One of the biggest player complaints my last campaign was Descending AC. Here we’ll review some back-of-the-envelope math to convert the various “to hit” tables from OSRIC to a THAC0/Ascending AC table.
Armor Class
Converting AC should be a simple enough matter. Descending AC works in a range from 10 (no armor) to -10 (godly) armor. This is a range of 20 points. Given that we can infer that Ascending AC should also convert to a 20 point range, 10 (no armor) to 30 (godly armor).
For players the OSRIC rules make our lives easy because the armor table1 lists modifiers instead of absolute ACs. For example plate armor confers a -7 bonus1 for a Descending AC of 3. We can simply make the minus a plus for an Ascending AC of 17. Hopefully it’s clear that in either case plate armor is conferring 7 points of armor to the wearer.
For monsters we’ll want a formula so we can convert their AC on the fly instead of having to re-write the monster manual. This is as simple as subtracting the monster’s Descending AC from 10 and adding that number to 10 to get the Ascending AC; (10 – Descending AC) + 10 = Ascending AC. Two examples. Cyclops2 Descending AC = 2; (10 – 2) + 10 = 18. Bulette3 Descending AC -2; (10 – -2) +10 = 22.
If we attempt to verify the math on the Fighter’s “to hit table”4 using the level 1 row we’ll note that a first level fighter needs an 18 to hit AC 2. In the case of the Cyclops our math tracks. In fact if you compare the math to all armor classes zero or greater (for a first level fighter) the math tracks.
The Ascending AC math breaks down in two dimensions. Negative ACs break our Ascending AC formula in the lower levels since the formula can produce Ascending ACs that are harder to hit than their Descending AC equivalent. Let’s put a pin in this and come back to it later. Fighters at levels higher than 1st need to roll lower numbers to hit AC 2(18). We’ll address this next.
To Hit
If we look at the fighter to hit table4 we’ll note that the fighter’s ability to hit armor improves each level. We’ll need to fit this improvement into a THAC0 and Ascending AC system.
Since AC is a static number whether it’s ascending or descending we’ll need to improve some number to reflect the fighter’s increasing chance to hit. THAC0 is simply lifted from the “to hit”4 table using the AC 0 column, it improves by 1 for each level gained. For Ascending AC we’ll give the fighter a “to hit bonus” which will also improve by 1 for each level gained. This improvement will start at 0 and can be expressed with the formula, Fighter Level – 1 = to hit bonus.
A 1st level fighter using either THAC0 or Ascending AC needs to roll an 18 to hit an AC 2/18. THAC0 (20) – to hit roll (18) = the AC hit (2). Ascending AC to hit roll (18) = the AC hit (18).
A 2nd level fighter using either THAC0 or Ascending AC needs to roll an 17 to hit an AC 2/18. THAC0 (19) – to hit roll (17) = the AC hit (2). Ascending AC (to hit roll (17) + to hit bonus (1) = the AC hit (18)).
Both track with our earlier math for first level fighters and address the higher level fighter’s increased ability to hit.
The improvement in the fighter’s ability to hit is coded into the system as either a THAC0 that improves by 1 each level or “to hit bonus” that improves by 1 each level starting at 2nd. The formula works for fighters, paladins and rangers but composing similar formula for other classes is somewhat more tedious. I’ve left the manual figuring aside and put the result in the table below.
Conversion of the class “To Hit” tables from OSRIC to THAC0(Ascending AC).
| Level | Fighter / Paladin / Ranger | Assassin / Thief | Cleric / Druid | Magic-User / Illusionist |
| 1 | 20(0) | 20(0) | 20(0) | 20(0) |
| 2 | 19(+1) | 20(0) | 20(0) | 20(0) |
| 3 | 18(+2) | 20(0) | 20(0) | 20(0) |
| 4 | 17(+3) | 20(0) | 18(+2) | 20(0) |
| 5 | 16(+4) | 19(+1) | 18(+2) | 20(0) |
| 6 | 15(+5) | 19(+1) | 18(+2) | 19(+1) |
| 7 | 14(+6) | 19(+1) | 16(+4) | 19(+1) |
| 8 | 13(+7) | 19(+1) | 16(+4) | 19(+1) |
| 9 | 12(+8) | 16(+4) | 16(+4) | 19(+1) |
| 10 | 11(+9) | 16(+4) | 14(+6) | 19(+1) |
| 11 | 10(+10) | 16(+4) | 14(+6) | 17(+3) |
| 12 | 9(+11) | 16(+4) | 14(+6) | 17(+3) |
| 13 | 8(+12) | 14(+6) | 12(+8) | 17(+3) |
| 14 | 7(+13) | 14(+6) | 12(+8) | 17(+3) |
| 15 | 6(+14) | 7(+13) | 12(+8) | 17(+3) |
| 16 | 5(+15) | 7(+13) | 10(+10) | 15(+5) |
| 17 | 4(+16) | 12(+8) | 10(+10) | 15(+5) |
| 18 | 3(+17) | 12(+8) | 10(+10) | 15(+5) |
| 19 | 2(+18) | 12(+8) | 9(+11) | 15(+5) |
| 20+ | 1(+19) | 10(+10) | 9(+11) | 13(+7) |
The Pin
Ascending AC breaks the “to hit” number for previously negative armor classes within a certain range.
A first level fighter using the OSRIC “to hit”4 table needs a 20 to hit a Bulette3 whereas the fighter using the Ascending AC conversion needs a 22. The Ascending AC fighter is therefore at a 2 point deficit to hit the vs the fighter using the OSRIC to hit table4.
In the Ascending AC system this deficit diminishes as the the fighter’s to hit bonus rises with level.
How serious is this deficit? If I were publishing a game this might be a problem to solve. Then again it might just be that some creatures are too tough for low level characters. Since the Bulette3 is a 9 HD creature it’s safe to assume that it’s not meant to be encountered by a low-level group.
Since I can certainly keep encounters in my home game “in bounds” I think the math is good enough for a house rule.
Conclusions
Personally I’m not all that interested in the fight over whether one formula is better than the other. Neither is all that difficult.
(THAC0 – (d20 + To Hit Modifiers) = Descending AC)
(d20 + To Hit Modifiers = Ascending AC)
What’s far more interesting?
Ascending AC was introduced to D&D with the release of 3E. As far as I’ve read 3E and 4E had rapidly escalating math that eventually led to the bounded accuracy of 5E.
Over this same period the ability of of fighters to hit with weapons was reduced to being the same as other classes. It’s true they gained various abilities over the same time. But whether that’s an improvement is down to individual judgement.
Foot Notes
- Stuart Marshall, Armour Table 1: OSRIC Updated 2nd Edition (Usherwood Publishing, 2008), 33.
- Stuart Marshall, Cyclops: OSRIC Updated 2nd Edition (Usherwood Publishing, 2008), 205.
- Stuart Marshall, Bulette: OSRIC Updated 2nd Edition (Usherwood Publishing, 2008), 275.
- Stuart Marshall, ROLL REQUIRED TO HIT ARMOUR CLASS: OSRIC Updated 2nd Edition (Usherwood Publishing, 2008), 15.
- I remember it being with 2E but it could have been far earlier.
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