What is the ELO Rating?
The ELO Rating gives a team's rating (and ranking) in a given format. It is designed to resolve a few problems with the ICC's official rating system: (a) the use of arbitrary cutoffs which determine which matches are included for consideration. (b) exclusion of the margin of the result in the rankings estimate. (c) exlusion of the composition of teams involved in a match. These ratings show that it is possible to estimate rankings and ratings without making these three problems.
Estimating the margin of a result
In any cricket match involving two teams A and B, the final score involve A scoring rA runs, losing wA wickets, and facing bA balls, and B scoring rB runs, losing wB wickets and bB balls. The cost in runs of 1 wicket in the match is given by:
rpw = (rA+rB)/(wA+wB)
The points accumulated by each team (pA, pB) per ball are given by:
pA = rA/bA + rpw*wB/bB
pB = rB/bB + rpw*wA/bA
If there is an outright winner, the win bonus (bonus) is added to the winning team's points tally, and is given by:
bonus = 0.5*(pA+pB)
Assuming A wins, the final points tally for the match is
pA = pA + bonus
pB = pB
This is normalized as a share of 1 point as follows:
pA = pA/(pA+pB)
pB = pB/(pA+pB)
Involving the composition of the playing XI
The match rating achieved by each team is attributed to each player in the team for the above match. In this way, at the start of a match, the average match rating achieved by the player in all matches before the current match. So, at the start of each match, we know the average match rating of each player in the XI. If a player is on debut, the player is given a base rating of 0.5.
Estimating the ELO Rating
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 rating for each contesting team is given by the average pre-match rating for each player in the team eleven. If this pre-match rating for each team is RA and RB, then the probabilities of A winning and B winning are
probA = 1/(1+10**(pB - pA))
probB = 1/(1+10**(pA - pB))
Using these probabilities, at the end of the match, assuming that the match point share for A and B is mA and mB respectively, the new rating for each team after match is:
newPA = pA + k*(mA - pA)
newPB = pB + k*(mB - pB)
These figures are applied to each individual player in each team to update the players record for use in the next match they play.
In this way, starting by giving each player on debut a rating of 0.5 and calculating the relative performance of each team in a match as probability (pA and pB above), we can estimate the rating for each team after each match without introducing arbitrary cutoffs for matches to be considered. The only assumption necessary is that teams are selected to win. This is a reasonable assumption. This method accounts for the margin of victory when updating the rating. It satisfies the three conditions set out above.
The match records presented in this website are sourced from ESPNCricinfo. They are cricket's publication of record and maintain the most complete database of matches. The Beehive data is sourced from whatever has been published by the BCCI at various times during the past decade. This site is intended as a repository of the different kinds of data and some of the fun modeling which can be done with these records. It is not, and is not intended to be exhaustive, or Live. This is a repository created to explore measurements and views of the game which are not presented in the classically designed scorecard. It places each match amidst other matches. To find a complete record, readers are requested to visit ESPNCricinfo or the websites of one of the Cricket Boards or the ICC.