A Theory of Small Steps

"I won't get that item, it's only a few more attack power."
"Why do I need epic gems? Nobody died when I healed with blues!"
"I'm not moving from the lightning because I can easily heal through it."
Who hasn't heard things like the quotes above in their World of Warcraft career? The idea that little improvements don't matter is widely spread. I realized this the other day when discussing the merit of the Tuskarr's Vitality enchant on boots with my guildmaster. WoW is a game of small steps and far too many people don't realize it. I will discuss the importance or unimportance of small steps in four cases below: Continuous improvement, improvement in discrete steps, improving the random number generator, and futile improvement.

Continous Improvement
The importance of small steps is easiest to understand when looking at a statistic that can be improved continuosly. A rogue's DPS increases with attack power¹, for example, so clearly gaining a lot of AP is desirable. The total amount of AP a rogue has consists of many smaller amounts of AP - some on every piece of gear, some from enchants, gems, buffs, consumables and so on. Each one of these parts may seem insignificant, but together they are what makes or breaks your DPS. Eschewing one of these parts - such as not using buff food - will only reduce your DPS by a little bit, but if you would use the same reasoning for all small steps you would do no damage at all. If you are operating on a tight budget, some steps may gain you more AP for your moeny than others and you should obviously get those first - but in the end there is no improvement that is to small to care about. None.

Quantized Improvement
There are many cases in which small steps don't create direct results. A tank with six more stamina will likely still die the same amount of times as if he didn't have that stamina. Increasing raid DPS by one percent won't kill the boss that always wipes you at ten percent. Increasing the healing output may have no effect if no one dies anyway. In these cases it is easy to dismiss improvements as irrelevant - in many cases they are not, however. If enough small improvements add up, they will push you over the edge, so to speak. Six stamina aren't a lot. But if you get another six in a few other places, get an armor buff and the priest's shields are pushed to slightly higher absorbtion you will suddenly find yourself surviving a hit that you wouldn't have survived otherwise - possibly turning a wipe into a kill.
As a healer it seems so obvious that there is no need to improve if nobody dies, or if you always wipe to a lack of raid DPS and not healing. If you think about it though, you will find that if your healers improve enough (one small step at a time) you will find yourself in a position where you can cut one healer from your roster and bring a DPS instead. Once again, small improvements alone might not change a thing, enough of them will help in a big way.

Playing the Random Number Generator
During the discussion and theorycrafting about Tuskarr's Vitality it was brought up that time saved is not increased DPS for a caster unless it allows them to cast a full additional spell. i.e. if you save only half of a fireball's cast time while running you won't get any extra DPS, therefore runspeed doesn't improve DPS. Once you look into detail here, you will see that there are indeed cases where the saved time doesn't get you an additional cast. It is also possible that it enables you to get one more cast in that you wouldn't have otherwise - even though you saved only a fraction of the cast time. If additional runspeed gives you time for 1/10th of an additional fireball then in 9 of 10 cases you won't get anything. In the 10th case you will get a full additional fireball. On average you gain 1/10th of a fireball every time, a continuous improvement even though reality only allows for discrete steps.

When Small Steps Fail
I believe in the power of small steps, in fact I'm pretty sure that they are what creates improvement in World of Warcraft. There are some cases, however, where a small step just isn't worth taking. We had a time where, due to summer issues, we spent quite some time each week on actually killing XT-002 Deconstructor's hard mode in 25 men when we should actually have been progressing on Thorim's hard mode. Tuskarr's Vitality is clearly superior to Icewalker on Thorim but it's arguably the other way around on XT. Improving our XT performance would clearly have increased the time we had on Thorim and it is out of question that a small step that takes us over the edge on XT would have had a huge effect on Thorim, even if we had to give up a little Thorim performance for it.
That said, our wipes on XT were really bad ones due to raid composition and there just weren't enough small steps that we could have taken in order to accumulate to any effect². If you have a case of quantized improvement but the available small steps just won't let you make the needed big step then they are, in fact, useless. I would say that in an unlimited timeframe there are always enough small steps to take to finally make the leap, that is what progression nights on bosses are all about. But if you have a limited time frame (summer in this case) after which the problem will be solved either way, and you are sure that small steps won't get you there in the meantime, then don't bother. (That is, if the small step gives you a disadvantage somewhere else. If the small step is a general improvement, still perform it of course!)

Conclusion
While there are a few cases where small steps will indeed not help you in any way, shape, or form, generally small steps are what eventually gets you to your goal. No improvement is too small to matter as the cumulative effect is what WoW is all about. Not using an advantage, no matter how small it is, hurts your chances of success.

Small note on the side
One small step you may not have noticed with 3.2 is, that using 2 hybrid spellpower gems gives you one more spellpower compared to using the respective 2 pure gems. i.e. 2 Reckless Ametrines gain you 24 sp and 20 haste while a Runed Cardinal Ruby and a Quick King's Amber only gain you 23 sp and 20 haste. Yes it's only 1 sp. It's still a waste of a small step not to take advantage of this if you can.

Many thanks to Maurice and Zorander for having the discuission about run speed with me - that really created the foundation for this post!


¹ I am aware that other stats than AP may be better for rogues. Please bear with me for the argument's sake.
² One may argue whether there really was no way to get enough improvement in this case or not. The point is that small steps don't matter if, and only if, there are not enough of them to take for success.