How do Odds Develop for Repeated Men's Singles Matches?
These posts expand the analysis from the previous two posts on repeated matches. In the first post, we discussed the test-retest reliability of badminton matches. Then, in the second post, we saw what the most frequent line-ups are and how often the matches between these players were won by the same player or pair.
In this post, we will discuss some of the most frequent men’s singles line-ups. Other disciplines will follow shortly.
Methodology
Each plot will show one black square for every match between the players in my database for which there is information about odds for the match winner. The position on the x-axis is given by the date of the match. For the position on the y-axis, we use the implied probability to win the match
\[p_{1,2} = \frac{\frac{1}{o_{1,2}}}{ \frac{1}{o_1} + \frac{1}{o_2} },\]where \(p_{1,2}\) is the probability for each player to win the match and \(o_{1,2}\) is the geometric mean of the oldest match winner odds for all bookmakers, whose odds are present in the database. Matches that are more likely to be won by the first player are lower than matches expected to be won by the second player. Thus below and above the plot the names of the players are given as the axes correspond to matches won with certainty by each player.
For each match we then add an arrow pointing in the direction of the winner of the match. If the match was won by the second player, the arrow points downwards, if the match was won by the first player, the arrow points upwards. In case of a match that was not properly finished there is no arrow. Thus the arrow points in the direction of the expected movement of the odds, if the first player had won a match, we would expect the subsequent matches probability for his win to be closer to 100%, thus lower on the plot.
Lin Dan - Lee Chong Wei
We begin the analysis with the great rivalry of Lin Dan and Lee Chong Wei. We can see that mostly the implied probabilities tend to follow the drift suggested by the won matches. The first match in the dataset has an implied probability for a win by Lee CW of about 30%. After this match is won by Lee CW, the next match has an implied probability of close to 50%. This match is then won by Lin Dan, the subsequent match then only has an implied probability of 45% for a win by Lee CW. This match is won by Lee CW and thus the implied probability increases to close to 60%.
The following matches are a bit more noisy.
From 2015 on, the pattern can be easily observed again. Following a win by Lin Dan in autumn 2016 the implied probability decreases. After each of Lee CW’s next three wins, the implied probability then increases again, only to fall again after Lin Dan’s next win.
Lee Chong Wei - Chen Long
The line-up of Lee Chong Wei and Chen Long had the most matches in our recent analysis. The plot seems to be more noisy than for the line-up between Lin Dan and Lee Chong Wei. However, we can still see some patterns, such as from 2013 to the end of the dataset in 2017, there are only two instances where the movement of the odds does not match the expected movement as indicated by the arrows. After Chen Long’s first win in 2014, the implied probability for him winning the next match gets lower. In 2016 after Lee CW’s first win the odds move in favor of Chen Long.
Chen Long - Viktor Axelsen
Here we see a distinct movement in the odds. From implied probabilities of around 10% for a win by Axelsen, the odds changed to an even match. This can easily explained by Axelsen’s age. As he is much younger, during their first meetings he was not the world-class player he later became. Thus the odds moved in favor of Axelsen despite Chen Long winning their first seven encounters. After that we can see a zigzag pattern that can be explained by the outcomes of the matches. This zigzag is overlaid with an upward trend due to Axelsen’s general improvements.
Viktor Axelsen - Kento Momota
Their first encounter was at the Junior World Team Championships in 2010 and was won by Axelsen. This is not in the dataset, as there were no odds on this match. The dataset begins in 2014 and mostly consists of matches won by Momota. We thus see a general upward trend, as the bookies were becoming more and more confident in wins by Momota. Only after Momotas long break in 2020 and 2021, the opinion shifted and Axelsen was correctly given a much larger winning probability.
Chou Tien Chen - Ka Long Ng
This line-up is also one with lots of matches and also shows some nice zigzag patterns. For example in 2018 when the first three matches were won by Chou, Ng and then Chou again. The implied probability for a win by Ka Long Ng correspondingly go down, up and then down again.
Conclusion
Mostly the resulting zigzag pattern is observable in the plots, even though we didn’t use any sophisticated analysis. A more thorough analysis could also include how clearly the match was won by the respective winner. Also other factors such as the age of each player, as shown in the case of the matches with Viktor Axelsen and Chen Long, would be of importance.