The individual player ratings are designed to contextualize the basic information available about each player's record (batting average, strike rate etc.). A rating is calculated for each player for each match. The rating for any player for a given set of matches (all matches, matches against a particular opponent, in a particular year etc.) are the simple average of the player's rating for each match in that set. The goal of the rating is to show how valuable the player's performance was.
How could one compare the performance of a player who scores 70 in a team total of 200 all out, with that of a player who scores 70 in a team total of 400 all out? A skillfull batsman may be good enough to score a century every three Tests, but is it equally valuable to do this in a team in which the other batsmen are not in a same class, as it is to do it in a team in which other batsmen are roughly equally good? Similar questions can be posed for bowlers (how does one compare Kumble, Grimmett and Herath on the one hand, with Warne on the other?) The player rating is an effort to answer such questions.
The test batting rating is calculated at the level of the individual match, and not of the individual inning in the match. It is given by the following formula:
test batting rating = [player's runs in match] x [player's runs_at_wicket ratio] x [player's run share] / [opposition bowling strength]
runs_at_wicket ratio is the ratio of the number of runs scored by the player, and the runs per wicket scored at the other end while the player was at the wicket.
run share is the player's share of the team's runs in the match.
opposition bowling strength is the expected bowling strength of the opposition according to the formbook test simulation model
The ODI batting rating is also calculated at the level of the individual match. It is given by the following formula:
odi batting rating = 10 x [player's runs in match ] x [player's runs_at_wicket ration] x [player's strike_rate_ratio] / [opposition bowling strength]
runs_at_wicket ratio is the ratio of the number of runs scored by the player, and the runs per wicket scored at the other end while the player was at the wicket.
strike_rate_ratio is the ratio of the player's scoring rate to the scoring rate of the other players in the team for that innings.
opposition bowling strength is the expected bowling strength of the opposition according to the formbook odi simulation model
Since the formbook model reports the bowling and batting strength of each team per 300 balls (the test model reports in terms of runs per wicket), the batting rating is multiplied by 10.
The bowling ratings for ODI and Test performances are calculated at the level of the individual match. Unlike the case of batting, bowlers in a given team compete for a share of the available opposition wickets (10 in ODI cricket, 20 in Tests). The rating is given by the following formula.
bowling rating = [player's wickets in match] x [opposition batting strength] x [player's share of team's bowling] x [player's share of available wickets] / [player's share of runs conceded by team]
available wickets: 10 wickets are available in ODIs, 20 in Tests.
In the rare instances where the player bowls but does not concede any runs, the denominator is taken to be 1. The opposition batting strength is taken from the formbook simulation model.
In T20, the approach to the racting is different. It is given by:
t20 batting rating = [balls faced in innings] x ([projected runs]/[opposition bowling strength]) x ([projected runs]/[expected projected runs])
In T20 cricket, the number of balls faced by each batsman in each innings exists in a relatively small range.
expected projected runs is the average number of runs scored per innings by all players who faced the number of balls faced in the innings for which the rating is being calculated.
projected runsThe number of runs which would accrue over 120 balls faced if the player's batting extended over that period. For example, 15(10) balls would mean a projected runs tally of 150, while 15*(10) would yield a tally of 180.
opposition bowling strength is the expectation of opposition bowling strength produced by the formbook t20 simulation model.
t20 bowling rating = [balls bowled per innings] x ([opposition batting strength]/[projected runs conceded])* ([expected runs conceded]/[projected runs conceded])
opposition batting strength is the expectation of the opposition batting strength produced by te formbook t20 simulation model.
projected runs conceded is the number of runs the bowler would conceded if he bowled the full 24 deliveries.
expected runs conceded is the average runs conceded by a T20 bowler who bowls the number of deliveries bowled in the innings under the consideration.