Trade Skill Yield Formula

A lot of you probably weren't here for my packet-to-boon calculation post, so I'll go ahead and restate this: I'm a huge geek, and I kind of like math. That being said, I thought some of you would be curious what formula I'd be using for downtime trade skill yield. As I said, this is a big sign saying, "Warning: Math Ahead." All you really need to know is that the higher your rank, the higher your yield every time you use a trade skill. The specifics are only for the curious.

For those brave souls still reading this, then, here is the formula I'll be using for trade skill yield:

F(r) = 0.02r^2 + 0.05r + 0.25

This returns the standard yield for a trade skill at a given rank. For example, if you have rank three Herbalism, your standard daily yield will be (0.02 * 3^2 + 0.05 * 3 + 0.25 = ) 0.58 gold pieces worth of herbs, or about one common herb per day. Those of you who remember your calculus will note that this is a mild quadratic curve, so the increase in yield grows larger with each rank.

Beyond the standard, I also intend to randomize the yield a bit. Production skills, which are more reliable, will generate from 85% to 115% the standard with each use. Gathering skills, which are a bit more random, will generate from 70% to 130% the standard with each use. Thus, the herbalist in the above example would generate between 0.406 and 0.754 gold pieces worth of herbs each day.

In case your head isn't spinning yet, here's another twist. Plot will be able to create world conditions that affect the yield of any trade skill they choose. For example, maybe town decimated the local dryad's grove, burning plants and corrupting the wildlife. Thus, until the situation is rectified in play, maybe all Herbalism is at 50% yield. Our poor herbalist would be reduced to 0.203 - 0.377 gold pieces worth of herbs per day. Just as an example... ;)

As I'm speccing out the system, I have plans to allow players to queue up daily as well as weekly trade skills. This doesn't matter much for production skills, which just accrue a straight gold piece value worth of production. Gathering skills, however, will stand a much better chance of getting uncommon and rare components with longer outings. Other than that, it's just a matter of convenience; sometimes you don't want to queue up the same trade skill seven times to fill the next week before the game.

I also plan to retain any remainder on gathering skills. For example, if you generate 0.61 gold pieces worth of herbs one day but only get a single common restorative herb (worth 0.6), that 0.01 remainder will be carried on to subsequent gatherings until it is used. You won't be able to see this, of course, but rest assured that you won't get jipped on your yield in the long run compared to production tradesmen.

That's the jist of it. I've got a lot of work to do to make it happen, but this should give you all an idea of what it will look like. Thoughts? Opinions? Tears of joy that the magic website will be keeping track of all of this instead of you?