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<!DOCTYPE html>
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<head>
<title>Archery Rating</title>
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<h1>Archery Rating - Guide</h1>
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<p>
<p>
<a href="#summary">[Summary of project]</a><br>
<a href="#howratingpointschange">[How do rating points change?]</a><br>
<a href="#ratingpointsmean">[What do the rating points mean?]</a><br>
<a href="#checkratingpoints">[What can I do to check my rating points?]</a><br>
<a href="#whyresistant">[Why are my rating points resistant to change with more tournaments I attend?]</a><br>
<a href="#morerounds">[Could Archery Rating consider any more rounds other than WA 720?]</a><br>
<a href="#eliminationorelo">[Couldn't Archery Rating use elimination events only or Elo?]</a><br>
<a href="#assumptions">[What assumptions does Archery Rating make?]</a><br>
<a href="#pros">[What are the pros of Archery Rating?]</a><br>
<a href="#cons">[What are the cons of Archery Rating?]</a><br>
<a href="#plackettluce">[What is the Plackett-Luce model?]</a><br>
<a href="#contributecomments">How can I contribute or give comments?]</a><br>
<a href="#references">[References and Acknowledgements]</a>
</p>
<h2 id="summary">Summary of the projet</h2>
<p>
Archery Rating aims to run a fairer archery ranking system
alongside official rankings. This would be a supplement for those
who enjoy numbers and statistics or archers wanting to assess their
performance.
</p>
<p>
This project came about in the UK when in 2018, the method to rank
archers nationally was changed. This caused a discussion on what
makes a good ranking system. There are two types of events in
archery, qualification and elimination. In qualification, archers
shoot either a WA 720 or WA 1440 round to produce a score. In
elimination, pairs of archers play matches against each other in a
single elimination format. A WA 720 qualification followed by
elimination is the format used for most World Archery events and the
Olympics.
</p>
<p>
Previously, archers were ranked based on their best five
qualification scores. However, this ignores the elimination format
completely. The new method rewards archers with points based on
their best five finishing positions in both formats. The problem
with this method is that it does not consider the playing field as
it may be easier to come first in one tournament over another.
</p>
<p>
Archery Rating was developed as a side project at university. It
uses the Plackett-Luce model. Rating points are earned or lost based
on who the archer wins or loses to using only WA 720 + elimination
events. This takes into account the playing field and is fairer
compared to previous official methods.
</p>
<h2 id="howratingpointschange">How do rating points change?</h2>
<p>
Each archer starts with 1440 rating points (to try and be similar to
the handicap score in the UK) and represents the middle of the pack.
</p>
<p>
Earn rating points by beating opponents with more rating points than
you. However, you will lose rating points by losing to opponents
with fewer rating points than you.
</p>
<p>
Your rating points may also be adjusted slightly if your opponents
attend an event which you do not. This is to reflect your opponents'
future performance and additional information from their opponents
too.
</p>
<p>
The rating points are estimated using WA 720 + elimination results
from Ianseo. These estimations are rather complicated and require a
computer to compute.
</p>
<h2 id="ratingpointsmean">What do the rating points mean?</h2>
<p>
The rating points can be used to estimate the probability that you
will beat an archer in a format where it is either WA 720 or
elimination chosen at random. If archer A has 400 more rating points
than archer B, then the odds of archer A beating archer B is 10:1.
The odds scale by a factor of 10 for every increment of 400 rating
points.
</p>
<p>
Consider archer A with \(R_A\) rating points and archer B with
\(R_B\) rating points. The formula for the probability that archer A
beats archer B is
\[
P(\text{A beats B}) = \dfrac{1}{1+10^{(R_B-R_A)/400}}
\]
</p>
<h2 id="checkratingpoints">What can I do to check my rating points?</h2>
<p>
Find your name in a category and click on it. This should list all
WA 720 + elimination events you have attended this season. You can
also check the list of pairwise comparisons which list all of your
opponents in qualification and elimination events along with the
outcome.
</p>
<p>
The pairwise comparisons table also lists your opponents’
rating points and the estimated probability of you winning a match
against them. These probabilities should be comparable with the
match outcome.
</p>
<h2 id="whyresistant">
Why are my rating points resistant to change with more
tournaments I attend?
</h2>
<p>
How much your rating points are prone to change after an event is
called the sensitivity. Because all of your events are treated
equally, your rating points are very sensitive initially but become
less sensitive with more events.
</p>
<p>
This may seem counter-intuitive but this is a typical property of
statistical estimation. This is similar to estimating the
probability of a coin flip landing heads. With one coin flip, your
estimate is very sensitive, it is either 0% or 100%. But with more
and more coin flips your estimate becomes less sensitive and will
almost surely be 50%, yet, each coin flip is treated equally.
</p>
<p>
Therefore, to exploit this ranking method, win against the best
archer once and stop playing. To tackle this, rating points
uncertainty has been provided, if available, which quantifies the
possible fluctuation in estimation. A smaller uncertainty suggests
that the archer has competed in more events with a larger playing
field.
</p>
<h2 id="morerounds">Could Archery Rating consider any more rounds other than WA 720?</h2>
<p>
Only WA 720 + elimination events are considered to reflect the
format of World Archery and Olympic events. The majority of WA 720 +
elimination results are available on Ianseo, making them accessible
without official means. Choosing a single format also keeps the
rating points more statistically interpretable.
</p>
<h2 id="eliminationorelo">Couldn't Archery Rating use elimination events only or Elo?</h2>
<p>
It is possible to only consider elimination events and make
pairwise comparisons only. However and typically, archers do not
play enough matches for any meaningful analysis. Using the single
elimination format, only half of the archers will only play one
match. In addition, the analysis will be very sensitive to upsets.
To soften the blow on upsets and to retrieve as much information as
possible, Archery Rating uses qualification events too.
</p>
<p>
A problem with Elo is that it requires numerous matches to estimate
one's initial Elo score. Archer Rating aims to estimate one's
rating points immediately.
</p>
<h2 id="assumptions">What assumptions does Archery Rating make?</h2>
<p>
Archer Rating treats each season individually (no rolling) and each
event equally. This means it assumes an archer's performance is
constant throughout a season.
</p>
<p>
Archery Rating also assumes each archer is expected to play with the
intent to win and not in collusion with other players by throwing
matches or not attending an event for example.
</p>
<h2 id="pros">What are the pros of Archery Rating?</h2>
<p>
Archery Rating is based on pairwise comparisons, who you win and
lose against. 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
tournament may be more meaningful compared to the 1st place in
another tournament.
</p>
<p>
Archery Rating overcomes these problems by using pairwise
comparisons. In bad weather, it is who you beat that matters, not
your score. In tournaments of different scales, you are rewarded or
punished depending on who you win or lose against which takes into
account the playing field.
</p>
<h2 id="cons">What are the cons of Archery Rating?</h2>
<p>
A disadvantage of Archery Rating is that it is complicated and not
very accessible compared to previous ranking systems. It is not very
clear how you can improve your rating points apart from beating
archers who have more rating points than you.
</p>
<p>
Archer Rating is harsher compared to previous official rankings.
Official rankings typically take your top scores or points and
ignore the lower ones. Archery Rating punishes bad performance. It
isn't a great feeling to pay and spend time for an event,
underperform AND lose rating points.
</p>
<p>
Archery Rating (and similar ranking systems) is also susceptible to
players protecting their rating points after a lucky win by not
attending any more events. This is why Archery Rating aims to run
alongside official rankings to not hinder player activity.
</p>
<h2 id="plackettluce">What is the Plackett-Luce model?</h2>
<p>
The Plackett-Luce model is for modelling partial rankings. If it is
possible to order a subset of archers from best to worst, it would
be appropriate for the Plackett-Luce model. For example,
in qualification, archers are ranked based on their scores.
In elimination, rankings are done in pairs for each match, ranking
the winner of the match over the loser.
</p>
<h2 id="contributecomments">How can I contribute or give comments?</h2>
<p>
Please visit the
<a href="https://github.com/shermanlo77/archeryrating">GitHub repo</a>
and raise an issue. Or find my contact details on my
<a href="https://github.com/shermanlo77">GitHub profile.</a> Thanks!
</p>
<h2 id="references">References and Acknowledgements</h2>
<p>Please cite:
<ul>
<li>Lo, S. (2023). Calling the shots: using a statistical model to rank archers. <i>Significance, 20(2)</i>,
pp.33-35. <a href="https://doi.org/10.1093/jrssig/qmad030">https://doi.org/10.1093/jrssig/qmad030</a></li>
<li>Turner, H.L., van Etten, J., Firth, D. and Kosmidis, I., (2020). Modelling rankings in R: The PlackettLuce
package. <i>Computational Statistics, 35(3)</i>, pp.1027-1057. <a
href="https://doi.org/10.1007/s00180-020-00959-3">https://doi.org/10.1007/s00180-020-00959-3</a></li>
</ul>
</p>
<p>Acknowledgements:
<ul>
<li>The results were extracted from <a href="https://www.ianseo.net">Ianseo</a> with the help of Tony Sze.
</li>
<li>Helpful discussions with students and academic staff at the University of Warwick.</li>
</ul>
</p>
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GPL-3.0 License
<br>
<a href="https://github.com/shermanlo77/archeryrating">Github: https://github.com/shermanlo77/archeryrating</a>
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