The ICC cricket ratings use a version of the ELO system, which was originally devised by the mathematician Arpad Elo to rank chess players. It is a method for calculating the relative performance of players in zero-sum games. Cricket is a zero-sum game, where each team’s gain or loss is balanced out by the loss or gain of the other participant. The ICC’s method considers matches in the four most recent years, with results in the two most recent years counting for twice as much as the two oldest years. Further, bonuses are awarded for series wins in some cases.
The ELO system consists of two complementary measurements. The first is the rating for each contestant, and the second is the probability of a specific outcome (usually a win) for one contestant against the other, given the ratings for each at the start of the game. This probability is then also factored in when updating the rating for each contestant depending on the outcome of the game.
The ICC’s rating system needs improvement in three areas.
First, it should be able to take into account the margin of a result.
Second, it should be able to take into account which players are in action and which ones are not. An Australia Test team in, say, 2003, with Glenn McGrath and Shane Warne in it is a very different proposition from an Australian team in the same year with one or both missing. The rating of a team at the start of a match should be able to account for this.
Third, the rating should not be subject to arbitrary cutoffs. Teams often play home and away cycles, and the peculiarities of scheduling in international cricket mean that a team’s position in the ICC’s ranking system is especially prone to being influenced by whether or not it has played primarily at home or away during the two most recent years. For example, India’s home and away touring schedule has tended to involve a period of away tours, followed by a period of home series, unlike England, whose schedule provides for home series during the English summer and away tours during the English winter.
The approach described in this article addresses the three issues above. It also arguably mitigates the effects of the touring schedule by eliminating the arbitrary cutoff and relying instead on the changes in personnel that regularly take place in international squads. The home-away effect is especially acute in the Test match format, and there may yet be a case for building separate home and away ELO ratings for Test cricket specifically.
The three problems can be resolved as follows. It assigns a share of a point to each team, depending on the result and the margin by which it was achieved. This is assigned to each player playing in the team in that match.
The rating of a team at the start of each match is the average rating of its playing XI. A player on debut gets a rating of 0.5. Defeats move this rating downwards, wins move this rating upwards. How much a player’s rating moves either way depends on the rating of the opposition. Thus each team’s rating is determined by the ratings of the players in its XI. The fact that squads and selectors use retirements and other strategies to put out the best possible XI to win each game enable the rating to remain updated without resorting to considering results from the most recent couple of years or some such.
The only assumption in this approach is that a team is picked with the goal of maximizing the chances of winning. ♦
