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Game Design: Geometrics vs Fibonacci!

Published on 2013-09-20, by in Game Design.

So I was on a phone interview for a cool company the other day. And towards the end and off the cuff, almost like a last parting thought as we’re about to finish up the interviewer says “Oh btw I was on your blog and wanted to find out why do you like Fibonacci for progression instead of say Geometrics.”

And it really caught me off guard, not because I had never thought of it before, I actually had, I just couldn’t remember what that reason was when asked out of blue so suddenly. So I thought this would be an excellent follow up to my previous Game Design posts You are a Game Designer – So what do you do? and Game Design: Creating A System Formula – 101

So as a quick refresher Fibonacci series is when you add the previous 2 integers to get a new integer. Fibonacci series by definition starts with 0 and 1. Which leads to 1 2 3 5 8 13 21… and so on. In game design I rarely start with a 0 and a 1, it makes sense in nature (flowers, pine cones etc) but for gaming there is rarely a reason to start at 0 or with two 1’s. Instead we might start with say 10 and 25. Which leads us to  35 60 95 155… and so on.

Geometrics on the other hand are when you multiply a predetermined number (called the common ratio) for example 2 4 8 16 32 64 is a common ratio of 2. 100 50 25 12.5 has a common ratio of .5. I use Geometrics in game design a lot. It’s easy to setup in excel, you can get large effects from minor decimal places. It gives a very smooth progression curve which means it’s steady and easy to predict. Fibonnaci on the other hand quickly spirals out of control (pun intended). It starts off very mild but then the distance between integers quickly ramps up out of control.

Arithmetic progression is simple to understand and arguably the most useful. Just add each number by a predetermined number. For example 1 3 5 7 9 11 has a common difference of 2.  Geo and Fib have a tendency to “get out of hand” at some point. So when making a long list of some kind Arithmetic progression or at least an Arithmetic base is generally preferred.

So why would we ever use Fibonacci instead of using Geometrics?

Photo credit: http://www.mathsisfun.com

Big chunky gaps.

Oh wait that doesn’t make enough sense to anyone else but me right? See  I don’t imagine it as a smooth spiral (which is probably what most people think of when they think of nature examples of Fibonacci) instead I see a big line up, then a line sideways, big line up, then sideways. I can picture it like a jagged spiral but what’s important to me are those long plateaus. Compare this vision with a line graph of a steady arithmetic progression. A nice straight line. Oh how dreadfully boring.

So the Fibonacci series gives us these ever increasing gaps or plateaus. Now we can’t always use this type of progression, for example damage and health it might not fit well. But it’s great for other things like XP leveling up or the cost for territory expansion. The reason being is it can start with relatively small (“fast”) numbers but eventually leads to long comfortable (“slow”) areas. These areas are places where we can plan for the players to begin slow down in their lifecycle.

Take for instance a game like DnD3.5 The basic handbook gives player levels up until about 20 or 40. There are also books that give Prestige classes and levels for players above 20 or 40. But there is a metagame phenomenon not described in these rules or charts. You see once the Player Characters reach a certain level they can reliably deal very high amounts of damage, buy really expensive gear and most notably have easy/constant access to flying. This makes it very hard to create balanced, fun and challenging levels for them to play on. How do you create interesting rooms and maps with varying heights that matter, when the players can readily break the laws of physics and fly, tunnel or walk through walls with little or no difficulty? This creates a sort of “sweet spot” in the leveling lifecycle, that sweet moment when you are powerful but not too powerful. A place or range in the leveling system where players feel much stronger than when they first started, but are not over powered yet (also known as “broken” because they are breaking the supposed boundaries of the system).

In this regards it becomes desirable to limit the players progression speed but without actually stopping them from progressing. For instance in the real life MMO or DnD “Living Campaign” Greyhawk characters must retire when they reach level 16. Having this level cap means that adventure makers don’t have to deal with anyone overpowered. But because of this shelf life for their character players began to do a very odd but useful thing… Players would begin multiclassing at levels 10-12, because of the XP penalty built into the DnD system for multiclassing, now they could play their character long and in more adventures before being forced into retirement.

Thus I propose the use of Fibonacci series as a good system for creating XP leveling guidelines. We want to identify and prolonge these “sweet spots”  and give the player time to enjoy them. This is preferable to a “Level Cap” (A common technique in online MMO’s) because the player is never prevented from progressing. It’s important to not deny the player a chance to progress, because we want players to feel rewarded while playing our games and a sense of progression is a great reward.

Thank you so much for reading. Can you come up with some reasons or places to apply a Fibonacci based progression system?

Bud Leiser

Game Designer

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