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Granted, my 20% MidfielderKimmich:DefenderKimmich dividend ratio estimate last night was completely top of the head so i figured why not try and actually work it out. Many thanks to @FI_KBrown without whose groundwork I wouldn't have been bothered to do this. #footballindex 1/ https://twitter.com/FootballIndexRC/status/1265377053542580226
This season DefKim (categorised solely and entirely as a defender) would have returned 42p in dividends. MidKim (a midfielder all season) would have returned 8p.
MidKim:DefKim = 19%. Decent first guess! 2/
MidKim:DefKim = 19%. Decent first guess! 2/
I've taken all of Kimmich's scores for the season and converted them into scores for MidKim and DefKim. These two scores are the same unless there's a clean sheet (the key and only in-game statistic that makes being categorised as a defender hugely beneficial!) 3/
In effect we've created two different players, MidKim and DefKim, with slightly different distributions of scores. Different peaks, different averages, different standard deviations. And, very importantly, competing for different positional dividends. Time to run the numbers. 4/
Now, modelling the distribution of scores to the extent where we can closely predict a player's chance of winning PB on a given day is far beyond my skill-set. However I'm not really looking for specific likelihoods, more the difference in likelihoods between our two players 5/
Using their average PB score and standard deviation we can calculate the chance of a player obtaining any score by assuming a normal distribution. I am aware that this is not an accurate representation of how scores in FI are distributed, but it still provides a great insight. 6/
Alternatively it's possible to look directly at past scores and say X% of the time the player scores more than Y, and build up a percentage likelihood of achieving a given score in that way. I did both methods, and pleasingly the results turned out to be very similar! 7/
Next I grabbed the average winning scores for each position and gameday from Karl to have a look at what chance MidKim and DefKim could be expect to have of winning their positional dividend 7/
Combining both the normal distribution and direct historic score method, I calculated the chance each player has of hitting Karl's numbers for their position on the given days. These percentages match quite well with those from Karl's thread. And they "feel" about right too. 8/
As I said, it's not the percentage chances themselves, but the difference between the chances of the two players that we are discussing. Using better models might make the numbers in this grid quite different, but the ratio between the two players should be very similar. 9/
DefKim is about twice as likely to win on a Bronze day than MidKim is. He's 5 times more likely to win on a Silver day & almost 7 times more likely on a Gold day.
MidKim:DefKim ranges from 15% to 51% depending on the type of day. We've seen evidence of very recently 10/
MidKim:DefKim ranges from 15% to 51% depending on the type of day. We've seen evidence of very recently 10/
Weighting these results to account for the number of each type of day (B/G/S) throughout the season and the dividends available on each day, I get an answer of 28%. Kimmich categorised as a midfielder will win 28% of the PB dividends he would win if categorised as a defender 11/
Given his media dividends are unaffected by position, and will probably account for no more than 5% of his career dividends I will improve my estimate. MidKim:DefKim = 30%. How's that @FootballIndexRC? Having done this, I I'd bid ~£2.50 for MidKim, and ~£7 for DefKim. Significant
