What would a diminishing returns mechanic look like for a d20 system?

[Greywander]

As you may know, d20 systems tend to have the opposite of diminishing returns, where each +1 actually gets stronger the higher the value gets. This can be easily demonstrated with AC (which is a nice bit of foreshadowing for later in this post). If an attack hits on an 11, that's a 50% chance to hit. +1 AC takes that to a 45% chance to hit, or a 10% reduction in the number of hits taken. If an attack hits on a 19, that's a 10% chance to hit. +1 AC takes that to 5% chance to hit, a 50% reduction in the number of hits taken. How would you turn this around and make each +1 less valuable the higher the stat got?

The specific context is that I'd like for a character to have adequate AC either by being lightly armored with high DEX, or by being heavily armored and ignoring DEX. But the thing is, I'd still like being heavily armored with high DEX to be better, but only slightly. I don't want to just add your DEX mod to whatever your armor's AC is, as that would make AC too high. The way vanilla limits DEX to AC with heavier armor feels very arbitrary and artificial, and means there's little benefit to having high DEX if you're already wearing heavy armor. Instead, I'd like to see something where DEX can still add to the AC of heavy armor, but AC has some kind of natural diminishing returns built in.

So, how would you change a stat like AC so that it had diminishing returns? Because the best I can think of right now is to pick an arbitrary value and say, after this point, you need two +1s to actually increase your AC by 1, and then after another point you'd need three +1s get increase it by 1, etc. And that just doesn't seem very elegant to me.

[MrStabby]

Well things like critical hits might count - on a certain roll something hits automatically so AC makes little difference. As your AC gets higher and higher a higher proportion of hits will be critical hits. If your base critical chance in a system is something like 15% (18+) then this could start to be a big deal.

You would get to the point where an extra point of AC would mean little to very low level enemies, more to enemies comparable to your level and then less again to higher powered enemies.

This by itself is probably not enough for diminishing returns but as an element of a broader system it might help.

Something radically different I remember from the old board game Blood Bowl. There was a system there where you got a benefit if you were stronger than an opponent then a second tier of benefits if you were at least twice as strong. So maybe if something like strength giving you a bonus to hit if above an armour score, and a further bonus if more than twice the score, and a penalty if less than the score...

[awa]

3rd edition sorta kinda does that already, as +2 armor is more than twice as expensive as +1 armor. Further doubling down on a single defense does not help when there are things like touch attacks/ ways to get flat footed, or effects that target saves instead. Thus over focusing on ac leaves you vulnerable by virtue of having less resources to spend on other defenses.

I run a home brew system though it is a d20 system and one way it uses diminishing returns albeit not for ac is in stats. The game runs on a point buy system and most stat increases just give more points for the point buy rather than a static number increase. Combined with the fact that all stats are useful for all characters means that most players would rather shore up a weak stat then pay for the very expensive maxing of a stat.

Porting this over to say d&d this means that a magic item to increase your best stat is extremely expensive but one to improve your worst stat will be pretty cheap.

[Dienekes]

Honestly, I wouldn’t aim for AC and instead hit the ability scores.

Let’s say a
10=0 bonus
11=+1
12-13=+2
14-16=+3
17-20=+4

Putting 2 points in Dex becomes very good for your AC, but slows down after that to the point it might be more useful to put points elsewhere.

After that, if you want to hit AC directly, I’d just make a straight “no AC bonuses stack after Dex and armor (and maybe shield, could maybe do something pitting Dex and shields against each other).”

Then having the special bonuses to AC cost dramatically more for each additional point.

And then I’d straight remove the Shield spell.

Edit: on reflection I think this works better, as it gives motivation to get to 20

10=0
11-12=1
13-15=2
16-19=3
20=4

[PhantomSoul]

Honestly, I wouldn’t aim for AC and instead hit the ability scores.

Let’s say a
10=0 bonus
11=+1
12-13=+2
14-16=+3
17-20=+4

Putting 2 points in Dex becomes very good for your AC, but slows down after that to the point it might be more useful to put points elsewhere.

After that, if you want to hit AC directly, I’d just make a straight “no AC bonuses stack after Dex and armor (and maybe shield, could maybe do something pitting Dex and shields against each other).”

Then having the special bonuses to AC cost dramatically more for each additional point.

And then I’d straight remove the Shield spell.

Hm... and extending this, ASI increases actually give you point-buy points (optionally more frequently and certainly with the ability to save them for future ASI increases), and the point-buy table gets extended to 20 (optionally higher) with a cap on how high a starting stat can be. Then the curve is wholly in stats (which frankly could have a greater effect in calculations to then increase the curve steepness).

[MrStabby]

Thinking about this, I think the key element of "diminishing returns" is what the reutrns are diminishing relative to. Part of getting this right must be having other attractive options. I thingk that in this context it is as much about flexablity as about focus.

So imagine you have a simple attack action for a "fighter" class. It uses your primary stat. If you are doing that on 80% of your turns, you need something pretty sweet to compete with something that boosts that. Now if we were to ensure that the class had abilities like "intimidate", "feint" or similar thematic abilities that both needed other stats but also targeted different defences, then diminishing returns are kind of made real by having some good alternatives to invest in thatmakes you less one dimensional. Of course this also needs a design element for the antagonists - the best way to overcome a particular defence should be to circumvent it by chosing another avenue of attack, rather than just having ever bigger bonuses to brute force your way through it. Forcing a different save should be more efficient than doubling down on being really good at overcoming an enemy's strongest defence.

[Halrax]

For this particular example (AC w/ armor and Dex) 3.5 actually gave a bunch of options for increasing the maximum Dexterity bonus to AC with heavy armor (the materials mithril and Blue Ice, the Nimbleness armor enchantment, I think there was a feat for it?, some class abilities?) that were much more expensive than the armor itself (though they were also often used with really high Dex scores and light armor). You could easily homebrew these options into 5e or any other d20 system and have it be an opportunity cost, which naturally gets worse as it increases since the gold/feats/etc. could be used on other things that scale more. Though in general D&D is designed so that not only do you get more stuff as you level, but the stuff you do have gets better (though the gap isn't as pronounced in 5e compared to 3.x). Some negative feedback loops include point buy and ability score rolls getting more expensive/unlikely as it increases, items of a specific bonus having costs that scale quadratically, the same bonus not stacking, high level spells having expensive material components, possibly some others. If you're designing an original system, you might want to look into reverse negative feedback loops, which help those behind rather than hurting those ahead.