The odds of this happening were very, very unlikely
June 26, 2018 by Alex Colucci and Aaron Howard in Analysis with 0 comments
Here at Ultiworld Disc Golf, we don’t particularly like highlighting the unfortunate out on the course and it certainly gave us no joy to see Simon Lizotte’s 884 rated second round pop up last Saturday on the Sula Open’s PDGA event page. But exploring strange anomalies comes with the territory.
There are a few empirical basics to describe up front. Lizotte collected most of his strokes over par on just two holes: 4 and 11, where he carded a 13 and a 12, respectively. The conditions in Langevåg, Norway weren’t ideal. Rain and strong winds added to the challenge.
You can hear Lizotte talk about hole 4 in the commentary for the final round here. He wasn’t the only player to struggle on the hole, many did, but there were also plenty of scores closer to par in round two. The Scoring Scratch Average during round two was 63.6 — Lizotte carded an 80 — which means each stroke was worth 7.1 ratings points. Ultimately this round rating won’t count towards his player rating, as it will be dropped.
Because a round rating this low from a player this good seems so unlikely, our first question upon seeing this was, what is the probability of this happening? It’s this question for which we provide a cursory exploration below.
The probability of a player with a PDGA rating equal to Lizotte’s 1042 throwing an 884 rated round at the Sula Open is 0.00027, which is about 1 in 3,700. As you can see from the plot below, Lizotte’s round is quite an outlier. Conversely, a round as good as Lizotte’s 884 rated round was bad, compared to his current rating, would be rated 1193.1 The odds of any 1042 rated player throwing an 1193-rated round at the 2018 Sula Open is also 3,700 to 1.
To calculate these values, we determined the mean and standard deviation of the difference between player’s second round ratings at the Sula Open and their current PDGA ratings. For example, Simon Lizotte’s rating is 1042 and his second-round rating was 884. So, his difference value would be -158. The average difference for the Sula Open was -3.35 with a standard deviation of 44.7. This means that Lizotte’s second round rating was over three standard deviations away from the mean.
To try to contextualize the 3,700 to 1 odds of an 884 rated round, or an 1193 rated round, being thrown by a 1042 rated disc golfer at the Sula Open, we compared those odds to sports betting odds to try to get a sense of just how unlikely these outcomes are.2 One of the longest sports betting odds to have ever paid off were the 5,000 to 1 odds that Leicester City would win the English Premier League in the 2016-2017 season, and bookmakers in the United Kingdom have avoided setting odds anywhere near that high for similar lines since. The odds for the Las Vegas Golden Knights to win the Stanley Cup at the beginning of last season were set at 500 to 1. Odds that Ben Curtis would win the 2003 British Open were set, pre-tournament, at 300 to 1. Currently, at Bovada, the futures odds for the University of Kansas to win the College Football Championship in 2019 are set at 1,000 to 1 (if you know anything about the recent history of football at Kansas, this feels low). Futures odds for the Cleveland Browns to win Super Bowl 53 (HA!) are 75 to 1. 3,700 to 1 odds are not good odds.
Back to PDGA round ratings. There are fewer than 25 rounds rated over 1100, ever, and most of those are within 10 points of 1100. The highest rated round ever is 1132. With an SSA of 63.6, the Sula Open course fits in the course ratings bracket where there have only ever been four rounds rated at 1100 or better — two of those four were 1100 and 1104.
Round ratings have been calculated since 2002. It should go without saying that an 1193 rated round doesn’t seem possible in 2018, or in the near future, or maybe ever — at least for a course with a comparable SSA.
This leaves questions as to how PDGA round ratings should be interpreted if something so improbable can actually happen, as well as how the PDGA ratings system interacts with the wide variety of courses that exist.
h/t Andrew Fish
Because this value is higher than any other round in disc golf history, by a long shot, this suggests that PDGA player ratings may not follow a normal distribution, which is an idea we will investigate in future articles. ↩
Comparing odds about the outcome of one round of a disc golf tournament to odds set by bookmakers is imperfect. Likewise, comparing those odds to odds for outcomes from season-long contests is also imperfect. ↩