# CLRG Scoring Analyzed

2022-Oct-09

Let’s take a look how how CLRG does its scoring! With math!

## How CLRG Scoring Works

As I am given to understand, the scoring works like so:

1. Adjudicators give you a “raw score”: a real number between 0 and 100
2. The scoring system ranks each dancer per adjudicator, based on raw scores
3. These rankings are mapped into “award points”
4. All of a dancer’s award points are summed
5. Final ranking is determined by comparing total award points

## Raw Scoring

The way raw scores translate into rankings and award points is a little confusing, so I’ve made a little tool you can play with to get a feel for how it works. Essentially, it’s a way of normalizing places to an adjudicator: score weights are only relative to the judge that assigns them.

Adjudicator A can assign scores between 80 and 100; adjudicator B can assign scores between 1 and 40; and they’ll both have a first, second, third, fourth place, etc. These places then get translated into award points.

## Award Points

Award points are handed out based on ranking against other dancers for that adjudicator. I obtained these values from a FeisWorx results page for my kid:

RankingAward Points

If there’s a 2-way, 3-way, or n-way tie, all tied dancers get the average of the next 2, 3, or n award points, and the next 2, 3, or n rankings are skipped.

## What’s with these values?

At first glance, the award points look like the output of an exponential function.

In an effort to figure out where these numbers came from, I ran some curve fitting against the data. Here’s the best I could come up with:

Ranking range Award Points Function Type of function
1 - 11 100 * x^-0.358 Exponential
12 - 50 51 - x Linear
51 - 60 14.2 - 0.46x + 0.00385x Polynomial
61 - 100 1 - x/100 Linear

If you, dear reader, are a mathematician, I would love to hear your thoughts on why they went with this algorithm.

There are a few points to note here:

• 1st place is a huge deal. Disproportionately huge.
• Places 2-10 are similarly big deals compared to places 3-11.
• Places 12-50 operate the way most people probably assume ranking works: linearly.
• Places 51-60 fit best to a second degree polynomial, but it doesn’t matter much for differences of hundreths of a point. This section is really weird, mathematically.
• Places 61-100 are all less than 1 point. If you’re a judge trying to tank a top dancer, anywhere in this range is equivalent to anywhere else.

## Consequences of Exponential Award Points

Playing around with this, I’ve found a few interesting consequences of the exponential growth in the top 11 places.

### 1st place is super important

1st place is weighted so heavily that one judge could move a 5th place dancer into 2nd.

You can adjust these values to get a better feel for how scoring works.

### Tanking a high-ranked dancer is another way to cheat

Because of that exponential curve, a low ranking from a single judge can carry a lot of weight.

### Being in 1st provides a nice buffer

Try playing around with Alice’s rankings with Adjudicators 2 and 3 here. She has to get ranked a lot lower before her overall ranking starts going down.