Arcanaville

Incidentally, I should mention that long before I actually did the calculations, I had a decent idea what the results would be. In my opinion, the practice of numerical estimation is something that I don't think is taught enough (or at all) so as one of my pet projects, I'll go back and analyze my own prior assertion: why was it reasonable for me to assert SS had virtually no chance to outdo Staff on AoE *before* doing these calculations, which I actually only did in response to Combat's calculations. How did I know it was worth the time to double-check them, because there was likely an error or set of errors in them?

Well, this is how I looked at the two sets. Staff has three AoEs, SS has one. If you do attack calculations often enough, you start to notice that DPC - damage per second over a cycle - tends to be similar for most attacks. It tends to lie in the range of 0.15 - 0.21 for single target attacks, and about 1/2 to 1/3 of that value for AoEs depending on AoE factor, and most cluster even tighter than that. And that's because of the damage/recharge formula that makes higher damage attacks have longer cycle times in almost (but not quite) direct proportion. And actually, higher damage attacks tend to have higher DPA but lower DPC.

Anyway, because DPC isn't all over the map, three is going to beat one. However, FS has a ten target cap and only one of Staff's AoEs has the same cap: the other two have five target caps. So really, its more like a two vs one comparison. That's still double.

Of course, SS has Rage. But can Rage *double* the output of an AoE? Of course not. If you're boosting damage by +80% on something that has about 200% base damage with slotting, you'll really be boosting damage by about 40% overall. Not enough.

In fact, if we say that Staff has 100% and FS alone is then 50%, Rage should make that about 100 vs 70, 40% more than 50.

And guess what: the calculations say its 71%. I got a little lucky there, because the margin for error is higher than that. But I did not get lucky at all that the number was *around* 70%, because that's where the numbers had to land approximately.

That's guestimate one. Guestimate two then says there are two more factors overlooked: Rage's crash should cost SS an additional 10% (slightly less than that, but I'm guestimating here) and the fact that Staff can saturate an AoE chain at the recharge cap means SS will benefit a little more from that last stretch of recharge above 350% or so. By about 15%ish or so. Those two factors roughly cancel out, maybe boosting SS's numbers by 5%. So my guestimate #2 with those factors included would have been something like 74%. And the fact that guestimate 2 is very close to guestimate 1 suggests that adding in further smaller factors wouldn't budge that number by much.

The two guestimates roughly bracket the final number, which is not surprising. If someone told me SS calculated to be 80% of staff's AoE, I would have assumed that was reasonable. I might not have even double checked. 90% would have triggered a red flag. Over 100% basically demands a double check, even if the calculations were mine: the guestimate doesn't have that much margin for error. It would imply that Footstomp was a *spectacular* AoE and it can't be: not with 20s recharge and about 2s cast time, unless its damage had a really big typo.


Estimation is, I think, a very important skill for anyone doing calculations. Because really its very difficult to triple check every single calculation you do, and even when you do you might still make an error. I make them all the time. Most never reach the forums, because most of the worst of them set off a guestimation alarm in my head where the numbers come out wildly wrong. I'm sure anyone who calculated SS's AoE to be fifty times Staff would know something was wrong. Ditto ten times. Most people would know it can't be five times. But when you get down to 1x: many people would think that could be possible. A good estimator would know it wasn't very likely and would double check. A really good estimator would know even 0.9x was something worth double checking. For me, the limit would have been about 0.80. For me, that number was possible, but unlikely, and thus worth double checking.

For that matter, anything lower than 0.65 would also have been worth double checking, because even though that's still within the margin for error, claiming Staff was anything better than the gross estimation, or conversely that SS was anything worse than the gross estimation, would have been a dangerous assertion to make. It would not have been justifiable given the rough estimate, which means the precise calculations would have needed to be as error free as possible.


Everyone has made the calculation errors that Combat made, myself included. They happen. The important thing is to always be a little skeptical of calculations, especially your own, and to double check them against rough estimates which are going to be fuzzier but also by virtue of being simpler have less chance for a major calculation error. Without that sense of general estimation, calculation is wandering the desert without a compass. There's no way to know if you're heading in the right direction, and no way to know when you've reached the right destination.