Linear versus Exponential Progression

The past few days I've been playing Clicker Heroes. Well, "playing". Like Cookie Clicker before it (or even earlier, Candy Box), the game is entirely about finding the most efficient path to getting bigger numbers. It is literally just progression and nothing but. Buy things to automatically do more DPS, which kills enemies faster, to get more money, to buy more things to automatically do even more DPS. It's totally ridiculous, yet it triggers some number-happy portion of my brain.

According to the legend on the right, I currently have 1,162 Quintillion Gold, or 1,162 x 10^18, or 1,162,000,000,000,000,000,000 gold.

To make the game mechanics work, all of these clicker games use exponential progression. It's pretty similar to how WoW does progression these days as well. The pro of exponential progression means that you absolutely must get the new tier's worth of gear to really make a dent in the next tier of content, allowing developers to easily put a stat/gear cap on progression.

In Clicker Heroes, I can't really wail away at level 97 using heroes that only gives me 1 Million DPS, not when enemies have 350 Quintillion health. That would take me over 31,000 years! Or in WoW, you can't use gear from TBC to defeat bosses from Cataclysm. Heck, it's difficult or impossible these days to hit the next tier of content with gear from the previous (i.e.: jumping straight from Heroic ToT to Heroic SoO and beating it completely without any SoO gear at all)

WoW's power curve, from my own calculations nearly a year ago.

It also means you really feel upgrades. Every upgrade feels weighty and like a huge difference to how powerful your character is. Contrast that with a linear power curve, and upgrades become less noticeable over time.

For example, imagine if you had 50 Strength and you find a set of armor that between all the pieces increases your Strength by 10. That's a 20% increase in power, and you'll feel that. But imagine the second set of armor only increases your Strength by 20, 10 more than previous. That's only a 16% increase in power from the previous set of armor (60 Strength + 10 more, versus 50 Strength + 10). Now imagine 5 tiers later, and you have a set of armor that again only increases your Strength by 10 over the previous tier. That'd only be a 9% increase in power that tier (110 + 10). Basically, the more tiers you have, the less each individual tier actually increases your total power.

But there are cases where a linear power curve is handy. If your system uses small numbers, like Paper Mario, an exponential power curve isn't going to be helpful. Or if you purposefully want the differences to be small. Look at D&D 5th Edition, for example:

The difference between a level 1 character and a level 20 character using a skill they're proficient in is only a difference of about +5 to +7 total once you take into account attribute boosts and proficiency bonus boosts. At best, a level 20 character can be twice as good as a level 1 character. Since everything is rolled on a d20, you're looking at values of 5 - 25 or so for a level 1 character, or 12 - 32 or so for a level 20 character. It allows lower level characters the chance (albeit small) to do really heroic things, and gives the level 20 character the chance to still fail at moderately complex tasks (rather than always succeed).

It also all depends on the scale of what you're building. If you expect a really long power curve--like in an MMO--exponential might be a better choice because of that diminishing returns on linear. But if your curve is relatively short, a linear curve is quite easy to balance and maintain.

Both are useful depending on the scenario, just like any other tool in a game designer's toolkit. Either case, you can balance encounters and enemies around them, and they'll feel relatively similar in the moment, but it's all about how things should feel if you're going backwards (or jumping ahead!) in content. Should a high-level character be defeatable by a mid or low-level character? Should even mid-level enemies potentially provide a challenge? Or should you only be able to be effective/balanced within a given tier of content? That's all up to the designer and how you want your game to play/feel.

#DesignExperiment, #DnD, #WoW