# Ranks Designed to "Flow" Part1  Lithium Alumni (Retired)

Hello and welcome back. It's been a while, so we'll review a bit throughout this article. Last time I described the concept of flow and discussed how it is governed by an individual's abilities and the challenges he encounters. I also talked about the connection between flow, gamers and superusers. In this miniseries of blogs, we'll apply this to optimize the ranking structure for your community. We all know that reputation matters. Here, we will show you the details that make it work.

Spacing the rungs of your ranking ladder

Previously, we discussed how games transport players into flow. A well designed game usually has many levels. with the difficulty between levels increasing slowly so that the gamers can easily find challenges that match their skills. By extrapolation, an engaging ranking ladder for the superusers should mimic the gradually increasing difficulty levels of a game. Although the ranking criteria may depend on any combination of metrics we collect, I will use the most common criterion, post count, as an illustrative example. A common mistake that many communities make is to use the convenient geometric progression as the post criterion for promotion to successive ranks. A geometric progression is a numerical sequence where successive terms are obtained by multiplying the current term by a fixed common ratio. For example, the post requirement for the first rank might be 10 posts, and then successive ranks require 20, 40, 80, 160, 320, 640, 1280, etc (blue ladder). Geometric progressions are terrible as ranking criteria because they grow very rapidly. In fact, the growth rate of geometric progressions is exponential! The example sequence above, with a common ratio of 2, grew over 1000 in just 8 terms.

So how should you space the rungs of your ranking ladder? There are two possible solutions. First is an arithmetic progression (a.k.a. linear progression), where the successive terms are obtained by adding a fixed value to the current term. For example, the first rank might require 10 posts, and then the higher ranks require 30, 50, 70, 90, 110, 130, 150, 170, 190, etc (red ladder). Because arithmetic progressions grow more slowly than geometric progressions, they are better suited for ranking criteria. However, because such ranking criteria are very regular, they may be too predictable to challenge highly competitive superusers.

If you want to challenge your superusers, I recommend using a sequence with a linear increment, where the difference between successive terms grows linearly. For example, the first rank might require 10 post, then subsequently, 30, 60, 100, 150, 210, 280, 360, 450, 550 etc (green ladder). Unlike the arithmetic progression, where the difference between successive terms is always 20, the difference between successive terms of this sequence increases linearly: (30-10)=20, (60-30)=30, (100-60)=40, etc. This sequence can be generated by the following ranking criteria formula, ,

where d is the incremental difference between successive terms and n is the rank number. The example I presented above has an incremental difference of 10, so it can be generated by . You can easily check that the third term is 60 = (10/2)(3+32) = 5×(3+9) = 5×12, and the forth term is 100 = (10/2)(4+42) = 5×(4+16) = 5×20, etc.

Keep in mind, the key is to have small gaps between the rungs of your ranking ladder. An ideal ladder might start with a geometric progression, since the early terms of a geometric progression are fairly closely spaced. As the gaps between the ranks increase, you can control them by switching the ranking criteria to a linear incremental scheme. And finally, you can move to an arithmetic progression to prevent the gap size between ranks from growing so large that it is nearly impossible to move up the ladder.

Now that you know how to build your ranking ladder, next time we'll scale it so that the ranking criteria are tuned specifically for the superusers in your community. Stay tuned at mich8elwu.

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