Tuesday, June 14, 2011

The indifference line

I have been spending a lot of time trying to figure out how to create a combat system with a lot of tactical opportunities so that tactically minded players can really delve in, but where more casual players aren't eclipsed. So far, I've found a lot of progress in two main areas of combat: removing tactical traps and ensuring that tradeoffs remain relevant across all actions during the turn. Both of these are best demonstrated through 3e examples, but the general principles apply equally to 4e.

Removing tactical traps
For players that love tactics and optimization, tactical traps are not an issue. They easily see through the trap and probably enjoy dodging them. But a lot of gamers are casual gamers who just want to show up and have fun and the designers should protect them from themselves (for lack of a better term). They shouldn't *have* to play the game in a way they don't want just because the game is riddled with problematic holes. Players should be able to trust that the options they are presented with are reasonable options. Tactical traps, then, should be minimized as much as possible.

The cleanest example of a tactical trap is 3e Power Attack at a 1:1 trade on attack for damage. Unless the character is high-attack/low-damage, the tradeoff is almost always a bad one. Even as high-attack/low-damage, the tradeoff is a bad one for most of the campaign once things like magic and specialization bring expected damage to a certain threshold. Moreover, the tradeoff becomes worse the more you invest in it. This is not to say that Power Attack didn't offer versatility, but it lured casual players into false beliefs that made them reduce their own effectiveness. One-handed Power Attack was rarely a good trade for most characters.

Let's prove this out a bit more. The table below has to-hit probabilities on one side and expected average damage (ave damage less DR or resistance) on the top. The red line down the center is  the indifference line or the line where +1 attack = +1 damage. To the left, damage is more valuable than attack. To the right, attack is more valuable than damage. The majority of the game is spent on the right side of the line, which means that for the majority of the game, the 1:1 power attack trade was a trap and the trap got deeper the farther right you went.

Before we go on, I'll explain the chart a bit more. The gray strip in the center is the zone where to hit probabilities are in general the most tense and most fun. This isn't to say that the game doesn't routinely go outside the zone, but, in general having to roll between a 7 and 14 to hit is an enjoyably tense range. The blue on the left shows the results of choosing between +2 atk and +2 dmg. From a base expected damage of 1.7, +2 atk brings us to expected damage of 2.0 while +2 dmg brings us to 2.8 damage. In other words, the incremental increase from +2 atk is 0.3 (2.0 less 1.7) and the incremental gain from +2 dmg is 1.1 (2.8 less 1.7) or about 4x as great.

The blue on the right shows the same choice but with opposite results. We gain 1.5 expected damage on attack and only 0.9 from the damage gain. The rate of return is reversed. The green squares highlight that at the indifference line, we are indifferent. One attack or one damage makes no difference.

So back to tactical traps. As the game proceeds, average damage increases as we gain magic items, specialization, higher stats, and more abilities. This pushes characters further right and makes the traps deeper. Tactical players get that they will eventually be on the right side of the indifference line and plan accordingly. Casual players don't and so we should help them out.

Relevant tradeoffs across all actions
The second area is that creates a gap amongst tactical players and casual players is that the tradeoffs are not consistent across all actions. Again considering 3e, the iterative attacks reside at very different places on the chart and so a mechanically sound decision for the primary attack is a woefully inept decision on the secondary or tertiary. Tactical players can maximize the output of the round as a whole, but casual players get lured into bad decisions to maximize the first attack at the expense of the others. This ends up with lower overall output and a bunch of time wasted on worthless attacks.

The easiest solution is to just make all attacks at the same modifier so they face the same tradeoffs (which also speeds up game play in general because the player is more familiar with a single number than multiple, can roll multiple dice simultaneously without having to designate which is which, etc). This is an area that 4e actually did pretty well.

What 4e didn't do well is provide a spectrum of tradeoffs that let a player familiar with their character quickly hone in on and evolve their strategy. In 3e, the fighter changed his Power Attack rate each round as he learned the opponents AC. The change was small and so was quickly resolved. In 4e, the players pick between different powers that trade substantial to-hit increase against substantial damage increases. Tactically minded players thrive, but casual players are now faced with a *more* difficult decision because the importance of the strategy has been exacerbated by making the differences in the powers greater. It is sort of an ironic twist that making things more distinct makes choosing between them more challenging, but it is understandable when you consider the complexity of the above table.

Longer than I intended, but I think understanding the indifference line is important for making combat that gives an edge to tactical players without making it too large an edge. I'll try and explore some ideas of how the indifference line can be used to build better combats soon.

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