Is there a way to change the math to get rid of the increasing value of a +1?

[Devils_Advocate]

All bounded accuracy is is that DCs don't increase as you level up. Which, to me, seems like a no-brainer.

It strikes me as a simple enough approach to preventing characters from succeeding at something "too often" even with high bonuses. You and others have been discussing frankly needlessly mathematically convoluted methods of accomplishing just that. And to what end? Even in a case where 1/20 of a success per roll is more beneficial the higher your odds of success already are, min/maxing is balanced by cost.

The great thing is, that doesn't even require a specific formula like 3E's quadratic bonus pricing. It only requires that different bonuses to the same thing have different costs per +1. That way the cost to pump up a modifier even higher goes up as the low-hanging fruit is exhausted and options become more expensive. In that context, it makes perfect sense that a Cloak of Protection and Ring of Protection have different rarities. Having unequally obtainable equal enhancements makes it harder, but still possible, to get better at something the better you are at it. So, to the extent that that's desirable... well, great!

But what really raises opportunity costs is that 1/20 of a success per roll is likely to have diminishing returns in most cases anyway. Let's consider a lone Tank, who doesn't have to worry about his allies getting attacked instead of him. The higher that character's AC, the more likely that enemies won't do things that AC helps against. They might use other attacks instead. They might run away! In some cases, that might qualify as victory, but in others it could be super bad. The Tank could wind up not being able to stop a minion from escaping to tell his crazy powerful boss about him because he went for endurance instead of speed. Oh noes!

I understand wanting to put all of your eggs in the best basket, but that's not always the best idea. Heck, even in optimizing for a particular type of roll, there can be different paths to the same result. A penalty to your enemy's attack roll is equivalent to a bonus to your AC, remember. Imposing disadvantage could very well be even better. If something only hits you on a 19, raising your AC by 1 reduces its hits by 50 percent, but giving it disadvantage on its attacks reduces its hits by 90 percent, plunging its rate of success below the normal 5% minimum.

This is an interesting read. Ideally the tank takes all the hits, but in practice it never works out that way.

Indeed. Intelligent beings on both sides of a fight will generally most want to attack the most vulnerable enemy, all being equal, and especially when the most vulnerable enemy is also the greatest threat (the whole "glass cannon" thing); and they'll also prefer to have the least vulnerable member of their own side attacked. I reckon that combatants generally have more control over who they attack, but also generally have more control over immediately obtainable information about themselves. Illusions are the fancy way to go, but even a small measure like a staff-wielding heavily-armored cleric wearing a robe over her armor in order to look like an unarmored wizard could fool enemies for a few rounds.

Shoring up the defenses of the weakest party members before that of the tank does seem like a more effective strategy. Whoever seems to consistently go down first is probably the one who needs an AC boost the most, which might be the tank, or it might be the wizard.

Yeah, I appreciate the straightforward empiricism of that approach. Someone in the MtG thread mentioned that "Theory is nice, but it's hard to argue with tournament wins". The same basic principle applies here. There's no real substitute for looking at how things actually work out in practice.

[stoutstien]

If you're looking for inspiration of a different way to handle action resolution there's a very rule lite game called mörk borg.
I found it interesting because it's built in a way that the DM never rolls dice unless they want to use a randomized table. It's an interesting spin on the d20 system.