Sherman Ip, 2019
The Plackett-Luce ranking is based on pairwise comparisons, who you win and lose against to. Each archer starts with 1440 points (to try and be similar to the handicap score in the UK). Each archer wins and lose points based on who they win and lose to, but also based on their opponents’ future performance.
The points are updated to reflect the statistical property of each archer. More specifically, it estimates the probability that you will beat an archer in a format where it is either matchplay or a WA 720 chosen at random. The formula for the probability that archer A beats archer B is \[ P(\text{A beats B}) = \dfrac{1}{1+10^{(R_B-R_A)/400}} \] where \(R_A\) and \(R_B\) are the points for archer A and archer B respectively.
This has numerous advantages over previous ranking systems. Score based ranking systems (add up your best 5 scores) do not take into consideration bad weather scores because they are typically low and are not used. Position based ranking systems do not take into account the playing field, the 1st place in a competition may be more meaningful compared to the 1st place in another competition.
The Plackett-Luce ranking system overcomes these problems by using pairwise comparisons. In bad weather, it is who you beat which matters, not your score. In tournaments of different scales, you are rewarded or punished depending on who you win or lose against to which takes into account the playing field. A disadvantage of this ranking system is that it is complicated compared to previous ranking systems. It is not very clear how you can improve your rank impart from beating archers who are ranked higher than you.
The method uses the maximum likelihood. This means that points will fluctuate rapidly at first but steadies out as more and more archery events are attended. This is similar to estimating the probability of a coin flip landing heads. With one coin flip, your estimate is either 0% or 100%, but with more and more coin flips your estimate will almost surely be 50%. Therefore, to exploit this ranking method, win against the best archer once and stop playing.
To tackle this, the uncertainty has been provided which quantifies the possible fluctuation in estimation. A smaller uncertainty suggests that archer has competed in more events.
The results were extracted from Ianseo with the help from Tony Sze. The PlackettLuce package in R was used with help from students and academic staff at the University of Warwick (Turner, H.L., van Etten, J., Firth, D. and Kosmidis, I. (2018). Modelling rankings in R: The PlackettLuce package. arXiv:1810.12068).