How rankings are calculated
The model for the calculation of the Dancehall Battle Rankings was developed over multiple months in the last part of 2019 during which time different formulas were tested and discussed. The main goal was to create formulas that allow ranking different dancers and countries across different events at different times at different locations.
In what follows we will explain six different types of rankings. Three for dancers and three for countries:
- Dancer
- Dancer (1 vs 1)
- Dancer (2 vs 2)
- Country
- Country (home)
- Country (away)
The following variables are used for the different formulas discussed later:
\(C\) is the set of all countries.
\(D\) is the set of all dancers.
\(B\) is the set of all battles.
\(c\) is a single country.
\(d\) is a single dancer.
\(b\) is a single battle.
\(b_{date}\) is the date that battle \(b\) took place.
\(D_c\) is the set of all dancers from country \(c\).
\(D_{c,i}\) is the dancer of country \(c\) at index \(i\).
The first index is 1.
\(B_d\) is the set of all battles won by dancer \(d\).
\(B_{d,i}\) is the battle of dancer \(d\) at index \(i\).
The first index is 1.
\(H_d\) is the set of all battles won by dancer \(d\) in their own country.
\(H_{d,i}\) is the battle of dancer \(d\) at index \(i\).
The first index is 1.
\(A_d\) is the set of all battles won by dancer \(d\) in a country that is not their own.
\(A_{d,i}\) is the battle of dancer \(d\) at index \(i\).
The first index is 1.
\(E_c\) is the set of all battles in country \(c\).
\(E_{c,i}\) is the battle of country \(c\) at index \(i\).
The first index is 1.
Dancer rankings
The dancer rankings award points to every dancer that participated in a battle in the last 12 months. Their points are calculated based on the number of battles they have won, together with how long ago the battles took place.
Difference between rankings
There are three rankings for individual dancers: "dancer", "dancer (1 vs 1)", and "dancer (2 vs 2)". The dancer ranking takes into account both 1 vs 1 and 2 vs 2 battles. The dancer (1 vs 1) ranking takes only into account 1 vs 1 battles. The dancer (2 vs 2) ranking takes only into account 2 vs 2 battles.
Calculate rankings
A dancer get points for every win in the past 12 months. Wins that happened more than 12 months ago are not taking into account. The more months that have passed since the battle took place, the lower the amount of points that is earned. For example, a dancer gets less points for a win from 6 months ago then for a win from 2 months ago. The points currently used can be found in the following table:
| # months ago | Points |
|---|---|
| 0 | 18 |
| 1 | 17 |
| 2 | 16 |
| 3 | 13 |
| 4 | 12 |
| 5 | 11 |
| 6 | 8 |
| 7 | 7 |
| 8 | 6 |
| 9 | 3 |
| 10 | 2 |
| 11 | 1 |
| \(\geq\) 12 | 0 |
The formula to calculate the total points \(points_d\) for a dancer \(d\) given a set of battles \(B_d\), which are won by \(d\), is $$points_d = \sum_{i=0}^{|B_d|} \text{pointsOfBattle}(B_{d,i})$$ where $$ \begin{align} \text{pointsOfBattle}(b) &= lookUp(\text{diff}(b_{date}, today)) \\ \text{lookUp}(months) &= \text{look up the points in the above table based on the months} \\ \text{diff}(date1, date2) &= \text{calculate the difference in months between 2 dates} \end{align} $$
Let us use these formulas with an example. Assume that today is 2019-12-15 and we want to calculate the points \(points_{boris}\) of a dancer called Boris who won the following three 1 vs 1 battles:
| Battle | Variable name | Date |
|---|---|---|
| Battle A | \(battle_a\) | 2019-06-24 |
| Battle B | \(battle_b\) | 2019-11-12 |
| Battle C | \(battle_c\) | 2019-12-01 |
The result is 47 points for Boris.
The aforementioned battles are 1 vs 1 battles. In case it are 2 vs 2 battles, then the points are divided in half: half of the points for each of the two dancers that won the battle. In our example, the points are then 6, 8.5, and 9, resulting in 23.5 points total for one dancer.
Country rankings
The country rankings award points to every country (represented by one of its dancers) that participated in a battle in the last 12 months. Their points are calculated based on the number of battles they have won, together with how long ago the battles took place.
Difference between rankings
There are three rankings for countries: "country", "country (home)", and "country (away)". The country ranking takes into account both home and away battles. The country (home) ranking takes only into account home battles. The country (away) ranking takes only into account away battles.
Calculate rankings
All three country rankings are based on the dancer rankings: for each country its total points depends on the points acquired by the individual dancers of that country.
Country ranking
The formula to calculate the total points \(points_c\) for country \(c\) is $$points_c = \sum_{i=1}^{|D_c|} \sum_{j=1}^{|B_{D_{c,i}}|} \text{pointsOfBattle}(B_{D_{c,i},j})$$
Let us use this formula with an example. We want to calculate the points of France \(points_{france}\) taking into account the following battles:
| Battle | Variable name | Battle's country | # months ago | Winner | Winner's country |
|---|---|---|---|---|---|
| Battle D | \(battle_d\) | France | 5 | Helen | France |
| Battle E | \(battle_e\) | Spain | 7 | Joseph | France |
| Battle F | \(battle_f\) | Ukraine | 2 | Maria | Italy |
\(D_{france}\) contains the dancers from France: Helen and Joseph. \(B_{helen}\) contains the battles won by Helen: Battle D. \(B_{joseph}\) contains the battles won by Joseph: Battle E.
$$ \begin{align} points_{france} &= \sum_{i=1}^{|D_{france}|} \sum_{j=1}^{|B_{D_{france,i}}|} \text{pointsOfBattle}(B_{D_{france,i},j}) \\ &= \sum_{j=1}^{|B_{helen}|} \text{pointsOfBattle}(B_{helen,j}) + \sum_{j=1}^{|B_{joseph}|} \text{pointsOfBattle}(B_{joseph,j}) \\ &= \text{pointsOfBattle}(battle_d) + \text{pointsOfBattle}(battle_e) \\ &= 11 + 7 \\ &= 18 \end{align} $$
The total points for France is 18, based on the wins by Helen and Joseph.
Country (home) ranking
The country (home) ranking is different from the country ranking because it only takes into account home wins for dancers. In other words, only wins where the country of the battle and the country of the winner are the same are taken into account.
The formula to calculate the total points \(points_c\) for country \(c\) is $$points_c = \sum_{i=1}^{|D_c|} \sum_{j=1}^{|H_{D_{c,i}}|} \text{pointsOfBattle}(H_{D_{c,i},j})$$
Let us use this formula with an example. We want to calculate the points of France \(points_{france}\) taking into account aforementioned battles.
\(D_{france}\) contains the dancers from France: Helen and Joseph. \(H_{helen}\) contains the battles in France won by Helen: Battle D. \(H_{joseph}\) contains the battles in France won by Joseph: it is empty, because Joseph did not win any battles in France.
$$ \begin{align} points_{france} &= \sum_{i=1}^{|D_{france}|} \sum_{j=1}^{|H_{D_{france,i}}|} \text{pointsOfBattle}(H_{D_{france,i},j}) \\ &= \sum_{j=1}^{|H_{helen}|} \text{pointsOfBattle}(H_{helen,j}) + \sum_{j=1}^{|H_{joseph}|} \text{pointsOfBattle}(H_{joseph,j}) \\ &= \text{pointsOfBattle}(battle_d) \\ &= 11 \end{align} $$
The total points for France is 11, based on the wins by Helen (and Joseph).
Country (away) ranking
The country (away) ranking is different from the country ranking because it only takes into account away wins for dancers. In other words, only wins where the country of the battle and the country of the winner are different are taken into account.
The formula to calculate the total points \(points_c\) for country \(c\) is $$ points_c = \text{round} \left( \frac{\sum\limits_{i=1}^{|D_c|} \sum\limits_{j=1}^{|A_{D_{c,i}}|} \text{pointsOfBattle}(A_{D_{c,i},j})} {\sum\limits_{k=1}^{|B|} \text{pointsOfBattle}(B_k) - \sum\limits_{l=1}^{|E_c|} \text{pointsOfBattle}(E_{c,l})} \cdot 100000 \right) $$
Let us use this formula with an example. We want to calculate the points of France \(points_{france}\) taking into account the aforementioned battles.
\(D_{france}\) contains the dancers from France: Helen and Joseph. \(A_{helen}\) contains the battles in other countries won by Helen: it is empty, because Helen did not win any battles outside France. \(A_{joseph}\) contains the battles in other countries won by Joseph: Battle E.
$$ \begin{align} points_{france} &= \text{round} \left( \frac{\sum\limits_{i=1}^{|D_c|} \sum\limits_{j=1}^{|A_{D_{c,i}}|} \text{pointsOfBattle}(A_{D_{c,i},j})} {\sum\limits_{k=1}^{|B|} \text{pointsOfBattle}(B_k) - \sum\limits_{l=1}^{|E_c|} \text{pointsOfBattle}(E_{c,l})} \cdot 100000 \right) \\ &= \text{round} \left( \frac{\sum\limits_{j=1}^{|A_{helen}|} \text{pointsOfBattle}(A_{helen,j}) + \sum\limits_{j=1}^{|A_{joseph}|} \text{pointsOfBattle}(A_{joseph,j})} {\sum\limits_{k=1}^{|B|} \text{pointsOfBattle}(B_k) - \sum\limits_{l=1}^{|E_c|} \text{pointsOfBattle}(E_{c,l})} \cdot 100000 \right) \\ &= \text{round} \left( \frac{\text{pointsOfBattle}(battle_e)} {\sum\limits_{k=1}^{|B|} \text{pointsOfBattle}(B_k) - \sum\limits_{l=1}^{|E_c|} \text{pointsOfBattle}(E_{c,l})} \cdot 100000 \right) \\ &= \text{round} \left( \frac{7} {\sum\limits_{k=1}^{|B|} \text{pointsOfBattle}(B_k) - \sum\limits_{l=1}^{|E_c|} \text{pointsOfBattle}(E_{c,l})} \cdot 100000 \right) \\ &= \text{round} \left( \frac{7} {34 - 11} \cdot 100000 \right) \\ &= \text{round} \left( \frac{7} {23} \cdot 100000 \right) \\ &= 30,435 \end{align} $$
The total points for France is 30,435, based on the wins by Joseph (and Helen). The fraction and the multiplication by 100,000 make it not meaningful to compare these points with points of other rankings. Furthermore, the multiplication is used to avoid points that only differ in the decimals.
In case you have questions or remarks about the rankings you can always contact us via email.