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Calculation of diving scores

Source: R/diving.R
diving.Rd

Functions to implement four ways to calculate the points awarded for a dive in a diving competition, including the way that is used in the Olympic Games.

Usage

dmean(
  x,
  DD = "DD",
  scores = paste0("J", 1:7),
  trim = 2/7,
  replace = TRUE,
  reorder = TRUE
)

dmedian(
  x,
  DD = "DD",
  scores = paste0("J", 1:7),
  type = 6,
  replace = TRUE,
  reorder = TRUE
)

dmode(x, DD = "DD", scores = paste0("J", 1:7), replace = TRUE, reorder = TRUE)

tables(x, type = 1, diverRanks = 1)

Arguments

x

A numeric matrix or data frame, ideally of the same format as daley.

DD

A character (or numeric) scalar giving the column name (or number) of x that contains the DD (degree of difficulty) values of each dive. The default is set up to work with the data in daley.

scores

A character (or numeric) vector giving the column names (or numbers) of x that contain the 7 scores for each dive. The default is set up to work with the data in daley.

trim

Only relevant to divemean. Passed to mean. The default, trim = 2 / 7, corresponds to the calculation using in diving competitions.

replace

A logical scalar. If replace = FALSE then a vector of the dive points is returned. If replace = TRUE then the DivePoints, DiveRank, TotalPoints, OverallRank and PointsBehind columns are updated in light of the new values of the dive points and this data frame is returned. If any of these named columns do not exist then the returned object is the same as the replace = FALSE case.

reorder

A logical scalar. If replace = TRUE then reorder determines whether the order of the divers is changed to reflect the new values of TotalPoints at the end of the competition.

type

Determines the form of a data frame returned as a summary table.

  • type = 0: Rank, Name, NOCcode (Country), TotalPoints at the end of the competition.

  • type = 1: DD, J1-J7 and dive points (those already in x).

  • type = 2: like type = 1 but gives dive points, and points based on the mean, median and mode.

  • type = 3: like type = 2 but gives only the total points accumulated over the competition, ordered by dive points.

  • type = 4: like type = 3 but totals are replaced by ranks.

diverRanks

The ranks of the divers that should be included in a table. For example, diverRanks gives the medalists.

Value

A numeric vector dive points if replace = FALSE or x does not have appropriately named columns. Otherwise, a dataframe of the same structure as x in which the columns DivePoints, DiveRank, TotalPoints, OverallRank and PointsBehind have been updated in light of the new dive points values.

Details

In the default case, e.g. dmean(daley), the 2 smallest and 2 largest scores of the 7 scores are removed; the sum of the 3 remaining scores is calculated; and the result is multiplied by the dive's degree of difficulty.

Another way to think of this is that we take the sample mean of the 3 middle scores, then multiply by 3, then multiply by the degree of difficulty.

In the dmean(daley, trim = 0) case we take the sample mean of all 7 scores, then multiply by 3, then multiply by the degree of difficulty. That is, we do not trim the 2 smallest and 2 largest values.

Similarly, in the dmedian(daley) and dmode(daley) cases we take the sample median or mode, respectively, of all 7 scores, then multiply by 3, then multiply by the degree of difficulty. If there is more than one sample mode then we use the sample mean of these modes.

See also

daley for Tokyo 2020 Olympics Diving Men's Individual 10m platform final results

Examples

# The calculation used in competitions (trimmed sample sums)
dmean(daley, replace = FALSE)
#>  [1] 102.00  81.60  97.20  97.20 101.75 102.60  90.10  94.50  89.25  91.20
#> [11] 102.60 112.75  98.60  91.20  91.80  80.50  94.35  91.80  75.20  91.80
#> [21]  85.75  81.00  94.35  86.40  68.80  91.80  91.80  73.80  83.25  86.40
#> [31]  83.20  79.20  88.20  56.10  75.00  80.00  72.00  86.40  75.85  86.40
#> [41]  35.70  75.60  57.60  61.20  74.25  76.50  72.00  88.80  68.80  72.60
#> [51]  39.60  88.80  69.70  68.40  60.80  79.20  46.20  79.55  56.10  72.00
#> [61]  67.20  59.40  48.60  69.70  66.60  72.15  67.20  59.40  59.50  42.50
#> [71]  72.15  81.00
#> attr(,"statistic")
#> [1] "DivePoints"

# An equivalent calculation without trimming
dmean(daley, replace = FALSE, trim = 0)
#>  [1] 100.54286  82.28571  96.42857  97.20000 102.27857 104.14286  88.88571
#>  [8]  93.00000  89.25000  92.01429 103.37143 113.33571  97.62857  91.20000
#> [15]  91.80000  81.00000  95.93571  91.80000  74.74286  90.34286  85.50000
#> [22]  79.45714  94.35000  86.40000  69.25714  93.25714  92.57143  74.05714
#> [29]  82.45714  84.08571  84.34286  78.49286  88.71429  56.10000  75.85714
#> [36]  79.54286  71.31429  87.17143  74.52857  85.62857  37.15714  74.82857
#> [43]  58.28571  61.71429  74.25000  76.50000  73.28571  91.17857  69.94286
#> [50]  72.12857  42.42857  89.59286  68.48571  68.65714  60.34286  79.90714
#> [57]  45.96429  80.07857  56.10000  71.31429  67.88571  60.94286  49.37143
#> [64]  67.02857  66.34286  73.73571  67.20000  59.40000  59.25000  43.71429
#> [71]  72.94286  79.45714
#> attr(,"statistic")
#> [1] "MeanPoints"

# An equivalent calculation based on a sample median
dmedian(daley, replace = FALSE)
#>  [1] 102.00  81.60  97.20  97.20  99.90 102.60  91.80  94.50  89.25  91.20
#> [11] 102.60 110.70  96.90  91.20  91.80  78.75  94.35  91.80  76.80  91.80
#> [21]  84.00  81.00  94.35  86.40  67.20  91.80  91.80  75.60  83.25  86.40
#> [31]  81.60  79.20  86.40  56.10  76.50  81.60  72.00  86.40  77.70  86.40
#> [41]  35.70  75.60  57.60  59.40  74.25  76.50  70.20  88.80  67.20  74.25
#> [51]  39.60  88.80  71.40  70.20  62.40  79.20  44.55  77.70  56.10  72.00
#> [61]  67.20  59.40  48.60  71.40  64.80  72.15  67.20  59.40  57.75  40.80
#> [71]  72.15  81.00
#> attr(,"statistic")
#> [1] "MedianPoints"

# An equivalent calculation based on a sample mode
dmode(daley, replace = FALSE)
#>  [1] 102.000  81.600  97.200  97.200  99.900 102.600  91.800  94.500  89.250
#> [10]  91.200 102.600 110.700  99.450  91.200  91.800  78.750  94.350  91.800
#> [19]  76.800  91.800  86.625  81.000  94.350  86.400  67.200  91.800  91.800
#> [28]  75.600  83.250  86.400  81.600  79.200  86.400  56.100  72.000  81.600
#> [37]  72.000  86.400  77.700  86.400  35.700  75.600  57.600  59.400  74.250
#> [46]  76.500  70.200  88.800  67.200  74.250  39.600  88.800  71.400  67.500
#> [55]  62.400  79.200  47.025  77.700  56.100  72.000  67.200  59.400  48.600
#> [64]  71.400  67.500  72.150  67.200  59.400  60.375  40.800  72.150  81.000
#> attr(,"statistic")
#> [1] "ModePoints"