Frequently Asked Questions About Cielo Ratings
What are Cielo Ratings?
Cielo Ratings are an objective racing ELO-based rating system. The first ELO rating system was created by physicist Arpad Elo for calculating the relative skill levels of players in zero-sum games such as chess. The ELO methodology has been extended to athletic sporting competitions such as soccer, tennis, football, baseball, and basketball to name a few.
ELO ratings have been primarily used in two-player competitions. In 2018, computer scientist Justin Moore extended the methodology to Formula 1 automobile racing. Cielo Ratings attempts to build upon these successful rating systems by adopting similar mathematics for other forms of racing.
Mathematically, ELO ratings have no theoretical limit; thus, ‘The Sky’s The Limit With ELO-Based Ratings.’ The name ‘cielo’ is the Spanish word for the sky which seems appropriate for fast cars and fast horses.
Cielo Ratings evoke memories of the 1982 USA Horse of the Year, CONQUISTADOR CIELO, and the Italian roadster with a sky roof, Maserati MC20 Cielo.
When Are Ratings Updated?
Eventually 24/7/365. Until then when I have spare time – approximately once a week on Tuesdays.
How Are Ratings Calculated?
Performance is not measured absolutely; it is inferred from wins, losses, and dead-heats against other racers. Racers’ ratings depend on the ratings of their opponents and the results scored against them. The difference in rating between two racers determines an estimate for the expected score between them. Both the average and the spread of ratings can be arbitrarily chosen.
Cielo Ratings have small differences from the original Elo formulations. Arpad Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score of approximately 0.75, and the USCF initially aimed for an average club player to have a rating of 1500. Cielo Ratings (revision 3.0.0) have likewise chosen the same arbitrary average rating. While previous versions of the Cielo Ratings established an average of 1000, the current version has gone with the unspoken de facto ELO standard of 1500 so it is intuitive to the reader.
A racer’s expected score is their probability of winning plus half their probability of drawing. Thus, an expected score of 0.75 could represent a 75% chance of winning, a 25% chance of losing, and a 0% chance of drawing. On the other extreme, it could represent a 50% chance of winning, 0% chance of losing, and a 50% chance of drawing. The probability of a dead heat, as opposed to having a decisive winner, is not specified in the ELO system. Instead, a dead heat is considered half a win and half a loss. In practice, since the true strength of each racer is unknown, the expected scores are calculated using the racer’s current ratings as follows.
If Racer A has a rating of RA and Horse B a rating of RB, the exact formula for the expected score of Racer A is
Similarly, the expected score for Racer B is
This could also be expressed by
and
where
and
Note that in the latter case, the same denominator applies to both expressions, and it is plain that EA + EB = 1.
This means that by studying only the numerators, we find out that the expected score for racer A is QA / QB times greater than the expected score for racer B. It then follows that for each 200 rating points of advantage over the opponent, the expected score is magnified ten times in comparison to the opponent’s expected score.
When a racer’s actual race scores exceed their expected scores, the ELO system takes this as evidence that the racer’s rating is too low, and needs to be adjusted upward. Similarly, when a racer’s actual race scores fall short of their expected scores, that racer’s rating is adjusted downward. Elo’s original suggestion, which is still widely used, was a simple linear adjustment proportional to the amount by which a player overperformed or underperformed their expected score. The maximum possible adjustment per pairwise comparison within a race called the K-factor, is usually set between 10 and 25. Cielo Ratings (version 3.0) is using a k-factor of 12 to mirror Justin Moore’s Formula 1 work.
Supposing Racer A was expected to score EA points but actually scored SA points. The formula for updating that player’s rating is
This update can be performed after each race. This rating update is done for each pairwise comparison within said race. In other words, a horse’s rating is adjusted upwards by each horse they out-finished and downwards by each racer by which they were beaten.
(sps – 2023-07-04)