Calculate the swiss tennis ranking classification

The Swiss tennis ranking is calculated using the classification value C

C is the sum of the match value W and the risk value R

I would like to calculate C with a function.

1. W = your match value
2. W0= your previous match value
3. Wi= the match value of the player you defeated
4. Wj= the match value of the player you lost to
5. s= sum of the matches you won
6. N= sum of the matches you lost

Now I would like to write a function that calculates C with a tibble input of the matches played and the match value of the opponents.
(I've already learned how to estimate a desired W)

results <- tibble(match=c(1,2,3),match_value_opponent=c(2.4,4.5,3.4), result=c("win","loss","win"))

The previous match value is a constant:
w0 <- 2

I think the function would look like this, but I am not sure how to implement the two formulas in R

calculate_w= function(results)(...)

Update1:

With the function from the kind answer from theN below I do not get the expected results, especially not expected W.

Reprex with the data from this accepted answer:

library(tidyverse)

calculate_c= function(tibble,w0){
  
  tibble_out <- tibble %>%
    mutate(e_pos_wi = case_when(result == "win"  ~ exp(match_value_opponent)),
           e_neg_wj = case_when(result == "loss" ~ exp(-match_value_opponent))) %>%
    summarise(sum_e_pos_wi = sum(e_pos_wi, na.rm = T),
              sum_e_neg_wj = sum(e_neg_wj, na.rm = T)) %>%
    mutate(e_pos_w0 = exp(w0),
           e_neg_w0 = exp(w0),
           W = (1/2) * (log(sum_e_pos_wi + e_pos_w0) - log(sum_e_neg_wj + e_neg_w0)),
           R = (1/6) * (log(sum_e_pos_wi + e_pos_w0) - log(sum_e_neg_wj + e_neg_w0)),
           C = W + R)
  
  return(tibble_out[,c("W","R","C")])
  
}


# make a tibble with 15 wins vs a player with a W of 3400 (same input as described in the question/answer on Mathematica linked above) 
results <- tibble(match=paste(1:15),match_value_opponent=c(rep(3.400,15)), result=c(rep("win",15)))

# calculate W with the same W0 as in the Mathematica question/answer
calculate_c(tibble = results, w0=2.354)
#> # A tibble: 1 × 3
#>       W     R     C
#>   <dbl> <dbl> <dbl>
#> 1  1.89 0.630  2.52

#expected output
# W at least 3.2

^{Created on 2023-04-22 with reprex v2.0.2}

Update2:

These are the formulas directly copied from the link above:

Update3:

Because of the comments (the given formulas might not be unequivocal), I contacted Swiss Tennis for clarification. They sent me updated formulas (sorry for the quality, these are the originals):


Where WA = W0
Unfortunately, they did not provide an example of the formula in use.

This should work, feel free to modify the function to return intermediate parts of the calculation if needed.

calculate_c= function(tibble){
  
  tibble_out <- tibble %>%
    mutate(e_pos_wi = case_when(result == "win"  ~ exp(match_value_opponent)),
           e_neg_wj = case_when(result == "loss" ~ exp(-match_value_opponent))) %>%
    summarise(sum_e_pos_wi = sum(e_pos_wi, na.rm = T),
              sum_e_neg_wj = sum(e_neg_wj, na.rm = T)) %>%
    mutate(e_pos_w0 = exp(2),
           e_neg_w0 = exp(-2),
           W = (1/2) * (log(sum_e_pos_wi + e_pos_w0) - log(sum_e_neg_wj + e_neg_w0)),
           R = (1/6) * (log(sum_e_pos_wi + e_pos_w0) - log(sum_e_neg_wj + e_neg_w0)),
           C = W + R)

  return(tibble_out[, "C"])
  
}

calculate_c(tibble = results)

W = function(res, w0) {
    # scores when you win
    wi = res$match_value_opponent[res$result == "win"]
    # first half of W
    w1 = log(sum(exp(wi)) + exp(w0))
    
    # scores when you lose
    wj = res$match_value_opponent[res$result == "loss"]
    # second half of W
    w2 = log(sum(exp(-wj)) + exp(-w0))

    return(0.5*(w1 - w2))
}

R = function(res, w0) {
    # scores when you win
    wi = res$match_value_opponent[res$result == "win"]
    # first half of W
    w1 = log(sum(exp(wi)) + exp(w0))
    
    # scores when you lose
    wj = res$match_value_opponent[res$result == "loss"]
    # second half of W
    w2 = log(sum(exp(-wj)) + exp(-w0))
    
    return((1/6)*(w1 + w2))
}

C = function(res, w0) {
    w = W(res, w0)
    print("W")
    print(w)
    r = R(res, w0)
    print("R")
    print(r)
    return(w + r)
}

I haven't written it in the most efficient way, but you have separate functions for calculating W and R if you need them.

If I run

results2 <- tibble(match=paste(1:15),match_value_opponent=c(rep(3.400,15)), result=c(rep("win",15)))
C(results2, 2)

I get

[1] "W"
[1] 4.062178
[1] "R"
[1] 0.6873927
[1] 4.749571

I think this makes more sense - your W score should be greater than 2 after winning 15 matches against players with match values of 3.4.