Recently, I taught myself the compound interest formula again. I learned it in school, sure, but I’m not at a point in life where I’m managing investment portfolios or doing other calculations where compound interest comes in to play. It just doesn’t happen. However, I do like to kill goblins. I like to kill goblins a lot. Enter Dungeon Defenders, where I can harass three of my friends to get on Skype, we can build some defenses, and (this may be a shock) defend against waves of enemies. Various items spill forth from the cartoon carcasses when you dispatch the enemies, and a key mechanic in the game is upgrading these items to improve your ability to dispatch more enemies. (The cyclical, Skinner-box reward system here is not the point of this post; please ignore it.)

It was here, at the upgrade screen, that I noticed something. Every time I upgraded my chainsword’s damage, it wasn’t a flat amount. So the first upgrade would take me from 100 to 115, while the next would take me from 115 to 131. I started doing math. Very rough math. It looked like it was compounding at a 15% rate. So, quickly to the Google I go and find a compound interest calculator. I begin using this to decide what weapons are better or worse. Sure, my chainsword does 567 damage right now, but if I upgrade this cutlass 22 times and its starting damage is 46, will it eventually be better than the chainsword? Math had come to the rescue, and a kind of math that I don’t use often. Playing Dungeon Defenders has retaught me compound interest.

I wish I could stop there, but sadly I can’t. My calculations were becoming dramatically incorrect. The numbers, oddly, weren’t adding up. So I enlisted my fellow defender’s aid, and we charted our weapon upgrades. Low and behold! A trend! Any time the added value was greater than 80, the game capped the upgrade at 80! So this forcibly inserted a wrench in my formula, and now we had no idea what we were doing! We were lost in a sea of uncertainty! How would we ever decide what killed goblins most effectively? We’d use Excel, of course.

Enter the spreadsheet. I’m not sure how much you know about Excel, but it does all sorts of handy things. Such as if-then-else statements. So now I’ve got an Excel sheet full of things that look like this: =IF(B2*0.1475 >= 80,B2+80,B2*1.1475). Now you’re thoroughly confused, of course. “Daniel!” you shout, “that’s adding 14.75% instead of the 15% you told us about earlier!” I hate to say this, but I was wrong. It turns out that weapons don’t upgrade at a normal rate at all. In fact, weapons upgrade at rates unique to the weapon and/or weapon type. So we recorded more data to reverse engineer the equations the best we can, and by using an average we can predict a rough final value +/- 2% of the actual, which is close enough.

In some ways, this is the story about why I wrote the Dungeon Defenders Upgrade Calculator, but it really is about more than that. It is about ways that we should pick recreation that helps encourage us to keep our brain active and healthy, and trick us in to having fun learning things, promoting critical thinking, and making sure those dirty, rotten goblins keep their hands off our crystals.