Eliminate epic special rules involving to hit roles.
• Change how ALL mobs roll to hit as follows...
  
  • Mobs now have extra d20's to hit instead of base + to hit. This change would be made so that mobs have the same average to hit roll. Extra d20's would be assigned until the mob has less then a static +11 to hit.
  • Critical hits would be assigned a percentile chance of occurring based upon the mobs previous crit range and would be assigned in the proper upper range of rolls possible. This is simple for a computer to do.
  • Automatic hits and misses would be assigned as a ~5% chance based upon the d20 rolls being done to preserve that these are the top 5% of rolls or bottom 5% of rolls possible from the range being rolled. This is very simple for a computer to do. Note, I would not be opposed to elimanting these automatic misses and hits entirely as the dynamic ranges are much much larger in my proposed system then the current system making these less critical.

In practice what would this mean?

• Mobs could roll worse (much worse) then normal meaning that even the most minor investments in AC would add some protection against incoming attacks. A mob with a truly massive to hit roll currently that had let's say a 1d20 + 90 would instead have a to hit roll of 9d20 + 6 meaning anything over a 15 AC would provide some added protection versus their attacks. Even a raging barbarian can manage over a 15 AC if they bothered to do so.
• Grazing hits are not needed because mobs can roll crazy high to hit players. That same mob above could roll to hit a 186 AC. Also this lifts some of the headache from the developers when designing new items with AC in mind as there is no longer a 'magic number' that must be avoided otherwise content becomes trivial.
• Massive AC numbers do provide extra protection, but at a degraded rate as mobs are less and less likely to roll each AC to hit the higher they go over their average (unlike the previous 1d20 system where the odds of them rolling that number is exactly the same as rolling the average).
• Lower AC numbers before a mobs average to hit provide more and more protection as you approach their average to hit.
• Developers can create mobs with smaller then prior average to hits without strong worries about creating 'invincible' players. Likewise their old favorites of super high to hit mobs fit better in the overall structure of the game. This provides lots of wiggle room for content designers as they are not constantly having to worry about falling off the dice.

If anyone wants practical examples of any math I should be able to provide it.

Call it opposed rolls and I'm all on board.

Simply put, our AC is currently 10+modifiers, if it was d20+modifiers then it has the exact same effect as monsters having 2d20 attack but keeps it d20 system and is an official variation of D&D rules in the DM guide iirc (for 3.5e).

Creates some interesting possibilities for making combat more variable by introducing critical defenses and critical fumbles but this isn't compulsory (1 and 20 on your defense roll doesn't need to have any significance).

[Ungood]

The AC system falls apart fairly quickly in game. Basically lower AC's are pointless and while leveling very high AC's are equally pointless.

So the goals here are simple to any rework...

• Lower AC's should make a difference against all mobs at all levels of play.
• Very High AC's should make a difference against all mobs at almost all levels of play (the extreme twinkage possible at the lowest levels of play is going to be deemed not important enough to worry about).
• Create a system where grazing hits are no longer needed to insure some incoming damage in raid type fights.
• Insure that AC still does not protect against 'spike' damage...ie no static type dr stuff for AC since spike damage helps retain the danger element in game.
• Create a system where there is less concern over that last point of AC being achieved which likewise frees the developers to be less wary when making new AC gear or other buffs.
• Insure that any future increases to mob to hits or player ACs will not break this system. IE make the AC system work well within the framework of an expanding game.
• Eliminate the needs for any 'special' AC related rules as band aid fixes on a broken system.

So what do I propose?

• Eliminate grazing hits.
• Eliminate epic special rules involving to hit roles.
• Change how ALL mobs roll to hit as follows...
  
  • Mobs now have extra d20's to hit instead of base + to hit. This change would be made so that mobs have the same average to hit roll. Extra d20's would be assigned until the mob has less then a static +11 to hit.
  • Critical hits would be assigned a percentile chance of occurring based upon the mobs previous crit range and would be assigned in the proper upper range of rolls possible. This is simple for a computer to do.
  • Automatic hits and misses would be assigned as a ~5% chance based upon the d20 rolls being done to preserve that these are the top 5% of rolls or bottom 5% of rolls possible from the range being rolled. This is very simple for a computer to do. Note, I would not be opposed to elimanting these automatic misses and hits entirely as the dynamic ranges are much much larger in my proposed system then the current system making these less critical.
  
  

In practice what would this mean?

• Mobs could roll worse (much worse) then normal meaning that even the most minor investments in AC would add some protection against incoming attacks. A mob with a truly massive to hit roll currently that had let's say a 1d20 + 90 would instead have a to hit roll of 9d20 + 6 meaning anything over a 15 AC would provide some added protection versus their attacks. Even a raging barbarian can manage over a 15 AC if they bothered to do so.
• Grazing hits are not needed because mobs can roll crazy high to hit players. That same mob above could roll to hit a 186 AC. Also this lifts some of the headache from the developers when designing new items with AC in mind as there is no longer a 'magic number' that must be avoided otherwise content becomes trivial.
• Massive AC numbers do provide extra protection, but at a degraded rate as mobs are less and less likely to roll each AC to hit the higher they go over their average (unlike the previous 1d20 system where the odds of them rolling that number is exactly the same as rolling the average).
• Lower AC numbers before a mobs average to hit provide more and more protection as you approach their average to hit.
• Developers can create mobs with smaller then prior average to hits without strong worries about creating 'invincible' players. Likewise their old favorites of super high to hit mobs fit better in the overall structure of the game. This provides lots of wiggle room for content designers as they are not constantly having to worry about falling off the dice.

If anyone wants practical examples of any math I should be able to provide it.

This is Brilliant!

[Sidewaysgts86]

This idea has been proposed before. I liked it then. I like it now. Its nice that ddo is based on DnD, but somethings can "only go so far". This system (or a modified version of it) stays true to the "spirit" of Dnd, but fits/works better in, imo, in ddo. Its easy for a Dm to control these things in a pnp game with some careful planning- Not so easy for a a mmo with very "set" rules. Its frustrating being a paladin with 65 ac working just "just as well" as my wizard friend with 12.

Seconding the notion of having vorpals/crits/misses/for sure hits playing off the first die roll.

[Cyr]

Yeah that was my suggestion in the other thread. IMO it's more intuitive than "2d20 rolls of 35-40 are treated as natural 20s for crits" (top 5.25%) and extending this pattern. In my suggestion the first roll also determined grazes, although I agree that in the OP's suggestion grazes would no longer be needed except (maybe) for players attacking monsters.

It is pointless what is 'more intuitive' this is all behind the scenes.

The method I listed preserves the aspect of critical threats corresponding to the top end of the AC range rolled which is preferrable then something that is 'more intuitive' that a player never actually sees.

If you just take the first roll to determine things you have monsters potentially critting on a low to hit roll and more importantly actually have mobs lose dps against higher AC foes.

[Cyr]

Sirgog put some nice numbers to the RoR (Rate of Return) based on AC increments in the current system. http://forums.ddo.com/showthread.php?t=365722

I believe that the mobs "to-hit" calculation needs to be changed for AC to be viable across a wider range. With your proposed system however, the viable AC range reaches to un-attainable levels.

7d20 puts the average AC threshold at 70. This is fine, but the amount of sacrifice it takes to get to that AC is substantial because of the limited amount of areas from which to draw AC, especially when they start removing some of the current stacking sources.

This is why I mentioned how much work AC tanks need to accomplish to get that extra 1-2 AC from equipment at the higher levels, when the AC starts to get into 80+. On a bell curve, the amount of work far exceeds the reduced damage seen.

Yup, there are trade offs for having all AC be valuable. The main one is that top end AC becomes more and more rare.

I am doing the math currently...using excel and matrixes which is really a poor way to do it, but at least it is accurate since I could not find my stats books last night (must have put them in my storage room /sigh).

These are the results for a 4d20 (working upwards on the dice since it takes larger and larger matrixes to solve)...

Note the average of 4d20 is 42. An increase of 5 AC decreases mob to hit percentage by ~15% from the average. Of course this rolls off, but you will note that a 61 AC gets you to the point of 5% hits while a 57 gets you to a 10% hit chance. Will post full charts upto 7d20 when I have them.

I can post the RoR math also when I get the rest done as it is trivial to do.

If I can get the grazing hit math for elite horoth from someone (as in horoths base damage and full damage) that will speed things up. Cheers.

Edit: Okay maybe you will have some trouble seeing...stupid formatting...anyone know how to get rid of the span junk and actually have the spaces show up?



Dice Roll # occurances odds of occurance Culmalitive odds</SPAN> </SPAN>3 0 0 0</SPAN>4 1 0.00000625 0.00000625</SPAN>5 4 0.000025 0.00003125</SPAN>6 10 0.0000625 0.00009375</SPAN>7 20 0.000125 0.00021875</SPAN>8 35 0.00021875 0.0004375</SPAN>9 56 0.00035 0.0007875</SPAN>10 84 0.000525 0.0013125</SPAN>11 120 0.00075 0.0020625</SPAN>12 165 0.00103125 0.00309375</SPAN>13 220 0.001375 0.00446875</SPAN>14 286 0.0017875 0.00625625</SPAN>15 364 0.002275 0.00853125</SPAN>16 455 0.00284375 0.011375</SPAN>17 560 0.0035 0.014875</SPAN>18 680 0.00425 0.019125</SPAN>19 816 0.0051 0.024225</SPAN>20 969 0.00605625 0.03028125</SPAN>21 1140 0.007125 0.03740625</SPAN>22 1330 0.0083125 0.04571875</SPAN>23 1540 0.009625 0.05534375</SPAN>24 1767 0.01104375 0.0663875</SPAN>25 2008 0.01255 0.0789375</SPAN>26 2260 0.014125 0.0930625</SPAN>27 2520 0.01575 0.1088125</SPAN>28 2785 0.01740625 0.12621875</SPAN>29 3052 0.019075 0.14529375</SPAN>30 3318 0.0207375 0.16603125</SPAN>31 3580 0.022375 0.18840625</SPAN>32 3835 0.02396875 0.212375</SPAN>33 4080 0.0255 0.237875</SPAN>34 4312 0.02695 0.264825</SPAN>35 4528 0.0283 0.293125</SPAN>36 4725 0.02953125 0.32265625</SPAN>37 4900 0.030625 0.35328125</SPAN>38 5050 0.0315625 0.38484375</SPAN>39 5172 0.032325 0.41716875</SPAN>40 5263 0.03289375 0.4500625</SPAN>41 5320 0.03325 0.4833125</SPAN>42 5340 0.033375 0.5166875</SPAN>43 5320 0.03325 0.5499375</SPAN>44 5263 0.03289375 0.58283125</SPAN>45 5172 0.032325 0.61515625</SPAN>46 5050 0.0315625 0.64671875</SPAN>47 4900 0.030625 0.67734375</SPAN>48 4725 0.02953125 0.706875</SPAN>49 4528 0.0283 0.735175</SPAN>50 4312 0.02695 0.762125</SPAN>51 4080 0.0255 0.787625</SPAN>52 3835 0.02396875 0.81159375</SPAN>53 3580 0.022375 0.83396875</SPAN>54 3318 0.0207375 0.85470625</SPAN>55 3052 0.019075 0.87378125</SPAN>56 2785 0.01740625 0.8911875</SPAN>57 2520 0.01575 0.9069375</SPAN>58 2260 0.014125 0.9210625</SPAN>59 2008 0.01255 0.9336125</SPAN>60 1767 0.01104375 0.94465625</SPAN>61 1540 0.009625 0.95428125</SPAN>62 1330 0.0083125 0.96259375</SPAN>63 1140 0.007125 0.96971875</SPAN>64 969 0.00605625 0.975775</SPAN>65 816 0.0051 0.980875</SPAN>66 680 0.00425 0.985125</SPAN>67 560 0.0035 0.988625</SPAN>68 455 0.00284375 0.99146875</SPAN>69 364 0.002275 0.99374375</SPAN>70 286 0.0017875 0.99553125</SPAN>71 220 0.001375 0.99690625</SPAN>72 165 0.00103125 0.9979375</SPAN>73 120 0.00075 0.9986875</SPAN>74 84 0.000525 0.9992125</SPAN>75 56 0.00035 0.9995625</SPAN>76 35 0.00021875 0.99978125</SPAN>77 20 0.000125 0.99990625</SPAN>78 10 0.0000625 0.99996875</SPAN>79 4 0.000025 0.99999375</SPAN>80 1 0.00000625 1</SPAN> </SPAN>

[Krago]

The numbers are a little intimidating at first glance.

My concern is that making AC viable at lower values, we have just burned the guys who actually cared about AC at the higher levels in that they will get hit more often instead of less.

[Monkey-Boy]

My concern is that making AC viable at lower values, we have just burned the guys who actually cared about AC at the higher levels in that they will get hit more often instead of less.

Yeah . . . but I'm not so sure about that and with the removal of grazes it might actually result in better damage mitigation.

[Cyr]

The numbers are a little intimidating at first glance.

My concern is that making AC viable at lower values, we have just burned the guys who actually cared about AC at the higher levels in that they will get hit more often instead of less.

It depends on if you hit the magic number or not under the old system really.

I will be doing the full math here, but so far it does indeed seem that if you were hitting the only hit on a 20 mark against big mobs then you would be suffering more damage under this proposed system.

Basically the difference between each point of AC towards that magic number means less in this type of setup. That IMHO is a very good thing as the magic number was one of the main problems the developers run into over and over again with the AC system.

I will post the math when I have it...and hopefully in a better format then that copy paste from excel was.

The initial math is demonstrating that even with this type of system you gain a greater % reduction of incoming hits for each point of AC. This rate does not increase as dramatically as the normal system however and is fairly smooth increase in the 0-95% range where each point of AC means 1% to 20% reduction in incoming hits compared to the current curve which hits RoR of 100% in the 95% range (the 95% range is what matters because mobs always hit 5% of the time).

[BOgre]

But, the big problem is that this strays from D&D into GURPS or Whitewolf PNPRPGs...

No, this isn't the 'big problem' as you put it. It's the solution. D&D AC is the worst system in all RPGhood. Straying into better AC systems is a good thing.

The bigger problems with this idea appear on the extreme high and low ends, but in all it's a good start. I'd love to hear from Turbine about where their plans lie.

[Cyr]

As requested 7d20 Math

Elite Horoth would have 7d20+10.

A currently only grazed or hit on natural 20 93 AC toon would be hit 26% of the with this change (but no grazes). That would be more incoming damage then they currently suffer without me having to do the 25% grazing hits math and 5% normal damage math (this would be 21% more normal damage with no grazes with 21% normal damage > 25% grazing hits damage).

Now let's say you didn't have a perfect tank for the job and had a 90 AC toon instead. You are then looking at 33% of incoming hits hitting you in the proposed system versus 15% plus another 15% grazes. Again clearly the old system is more favorable.

Role that back to an 80 AC toon which is hit fully 65% of the time in the current system. In this proposed system you would be hit 58% of the time instead. The cross over comes a little bit inbetween these 80 and 90 AC.

In the current system an 83 AC grants 50% miss chance for horoth. In the new system this is the same percentage.

Now flip this around to a very high AC toon (let's say Turbine uses this suggestion and decides that AC is no longer to be something to be feared when creating new items and enhancements)...

A 100 AC toon (7 higher then the current magic number) would grant a 14% hit chance. That would probably be pretty close to a current magic number 93 AC toon and beat out anything under that. I would have to do the math to be sure of this.

So clearly this type of change would make very high AC tanks less powerful if they could hit the magic number, but more powerful against mobs which they could not get above the average roll before. Of course, this math can be tinkered with if the mob average to hit is lowered under this type of implimentation as you can see a simple ten point shift on horoth makes a huge difference. Likewise, more math oriented solutions could create uneven distributions for mob to hits that rolled off less sharply on the negative side and more sharply on the positive side (for more lower end AC being even more effective and higher end AC not requireing as many points to make a bigger difference), but this is a more complicated approach (although the one that I have always favored if you see my past posts about the AC issue).

The ideal approach here would be both relatively simple and effective at achieving the goals laid out. There could be an alternative approach here that relies on a weighted dice approach...something like a dice that is fully as large as the average attack * 2 which if it rolls above the average has the difference above the average divided by some constant and then added to the average...so let's take elite horoth...he would be 1d166 and if you rolled above 83 you would then divide the amount above 83 by let's say 2 and add that onto 83 (ex horoth rolls 122 to hit you and then he actually hits 103 AC and misses 104 AC)...that kind of an approach would kind of hit the goal of low end being effective to have and high end not requiring as large of an AC to get to the awesome stage.

I now have full math for 2d20-7d20 if anyone is interested. The 7d20 is displayed below.


total 1280000000 7d20

Dice Roll # occurances odds of occurance Culmalitive odds % Reduction in hits for one more AC

7 1 0.000% 0.000% 0%
8 7 0.000% 0.000% 0%
9 28 0.000% 0.000% 0%
10 84 0.000% 0.000% 0%
11 210 0.000% 0.000% 0%
12 462 0.000% 0.000% 0%
13 924 0.000% 0.000% 0%
14 1716 0.000% 0.000% 0%
15 3003 0.000% 0.001% 0%
16 5005 0.000% 0.001% 0%
17 8008 0.001% 0.002% 0%
18 12376 0.001% 0.002% 0%
19 18564 0.001% 0.004% 0%
20 27132 0.002% 0.006% 0%
21 38760 0.003% 0.009% 0%
22 54264 0.004% 0.013% 0%
23 74613 0.006% 0.019% 0%
24 100947 0.008% 0.027% 0%
25 134596 0.011% 0.038% 0%
26 177100 0.014% 0.051% 0%
27 230223 0.018% 0.069% 0%
28 295961 0.023% 0.092% 0%
29 376544 0.029% 0.122% 0%
30 474432 0.037% 0.159% 0%
31 592305 0.046% 0.205% 0%
32 733047 0.057% 0.263% 0%
33 899724 0.070% 0.333% 0%
34 1095556 0.086% 0.418% 0%
35 1323883 0.103% 0.522% 0%
36 1588125 0.124% 0.646% 0%
37 1891736 0.148% 0.794% 0%
38 2238152 0.175% 0.969% 0%
39 2630733 0.206% 1.174% 0%
40 3072699 0.240% 1.414% 0%
41 3567060 0.279% 1.693% 0%
42 4116540 0.322% 2.014% 0%
43 4723495 0.369% 2.383% 0%
44 5389825 0.421% 2.805% 0%
45 6116880 0.478% 3.282% 1%
46 6905360 0.539% 3.822% 1%
47 7755230 0.606% 4.428% 1%
48 8665650 0.677% 5.105% 1%
49 9634920 0.753% 5.857% 1%
50 10660440 0.833% 6.690% 1%
51 11738685 0.917% 7.607% 1%
52 12865195 1.005% 8.613% 1%
53 14034580 1.096% 9.709% 1%
54 15240540 1.191% 10.900% 1%
55 16475900 1.287% 12.187% 2%
56 17732660 1.385% 13.572% 2%
57 19002060 1.485% 15.057% 2%
58 20274660 1.584% 16.641% 2%
59 21540435 1.683% 18.324% 2%
60 22788885 1.780% 20.104% 2%
61 24009160 1.876% 21.980% 3%
62 25190200 1.968% 23.948% 3%
63 26320890 2.056% 26.004% 3%
64 27390230 2.140% 28.144% 3%
65 28387520 2.218% 30.362% 3%
66 29302560 2.289% 32.651% 4%
67 30125830 2.354% 35.004% 4%
68 30848650 2.410% 37.414% 4%
69 31463320 2.458% 39.873% 4%
70 31963240 2.497% 42.370% 5%
71 32343010 2.527% 44.896% 5%
72 32598510 2.547% 47.443% 5%
73 32726960 2.557% 50.000% 5%
74 32726960 2.557% 52.557% 6%
75 32598510 2.547% 55.104% 6%
76 32343010 2.527% 57.630% 6%
77 31963240 2.497% 60.127% 7%
78 31463320 2.458% 62.586% 7%
79 30848650 2.410% 64.996% 7%
80 30125830 2.354% 67.349% 8%
81 29302560 2.289% 69.638% 8%
82 28387520 2.218% 71.856% 8%
83 27390230 2.140% 73.996% 9%
84 26320890 2.056% 76.052% 9%
85 25190200 1.968% 78.020% 9%
86 24009160 1.876% 79.896% 10%
87 22788885 1.780% 81.676% 10%
88 21540435 1.683% 83.359% 11%
89 20274660 1.584% 84.943% 11%
90 19002060 1.485% 86.428% 11%
91 17732660 1.385% 87.813% 12%
92 16475900 1.287% 89.100% 12%
93 15240540 1.191% 90.291% 13%
94 14034580 1.096% 91.387% 13%
95 12865195 1.005% 92.393% 14%
96 11738685 0.917% 93.310% 14%
97 10660440 0.833% 94.143% 15%
98 9634920 0.753% 94.895% 15%
99 8665650 0.677% 95.572% 16%
100 7755230 0.606% 96.178% 16%
101 6905360 0.539% 96.718% 17%
102 6116880 0.478% 97.195% 18%
103 5389825 0.421% 97.617% 18%
104 4723495 0.369% 97.986% 19%
105 4116540 0.322% 98.307% 20%
106 3567060 0.279% 98.586% 20%
107 3072699 0.240% 98.826% 21%
108 2630733 0.206% 99.031% 22%
109 2238152 0.175% 99.206% 23%
110 1891736 0.148% 99.354% 24%
111 1588125 0.124% 99.478% 25%
112 1323883 0.103% 99.582% 26%
113 1095556 0.086% 99.667% 27%
114 899724 0.070% 99.737% 28%
115 733047 0.057% 99.795% 29%
116 592305 0.046% 99.841% 30%
117 474432 0.037% 99.878% 32%
118 376544 0.029% 99.908% 33%
119 295961 0.023% 99.931% 35%
120 230223 0.018% 99.949% 37%
121 177100 0.014% 99.962% 39%
122 134596 0.011% 99.973% 41%
123 100947 0.008% 99.981% 44%
124 74613 0.006% 99.987% 47%
125 54264 0.004% 99.991% 50%
126 38760 0.003% 99.994% 54%
127 27132 0.002% 99.996% 58%
128 18564 0.001% 99.998% 64%
129 12376 0.001% 99.998% 70%
130 8008 0.001% 99.999% 78%
131 5005 0.000% 99.999% 87%
132 3003 0.000% 100.000% 100%
133 1716 0.000% 100.000% 117%
134 924 0.000% 100.000% 140%
135 462 0.000% 100.000% 175%
136 210 0.000% 100.000% 233%
137 84 0.000% 100.000% 350%
138 28 0.000% 100.000% 700%
139 7 0.000% 100.000%
140 1 0.000% 100.000%

sums 1280000000 1

Please note that anything above a 108 AC for elite horoth would not grant anymore protection as horoth would still hit 5% of the time on the top end no matter what your AC was. This means the dynamic range is now 58 to 108 as opposed to 74 to 93.

[Cyr]

Take average to hit and convert to a 1d(X-20)*2 + 20 of that number. If a number above the average is rolled divide the difference by (=average to hit/30 rounded up) and add it to the average to get the to hit. If the mob has less then +20 to hit ignore this.

Elite Horoth

+83 Average to hit

1d126+20 average = 83

Dice Roll odds of occurance Culmalitive odds % Reduction in hits for one more AC

21 0.794% 0.794% 1%
22 0.794% 1.587% 1%
23 0.794% 2.381% 1%
24 0.794% 3.175% 1%
25 0.794% 3.968% 1%
26 0.794% 4.762% 1%
27 0.794% 5.556% 1%
28 0.794% 6.349% 1%
29 0.794% 7.143% 1%
30 0.794% 7.937% 1%
31 0.794% 8.730% 1%
32 0.794% 9.524% 1%
33 0.794% 10.317% 1%
34 0.794% 11.111% 1%
35 0.794% 11.905% 1%
36 0.794% 12.698% 1%
37 0.794% 13.492% 1%
38 0.794% 14.286% 1%
39 0.794% 15.079% 1%
40 0.794% 15.873% 1%
41 0.794% 16.667% 1%
42 0.794% 17.460% 1%
43 0.794% 18.254% 1%
44 0.794% 19.048% 1%
45 0.794% 19.841% 1%
46 0.794% 20.635% 1%
47 0.794% 21.429% 1%
48 0.794% 22.222% 1%
49 0.794% 23.016% 1%
50 0.794% 23.810% 1%
51 0.794% 24.603% 1%
52 0.794% 25.397% 1%
53 0.794% 26.190% 1%
54 0.794% 26.984% 1%
55 0.794% 27.778% 1%
56 0.794% 28.571% 1%
57 0.794% 29.365% 1%
58 0.794% 30.159% 1%
59 0.794% 30.952% 1%
60 0.794% 31.746% 1%
61 0.794% 32.540% 1%
62 0.794% 33.333% 1%
63 0.794% 34.127% 1%
64 0.794% 34.921% 1%
65 0.794% 35.714% 1%
66 0.794% 36.508% 1%
67 0.794% 37.302% 1%
68 0.794% 38.095% 1%
69 0.794% 38.889% 1%
70 0.794% 39.683% 1%
71 0.794% 40.476% 1%
72 0.794% 41.270% 1%
73 0.794% 42.063% 1%
74 0.794% 42.857% 1%
75 0.794% 43.651% 1%
76 0.794% 44.444% 1%
77 0.794% 45.238% 1%
78 0.794% 46.032% 1%
79 0.794% 46.825% 2%
80 0.794% 47.619% 2%
81 0.794% 48.413% 2%
82 0.794% 49.206% 2%
83 0.794% 50.000% 5%
84 2.381% 52.381% 5%
85 2.381% 54.762% 6%
86 2.381% 57.143% 6%
87 2.381% 59.524% 6%
88 2.381% 61.905% 7%
89 2.381% 64.286% 7%
90 2.381% 66.667% 8%
91 2.381% 69.048% 8%
92 2.381% 71.429% 9%
93 2.381% 73.810% 10%
94 2.381% 76.190% 11%
95 2.381% 78.571% 13%
96 2.381% 80.952% 14%
97 2.381% 83.333% 17%
98 2.381% 85.714% 20%
99 2.381% 88.095% 25%
100 2.381% 90.476% 33%
101 2.381% 92.857% 50%
102 2.381% 95.238% 100%
103 2.381% 97.619%
104 2.381% 100.000%



+43 Average to hit

1d46+20 average = 43

Dice Roll odds of occurance Culmalitive odds % Reduction in hits for one more AC

21 2.174% 2.174% 2%
22 2.174% 4.348% 2%
23 2.174% 6.522% 2%
24 2.174% 8.696% 2%
25 2.174% 10.870% 2%
26 2.174% 13.043% 3%
27 2.174% 15.217% 3%
28 2.174% 17.391% 3%
29 2.174% 19.565% 3%
30 2.174% 21.739% 3%
31 2.174% 23.913% 3%
32 2.174% 26.087% 3%
33 2.174% 28.261% 3%
34 2.174% 30.435% 3%
35 2.174% 32.609% 3%
36 2.174% 34.783% 3%
37 2.174% 36.957% 4%
38 2.174% 39.130% 4%
39 2.174% 41.304% 4%
40 2.174% 43.478% 4%
41 2.174% 45.652% 4%
42 2.174% 47.826% 4%
43 2.174% 50.000% 10%
44 4.348% 54.348% 11%
45 4.348% 58.696% 12%
46 4.348% 63.043% 13%
47 4.348% 67.391% 15%
48 4.348% 71.739% 18%
49 4.348% 76.087% 22%
50 4.348% 80.435% 29%
51 4.348% 84.783% 40%
52 4.348% 89.130% 67%
53 4.348% 93.478% 200%
54 4.348% 97.826%
55 2.174% 100.000%

+31 average to hit Just above the threshold for this to occur

1d22 + 20 average = 31

Dice Roll odds of occurance Culmalitive odds % Reduction in hits for one more AC

21 4.545% 4.545% 5%
22 4.545% 9.091% 5%
23 4.545% 13.636% 6%
24 4.545% 18.182% 6%
25 4.545% 22.727% 6%
26 4.545% 27.273% 7%
27 4.545% 31.818% 7%
28 4.545% 36.364% 8%
29 4.545% 40.909% 8%
30 4.545% 45.455% 9%
31 4.545% 50.000% 22%
32 9.091% 59.091% 29%
33 9.091% 68.182% 40%
34 9.091% 77.273% 67%
35 9.091% 86.364% 200%
36 9.091% 95.455%
37 4.545% 100.000%

This type of approach preserves the more desirable bottom end spread and decreases the top end creep. The top end you want to have some more room for improvements then the current system has as mob to hits go up and up, but this does so in a more limited fashion then the strictly d20 methodology. As before this approach would preserve the normal % crits and automatic hit/miss at the proper part of the AC curve. Of course the above is not a fully fleshed out idea, but the basic premise is being demonstrated.

This might overall be a better approach then the strict d20 approach as it keeps the lower ranges of AC more in play throughout the game and into the future. It keeps the same top end expansion, but allows a method of limiting based upon the desired method of division which could be something a little better then what I threw out there...the rounding part is the real killer on the low end.

Note that for elite horoth the dynamic range of AC's that did something would be 28 to 102 as opposed to the d20 solution which would have a slighly higher 108, but a much less dynamic low end of 58.