I'm going to try to start a new series called "Concepts in Crafting", where I'll present, and try to elucidate, concepts that I think are fundamental to being a successful crafter. More importantly, I hope this will spur discussion, learning, and perhaps new discoveries on these topics.


Expected Value

you'll most often hear this concept referenced via "The Law of Averages". I use "Expected Value" (EV) here because it better describes the concept I'm discussing (The Law of Averages is related, but not quite the same thing). I borrow the term from poker theory, which probably borrows it from statistics.

consider a wager where you bet on a coinflip against a friend. If you guess correctly, you win $50 from her; if you lose, you give her $100. The EV of this scenario is -$25. Why? Well, obviously the only 2 possible outcomes of a single flip are that you a) lose $100 or B) win $50. However, when you flip 500 or 50,000 times, all those wins and losses will be played off against each other, and you will lose, on average, $25 PER FLIP. We calculate this by taking a weighted average of each of the outcomes:

hopefully I haven't bored anyone off with that intro, I know it's pretty basic. The thing is, crafting successfully is just as basic. Imagine you are trying to decide whether you should craft Amemet Mantles for profit. Assume that tier2 gives you 1/3 chance of HQ, each synth costs 90k, and NQs and HQs sell for 2k and 400k respectively. We'll ignore breaks. You perform the same analysis, IE:

so we expect to make 43k for every Mantle that we synth, even though the only possible outcomes are (ignoring breaks), HQing for a profit of 310k, or NQing for a loss of 88k. You have to pay attention to the long term.


this brings us to a related concept: Variance. Variance is basically a measure of how far you will deviate from your EV. In FFXIO, this will come from having a good (or bad) run of HQing. When you've gone on a hot streak, you may feel as if you're on top of the world, and start attempting any and all synths, looking for that big score. Instead, rein your emotions in and only choose actions that are +EV (positive expected value). Only by consistently and constantly doing +EV synths can you hope to be successful in the long run.


as an aside -- I believe that all crafters have had, and will get, lucky streaks. I think it was elowan who long ago pointed out that when you do a large number of synths, you will inevitably have long streaks of HQs and long streaks of NQs. This is just a less extreme case of the idea that when you do an infinite number of synths, you are GUARANTEED to have ARBITRARILY LONG streaks of HQs and NQs. What separates the successful crafters from the lucky ones is the ability of the former group to turn their luck into lasting profit. As I've said, everyone gets lucky, but we all know that not everyone gets rich.


so, applying Expected Value to your profit synths:
1. calculate the profit/loss on each possible result
2. calculate the likelihood of each result
3. take the weighted average of all results
4. choose those syntheses with positive EV

of course, if you only have time/materials/gil for a few syntheses, you should be choosing those recipes that have the HIGHEST positive Expected Value.

Corwen astutely notes that it's useful to think about EV as a percentage value in addition to an absolute value. You definitely want to balance these 2: too low an absolute value means you're wasting your time for small profit, while too low a percentage means you're risking too much to Variance (covered in more detail later on).


note that the Expected Value analysis only takes into account the profitability of the synthesis itself. Other factors like how quickly you can sell products and what you expect the price to be in the future are outside the scope of EV. Put another way, EV is just one of the tools in a successful crafter's repetoire.


next time, I'll probably expand on Variance and how it affects your crafting, and how you can help mitigate its effects.

This is a good post, and i have most of the times been working by these rules when i craft. The problem is often how to calculculate the expected hq rate.

For T2 and no subs, i have generally worked with 1/4 or 1/5 hq (i expect to hq 1/4 or 1/5). With these expectations i have profited a lot when i have bought materials accordingly.

In these less profitable times, i guess it is possible to stretch these expectations closer to 1/3, but profits will tend to be marginal.
(i guess there is no secret that i talk about ele staves :P)

Btw, i will be playing some this weekend. I may be out of work soon, so i want to try and see if i can get motivation to play again :)

too many different numbers are tossed around about HQ rates. Somet ime ago I grew tired of them and started keeping my own records. You can then use your own past rate to predict future profits, and if you do those synths, you can use those results to update your records.

I've even recently started to keep track of t0 synths (something I should've done a long time ago).

Well said post Odango.

And like Legolars, I usually only attempt T2 synths (like Amemets) when I can go 1/4 or 1/5 and still break even at the very least. Otherwise I just don't feel the risk is worth it since a "bad" crafting day/streak can hurt alot as I've personally experienced.

I've been slacking off as of late with keeping records, but I did kep track of the synths I did today which was rather informative.

Another thing to keep in mind, which I didn't see mentioned, you should also consider the EV as a percentage of profit. For example: A +10k EV on a 1 mil synth is not the same as a +10k EV on a 50k synth. One of these is a 20% profit, the other is a 1% profit, thus you are much more likely to get screwed from bad luck on the 1 mil synth due to variance in HQ rates as opposed to the 50k synth, thus I would much more likely want the +10k EV on the 50k synth as opposed to the 1 mil synth.