Difference in indifference

We return to the indifference line. I’ll repost the imagine in the bottom of this thread for ease of reference and hopefully the puts it low enough that it doesn’t get blocked by the sidebar. [As an aside, I find the followers widget annoying. That is probably due in part to how it is sad and empty, but I don't subscribe to sites either. Most people I know bookmark sites they like instead of “Following” or RSS feeds. I’ll leave it if anyone cares, just shout out if you think it’ll do the site any good and it’ll stay.]

The greatest benefit on the graph occurs when we move horizontally or vertically. This should not be surprising because it represents a pure benefit (“I was +6, d8+4 and now I am +6, d8+5!”). For any spot on the graph, you want to move towards the indifference line traveling right or down. Once there, you are indifferent about continuing to move right or down; they’re both good.

This all describes offensive power acquisition. The opposite is true when acquiring defensive powers. That is, you want to move left and up with the same other rules (get to the indifference line, then move horizontally or vertically). Left means you are reducing the expected damage taken, either by having Resistance or reliably having temporary hit points.  Up means you are reducing their chance to hit.

Diagonal movement is much more interesting, especially when it cuts perpendicular to the indifference line. That movement includes a benefit and a penalty which allows us to provide a smaller, but still worthwhile, benefit. Because D&D is tied to integers, there are only so many plusses you can give out before the math is broken. Moving diagonally expands your set of options.

If my big takeaway was that -2 attack for +5 damage is a more nuanced benefit than +5 damage, I’d be sad. What I actually learned from this graph is that the tradeoffs are too complex and too varied by starting place for me to think I can actually manage all of them. Third edition especially introduced options that made it possible to trade resources to move in any direction on the graph. Sometimes those resources were feats, sometimes spells, magic items, whatever. You could move around really easily and that let optimizers optimize really easily. I’m not smart enough to not accidentally introduce all those same issues. I am smart enough to recognize that, though, and begin putting in safeguards to protect myself from... myself.

As a result, most powers that allow you to reliably (that is, often or reliably) move on the grid will move you perpendicularly to the indifference line. This won’t be true of base powers intended to get characters into the basic range of power, so casual players will easily produce effective characters. Optimizing players will have the opportunity to push away from that general zone, and will be rewarded for it, but only so far. The idea is that by continuously forcing optimizing players to trade a finite resource for another, eventually it stops being a bargain. Earlier editions let you trade either resource and, all too often, you could trade both against each other and somehow wind up ahead. All of 3e was one big arbitrage exercise; Goldman Sachs owned 3e.

Here’s how it would play out in a simple example. Say you have a starting point of 100% chance to hit for 10 damage. An opportunity exists to trade one attack for two damage. Here are the payouts:

To hit	Hit dmg	Expected dmg	Gain
100%	10	10.0	0
95%	12	11.4	1.4
90%	14	12.6	1.2
85%	16	13.6	1.0
80%	18	14.4	0.8
75%	20	15.0	0.6
70%	22	15.4	0.4
65%	24	15.6	0.2
60%	26	15.6	0.0
55%	28	15.4	(0.02)

Imagine that each of those steps is a different effort to optimize. Each incremental effort pays a diminished payout because it cuts away at all previous payouts. The two damage for one attack remains a “profitable” trade on its own, but became punitive because the optimizer isn’t trading on just his decision to swap two damage for one attack, but also all previous optimizations. Here is the same set of tradeoffs made by a different player who began at 100 damage instead.

To hit	Hit dmg	Expected dmg	Gain
100%	100	100.0	0
95%	102	96.9	(3.1)
90%	104	93.6	(3.3)

Right out of the gate he finds this strategy to be punitive because he is already too good. For the casual player the first few steps of optimization come really easily and they get to be a little more competitive. The tactical player, though, has already gotten the easy stuff and has to grind each incremental step. By ensuring each incremental step is made up the same big-ass hill, you can ensure it is consistently challenging as well.