Tuesday, June 10, 2014

D&D Combat Math: The Internet Stikes Back

Last week I wrote a column on the notion of compatibility between the upcoming D&D 5th Edition and its elder brethren (and their OSR cousins). I started out the discussion with the very basic comparison of the progression of attack bonuses to see if I could draw any hypothesis based on the numbers presented by the different iterations.

This proved to be insufficient analysis for the internet at large. It is true that I was taking a very narrow slice of the math in the system as a whole, looking solely at the attack bonuses by level and doing a very rudimentary comparison with the different Armor Classes presented in the play test for monsters thus far. Since the monster math of the new edition was not at all final in the play test, my analysis drew some additional critique, which I can understand.

In my defense, I was not attempting a PhD level analysis on the math, but just throwing some suppositions at the wall to see what stuck... But I should know better that to just throw ideas out to the internet as a whole without qualifications or caveat.

So this week I'm going to briefly revisit this topic because I am a masochist.

Fy-TorCaveats and Qualifications


I've just taken a look at a basic STR 17 Fighter with a long sword in AD&D and D&D Next to see what kind of damage output can be expected from both. I have not factored in any other to-hit boosts or stat bumps. I understand that (as of the last play test) 5th Edition characters can choose between a stat bump or a feat at certain levels. I have not factored this in order to keep the analysis simple. I am attempting to present the two scenarios with all other things being equal. Below you can see my admittedly rudimentary results.

Level 1

AD&D L1 Fighter vs. AC 5 [15]:
The level 1 fighter (+0 to hit) with a 17 STR (+1) will hit an AC 5 [15] with a 14 (30% of the time) and do 1d8 +  1 (avg 5.5 HP) per hit. Over 10 rounds, that average is 16.5 damage.

AD&D L1 Fighter vs. AC 0 [20]:
The level 1 fighter (+0 to hit) with a 17 STR (+1) will hit an AC 0 [20] with a 19 (10% of the time) and do 1d8 +  1 (avg 5.5 HP) per hit. Over 10 rounds, that average is 5.5 damage.

D&D Next L1 Fighter vs. AC 15:
The level 1 fighter (+1 proficienct) with a 17 STR (+3) will hit an AC 15 with an 11 (50% of the time) and do 1d8 + 3 (avg 8 HP) per hit. Over 10 rounds, that averages to 40 damage.

D&D Next L1 Fighter vs. AC 20:
The level 1 fighter (+1 proficienct) with a 17 STR (+3) will hit an AC 20 with a 16 (25% of the time) and do 1d8 + 3 (avg 8 HP) per hit. Over 10 rounds, that average is 20 damage.

Level 5  

Note: D&D Next Level 5 Fighter gets 2 attacks per round.

AD&D L5 Fighter vs. AC 5 [15]:
The level 5 fighter (+4 to hit) with a 17 STR (+1) will hit an AC 5 [15] with a 10 (55% of the time) and do 1d8 +  1 (avg 5.5 HP) per hit. Over 10 rounds, that average is 30.25 damage.

AD&D L5 Fighter vs AC 0 [20]:
The level 5 fighter (+4 to hit) with a 17 STR (+1) will hit an AC 0 [20] with a 15 (30% of the time) and do 1d8 +  1 (avg 5.5 HP) per hit. Over 10 rounds, that average is 16.5 damage.

D&D Next L5 Fighter vs. AC 15:
The level 5 fighter (+2 proficienct) with a 17 STR (+3) will hit an AC 15 with a 10 (55% of the time) and do 1d8 + 3 (avg 8 HP) per hit. Over 10 rounds, that averages to 88 damage with the extra attacks.

D&D Next L5 Fighter vs. AC 20:
The level 5 fighter (+2 proficienct) with a 17 STR (+3) will hit an AC 20 with an 15 (30% of the time) and do 1d8 + 3 (avg 8 HP) per hit. Over 10 rounds, that average is 48 damage with the extra attacks.

Level 10

AD&D L10 Fighter vs. AC 0 [20]:
The level 10 fighter (+8 to hit) with a 17 STR (+1) will hit an AC 0 [20] with an 11 (50% of the time) and do 1d8 +  1 (avg 5.5 HP) per hit. Over 10 rounds, that average is 27.5 damage.

D&D Next L10 vs. AC 20:
The level 10  fighter (+3 proficienct) with a 17 STR (+3) will hit an AC 20 with a 14 (35% of the time) and do 1d8 + 3 (avg 8 HP) per hit. Over 10 rounds, that average is 56 damage with the extra attacks.

Analysis


One thing I did not take into account in the last post was the strength bonus. I forgot that the early editions of D&D gave stat bonuses only to the very top tiers (17+). The strength bonus makes a significant difference in the to-hit probabilities, so even though the attack bonus progression is smaller in 5th Edition, the stat bonuses more than makes up the difference. At low levels, the 5e Fighter is much more capable than his AD&D counterpart due to the stat bonus alone. At level 5, the AD&D fighter's attack bonus catches up with his 5th Edition cousin, but the extra attacks granted to the 5e Fighter doubles his average damage output.

As the Fighters progress to higher levels, the AD&D attack bonus will eventually out-pace the 5e bonuses, but the damage output delta is still so significant that the AD&D Fighter's damage curve falls far behind. As one G+ user noted in the comments, a D&D Next Fighter will hit a high-AC monster less frequently, but when he does, that monster explodes (if using the old school HP / stat blocks).

Conclusions

In the prior post, I supposed that it may be workable to use the old school stat blocks with 5th Edition with a few additional caveats -- HPs will be too low and the GM will have to on-the-fly house rule saving throws since early edition monsters do not have attributes other than INT. 

However, when looking at the damage output more closely, it is more apparent that, even if the older edition has higher armor classes across the board (which is still uncertain until Basic D&D monsters are released), AD&D monsters look like they will be too squishy for 5th Edition PCs. We will have to wait until the PDF includes the Bestiary or the Monster Manual is released to use any of our old modules because it seems one will have to swap in the stat blocks for 5th Edition for our older AD&D and OSR adventures. I am also very curious as to what other compatibility advice will appear in the Dungeon Master's Guide.

That's going to hurt.
In terms of encounter design, it seems like the numbers may be OK as long you use 5th Edition stats. The challenge level of 4 Kobolds in AD&D will likely be similar enough to the challenge of 4 Kobolds in 5th Edition that it won't matter... Will the challenge of 4 Ogres be equivalent? Or 2 Owlbears? That's a little less clear, though it does appear that the designers are looking to allow DMs to use the vast majority of their old gaming materials. High level play will likely be the place where the encounter challenge has the most swing. Anything in the first 10 levels is likely to have a much smaller variation in terms of challenge rating.

From the old school perspective, encounter balance is not a touch stone of play. Every encounter can potentially be much deadlier than the PCs are ready for. What matters is that the players have the opportunity to observe their adversaries and make an informed decision on whether to engage. If they do not take those precautions, there is no guarantee any melee will be a "balanced encounter"... and this is how it should be.

If anyone has some additional power curve examples like the ones I outlined above, please share them in the comments.
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