Examples

Single Dances

Following Wikipedia, we can obtain places for the following results after judging:

Results with a Clear Majority for Each Place

With judges as A,...,E and competitors 11, 12 and 13, we have the following places:

We create a DataFrame with these results

results = DataFrame(Number = [11, 12, 13],
        JudgeA = [1, 2, 3],
        JudgeB = [1, 2, 3],
        JudgeC = [2, 1, 3],
        JudgeD = [1, 3, 2],
        JudgeE = [2, 1, 3])

and obtain the final results by

calculation, places = skating_single_dance(results)

The output contains the full calculation as a dataframe

calculation

as well as just the places:

places

No Majority

With the following judgements

we obtain

results = DataFrame(Number = [11, 12, 13],
        JudgeA = [1, 2, 3],
        JudgeB = [1, 2, 3],
        JudgeC = [2, 1, 3],
        JudgeD = [2, 1, 3],
        JudgeE = [3, 2, 1])
calculation, places = skating_single_dance(results)
calculation

Shared Places and Wins with 2nd Place

gives

results = DataFrame(Number = [11, 12, 13, 14],
        JudgeA = [1, 2, 3, 4],
        JudgeB = [1, 2, 3, 4],
        JudgeC = [3, 2, 4, 1],
        JudgeD = [3, 2, 1, 4],
        JudgeE = [4, 2, 1, 3])
calculation, places = skating_single_dance(results)
calculation

Multiple Dances

1st Example

The following examples are from the TSO Homepage (in German).

Assume we have a tournament with the following dances

• Waltz (abbreviated W)
• Tango (T)
• Viennese Waltz (V)
• Slowfox (S)
• Quickstep (Q)

and the following individual placements from the judges:

We set up the results as follows:

dances = ["Waltz", "Tango", "Viennese Waltz", "Slowfox", "Quickstep"]

resultsW = DataFrame(Number = [25, 35, 45, 55, 65, 75],
    JudgeA = [1, 2, 4, 3, 6, 5],
    JudgeB = [1, 2, 5, 3, 6, 4],
    JudgeC = [2, 5, 3, 6, 1, 4],
    JudgeD = [5, 2, 1, 3, 4, 6],
    JudgeE = [3, 5, 1, 6, 4, 2])

resultsT = DataFrame(Number = [25, 35, 45, 55, 65, 75],
    JudgeA = [1, 5, 3, 4, 2, 6],
    JudgeB = [2, 3, 1, 4, 5, 6],
    JudgeC = [2, 1, 3, 4, 5, 6],
    JudgeD = [3, 2, 1, 4, 5, 6],
    JudgeE = [4, 2, 3, 1, 5, 6])

resultsV = DataFrame(Number = [25, 35, 45, 55, 65, 75],
    JudgeA = [1, 3, 5, 2, 4, 6],
    JudgeB = [1, 2, 3, 6, 4, 5],
    JudgeC = [2, 1, 3, 6, 5, 4],
    JudgeD = [2, 1, 6, 3, 5, 4],
    JudgeE = [3, 2, 1, 4, 6, 5])

resultsS = DataFrame(Number = [25, 35, 45, 55, 65, 75],
    JudgeA = [2, 1, 5, 3, 6, 4],
    JudgeB = [2, 1, 6, 3, 4, 5],
    JudgeC = [5, 2, 3, 1, 6, 4],
    JudgeD = [1, 5, 2, 3, 6, 4],
    JudgeE = [5, 2, 3, 6, 4, 1])

resultsQ = DataFrame(Number = [25, 35, 45, 55, 65, 75],
    JudgeA = [2, 1, 3, 5, 4, 6],
    JudgeB = [6, 5, 2, 1, 4, 3],
    JudgeC = [2, 1, 4, 5, 6, 3],
    JudgeD = [6, 5, 2, 1, 3, 4],
    JudgeE = [1, 2, 4, 3, 6, 5])

results = [resultsW, resultsT, resultsV, resultsS, resultsQ]

We calculate the final result by

places_text, rule10_11, reports, places = skating_combined(dances, results)

We can see the final placement in the places DataFrame:

places

The calculation of the sum of the individual places can be found in the first return value

places_text

In this example, Rule 11 needed to be applied. The separate calculations are reported for Rule 10 in

rule10_11[1]

and for Rule 11 in

rule10_11[2]

Finally, reports contains the calculations for the individual dances (similar to the first section).

2nd Example

Consider the following results

We set up and run the calculations:

dances = ["Waltz", "Tango", "Viennese Waltz", "Slowfox", "Quickstep"]

resultsW = DataFrame(Number = [27, 37, 47, 57, 67, 77],
        JudgeA = [2, 3, 4, 1, 6, 5],
        JudgeB = [2, 3, 5, 1, 6, 4],
        JudgeC = [5, 6, 3, 2, 1, 4],
        JudgeD = [2, 3, 1, 5, 4, 6],
        JudgeE = [5, 6, 1, 3, 4, 2])

    resultsT = DataFrame(Number = [27, 37, 47, 57, 67, 77],
        JudgeA = [1, 3, 2, 4, 6, 5],
        JudgeB = [2, 1, 5, 4, 6, 3],
        JudgeC = [2, 3, 5, 4, 6, 1],
        JudgeD = [3, 1, 5, 4, 6, 2],
        JudgeE = [4, 3, 5, 1, 6, 2])

    resultsV = DataFrame(Number = [27, 37, 47, 57, 67, 77],
        JudgeA = [1, 2, 3, 4, 5, 6],
        JudgeB = [1, 3, 4, 5, 2, 6],
        JudgeC = [1, 4, 5, 6, 2, 3],
        JudgeD = [1, 5, 6, 2, 3, 4],
        JudgeE = [1, 6, 2, 3, 4, 5])

    resultsS = DataFrame(Number = [27, 37, 47, 57, 67, 77],
        JudgeA = [3, 1, 4, 5, 2, 6],
        JudgeB = [3, 1, 5, 6, 2, 4],
        JudgeC = [1, 2, 4, 3, 5, 6],
        JudgeD = [3, 5, 4, 2, 1, 6],
        JudgeE = [6, 2, 1, 3, 5, 4])

    resultsQ = DataFrame(Number = [27, 37, 47, 57, 67, 77],
        JudgeA = [2, 4, 1, 6, 5, 3],
        JudgeB = [6, 4, 5, 3, 1, 2],
        JudgeC = [2, 6, 1, 3, 5, 4],
        JudgeD = [6, 3, 5, 4, 1, 2],
        JudgeE = [1, 6, 2, 5, 4, 3])

results = [resultsW, resultsT, resultsV, resultsS, resultsQ]
places_text, rule10_11, reports, places = skating_combined(dances, results)

We obtain the following final places

places_text

Calculations for Rule 10:

rule10_11[1]

...and for Rule 11:

rule10_11[2]