# Monthly Archives: April 2010

Every week, I find myself spending some time checking out the newest interesting-looking flash games on Kongregate. Most of them end up not being so interesting, but every once in a while I come across a well-done innovative game (Level Up! and Little Stars for Little Wars are two that seem to be memorable at the moment). But I also get a chance to see the same games made over and over again in different skins.

You know, I don’t have that much of a problem with the same game being made over and over. It’s like speciation, this game is randomly varying itself on the little choices to find what works best. What annoys me is when I see a bad decision repeated again and again, for which the only reason I can think is convention. Today I will discuss the top such bad decision on my list: upgrades.

Upgrade systems are becoming quite ubiquitous among flash games. Play the game for a while and accumulate points, then spend the points on upgrades to make yourself more powerful. Upgrading yourself and feeling your power increasing is a great feeling, and providing a choice of which upgrades to buy allows the game to (ostensibly) diverge into many different games with unique dynamics, depending on the player’s choices. However, there is a common design that stifles this divergence.

Let me explain with a typical example. You start with a ship that has everything in level I. Between battles, you may level up one of three tracks — Guns, Engines, or Shields — according to the cost matrix below.

 Guns I, 5 damage Guns II, 10 damage (+100%), $100 Guns III, 15 damage (+50%),$500 Guns IV, 20 damage (+33%), $2500 Engines I, 1 m/s Engines II, 2 m/s (+100%),$200 Engines III, 3 m/s (+50%), $500 Engines IV, 4 m/s (+33%),$1000 Shields I, absorb 2 damage Shields II, absorb 3 damage (+50%), $400 Shields III, absorb 4 damage (+33%),$1600 Shields IV, absorb 5 damage (+25%), $6400 I have added a percentage, roughly estimating how much more badass you will be after acquiring each upgrade. For independent gameplay elements, upgrades usually increase your strength by roughly a factor (as opposed to a constant): if you make yourself shoot three times as fast and also shoot three times as many bullets, then you will be nine times more powerful. In this post, I am addressing the particular way the prices are distributed. Their cost always seems to increase geometrically along each track. Sometimes, as is the case here, returns (expressed as factor of increase) will also diminish along a track, sometimes they will stay constant, but they seldom increase. So let’s say I’m the kinda guy who likes tanks: slow with lots of firepower. In my first two turns I have invested$600 into firepower, and now here are my choices:

 Upgrade Cost per % increase Guns IV, +33%, $2500$75 Engines II, +100%, $200$2 Shields II, +50%, $400$8

Comparing the cost/benefit ratio in the second column, engines appear four times better than shields, and shields appear eight times better than guns. Guns are a terrible investment, and will remain so until engines and shields are also at level III. This upgrade system only enables multiple styles of gameplay for people who are terrible with their money (aka people who are playing far below optimally) — shrewd investors will notice that the right strategy is (rougly) to get everything of level II, then everything of level III, then everything of level IV: getting uniformly stronger throughout the game, rather than specializing to one style.

I can imagine this convention emerging by deciding that upgrades are bought with points before considering the consequences. After the decision has already been made, the designer observes that as you get more upgrades, it becomes easier to get the same number of points. Therefore, upgrades had better get more expensive throughout the course of the game, otherwise it will either be way too long before you get your first upgrade, or you will finish them all off too fast.

Another way of phrasing that is: to achieve an upgrade system that encourages diversity and specialization, you have to discard the assumption that upgrades are purchased with points (or somehow design around an increasing rate of point gathering, but that’s no fun because people like to see ever bigger numbers). As an alternative, I suggest separating scored points from upgrade points. Award upgrade points by time (say, one at the end of each level), or by the inverse of the typical point-acquiring growth rate. For example, let’s say each upgrade adds 1 to the multiplier. Every point the player gets is multiplied by the multiplier first and then added to his score. So, assuming for simplicity that he gets one point in between each upgrade, his score as a function of the number n of guys he kills will be $\sum_{i=1}^{n} i = n (n+1) / 2 = O(n^2)$, and you should award upgrade points at quadratically increasing scores1, say 100, 400, 1600, 2500, 3600, ….

After you have this corrected upgrade points currency, assign each upgrade a cost in the same order of magnitude, no matter how deep it is in the tree. Then the player will have a bunch of choices which are all approximately equal according to the first-order cost/benefit analysis, and to pick the right one, he has to think about (gasp!) what they actually do!

1 I have a beef with Geometry Wars 2, which uses the aforementioned multiplier system, because extra lives and bonuses are awarded at exponentially increasing scores. The ratio of an exponential to a quadratic is still exponential, so it gets exponentially harder (essentially impossible after a point) to get bonuses throughout the game. I have an incling that the designers did not realize this, probably due to a common incorrect perception that any superlinear function is “exponential”.