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| title | date | tags | stylesheets | scripts | |||
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| CLRG Scoring Analyzed | 2022-10-09 |
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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:
- Adjudicators give you a "raw score": a real number between 0 and 100
- The scoring system ranks each dancer per adjudicator, based on raw scores
- These rankings are mapped into "award points"
- All of a dancer's award points are summed
- 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:
| Ranking | Award 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.
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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.
| Alice | Bob | Carol | |
|---|---|---|---|
| Adj. 1 | |||
| Adj. 2 | |||
| Adj. 3 | |||
| Award Points | |||
| Ranking |
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.
| Alice | Bob | Carol | |
|---|---|---|---|
| Adj. 1 | |||
| Adj. 2 | |||
| Adj. 3 | |||
| Award Points | |||
| Ranking |
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.
| Alice | Bob | Carol | Dave | Erin | |
|---|---|---|---|---|---|
| Adj. 1 | |||||
| Adj. 2 | |||||
| Adj. 3 | |||||
| Award Points | |||||
| Ranking |