A Ratings Method for ODI Cricket

October 03, 2007

This is a method that I've been developing over the last 3-4 years. It's gone through many modifications as one might expect. The motivation for developing this method was to measure the relative performance of teams in a way which takes into account the peculiarities of international cricket. I have developed a method for Test Cricket as well.

In this post, I explain the method and the basic assumptions which guide it. The approach used in designing this rating is to measure performance per delivery in a limited overs game. Even though the fall of wickets does affect the result of an ODI game, it is not mandatory to bowl a side out in an ODI game. The Ratings method takes into account the three parameters which describe an ODI game, and affect its outcome. RUNS/BALL and WICKETS/BALL are fundamental towards describing an ODI game. The RUNS/WICKET ratio is calculated for each ODI game, and a factor correlated RUNS and WICKETS is thus derived. Points are then calculated based on RUNS scored per BALL and WICKET taken per ball. The following example illustrates an example of how a Rating is calculated:

Consider a contest between 2 teams, A and B. The contest is 50 overs a side. Suppose Team A bats first and made 270/8 in 50 overs. Team B chasing makes 272/4 in 44 overs, and hence wins the game by 6 wickets, with 6 overs to spare.

This game would be measured as follows:

Total number of runs scored in the game = 270+272 = 542
Total number of wickets fallen in the game = 8+4 = 12.

The average cost of 1 wicket during the game = 542/12 = 45.16 Runs

So the Points earned by Team A during the game is calculated as follows.

Team A scored 270/300 + 4*45.16/264 = 1.584 (264 is the number of balls in 44 overs, wides and no balls are not considered as they are included in the score) (PA)

Team B scored 272/(44*6) + 8*45.16/300 = 2.408. (PB)

A Win Bonus is awarded to the Winning side, which is the average performance per ball in the match, i.e. (1.584+2.408)/2 = 1.996

So the total points earned by the winning side: Team B in the match = 2.408+1.996 = 4.404 points, while, Team A earns 1.584 points.

So the Rating for Team A is 4.404/(4.404+1.584) = 0.735
The Rating for Team B is 1-0.735 = 0.265

If only 1 match were to be measured, then at the end of this match the Rating would be

Team A 0.735
Team B 0.265

However, its not quite as simple as that when you are trying to measured 8 teams and not just two. Some teams are stronger than other teams. Performances against stronger teams should be worth more than performances against weaker teams. That is to say, that a win against a stronger team should improve a teams rating more than performance against a weaker team. This is achieved by introducing a handicap for each team. This handicap is measured as:

(Total performance per ball by Team) - (Total performance per ball against Team)

This value is added to the total point score of the team which beats this team.

This as you have probably realized can be either positive or negative. Tables 1 and 2 at the end of this post provide an overview of the matches considered, the rating and the win bonus records of the eight teams considered for these ratings.

The ratings take into account the 5 latest matches played by a team against each of the other teams. Therefore a total of 35 matches are considered. A rating which takes into account matches in sequential order cannot provide an accurate measure of the relative performance of a side with relation to all other sides, because a side in a longish sequence against lower ranked teams will perform better than a side with a longish sequence against higher ranked teams. Since ratings by definition are relative (as are rankings), this set of matches is considered to offer a better representation of the relative quality of sides.

The ICC's approach is to consider the sequence of games and then use each teams existing rating to measure the "handicap". The ICC does not take into account extent of victory, which in my view is a crippling drawback of the official rating.

Until now we have seen how one match is measured, and how many and which matches are considered in the rating. Three distinct values are calculated:

1. Points scored by the Team (P)
2. Win Bonus for the game (W)
3. Win Bonus handicap against the losing team (H)

Total points (T)
if Team A wins,
total points for Team A = PA + W+ HB
total points for Team B = PB

if Team B wins,
total points for Team A = PA
total points for Team B = PB + + W + HA

where W = (PA+PB)/2

If we consider the 5 latest games between A and B (1,2,3,4 and 5, 1 being the latest) then the win bonus against A would be:

average of (PA1 ,PA (1+2)/2, PA(1+2+3)/3), PA(1+2+3+4)/4, PA(1+2+3+4+5)/5)

This ensures that the latest performance is given higher weightage than the oldest performance. Similarly, when calculating the rating, the average is weighted. Two steps are carried out. First the 5 weighted values are measured:

TA1, (TA1+TA2)/2, (TA1+TA2+TA3)/3, (TA1+TA2+TA3+TA4)/4, (TA1+TA2+TA3+TA4+TA5)/5
TB1, (TB1+TB2)/2, (TB1+TB2+TB3)/3, (TB1+TB2+TB3+TB4)/4, (TB1+TB2+TB3+TB4+TB5)/5

for each of these, the rating is normalized to a scale of 1. So, for A it would be TA1/(TA1+TB1), ((TA1+TA2)/2)/(((TA1+TA2)/2)+((TB1+TB2)/2))) and so on..... and for B it would be 1-the corresponding value for A.

The final rating is the simple average of the 35 total values determined against the other 7 top teams in this way. Sometimes, this measured shows very different ratings values for similar or even same win-loss records over the 35 games in question. In order to illustrate why this is so, i have listed the percentage matches won in the last 5 (a total of 35 games) and the last 3 (a total of 21 games) in Table 1 below. Teams which have improved win-loss records over the last 3 as against the last 5 rate higher, even if their win-loss records over the last 5 are similar (Australia, South Africa; England, India).

SOUTH AFRICA693162380.559
NEW ZEALAND604057430.533
SRI LANKA406048520.499
WEST INDIES376343570.428

Table 1. Win/Loss & Ratings

SOUTH AFRICA2602372582520.199
NEW ZEALAND2442412512450.026
SRI LANKA2482402562260.051
WEST INDIES229254229254-0.285

Table 2 Runs scored, Runs Conceded and Win Bonus

The rating is intended to be only one part of a set of descriptive statistics which explain the relative status of the teams and also where they are headed. This set of statistics would include Tables 1 and 2 for now, but is very much still a work in progress.  The ratings themselves are listed on CricketingView. I wrote this post mainly to write an updated explanation for the ratings. The latest change I made is to ignore results against Zimbabwe due to the fact that they have won only 1 out of their last 40 games (5 latest against the 8 teams in the current rating). This rating is proposed as an alternative to the ICC's rating (which I don't agree with).

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A Ratings Method for ODI Cricket


Author: Kartikeya


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October 3, 2007
01:36 AM

Quite complicated :-)

Anyway, i ran through your first equation. I will run through the second half later.

One of my concerns with the first equation is the weight on the number of wickets taken by the winning team and similarly the weight on the number of wickets taken by the losing team.

Assuming 2 hypothetical scenarios

Team A scores 350 all out in 50 overs and Team B scores 300 allout in 50 overs, ratings of 0.68 and 0.32

In another scenario, Team B scores 350 all out in 50 overs and Team B scores 200/3 in 50 overs, ratings of 0.62 and 0.38.

In other words, team B in scenario 2 scores more than team B in scenario 1 despite losing the match by a larger margin and playing absolutely boring cricket.

Please correct me if there is an error in my basic calculation. In that case my interpretation is incorrect. More later


October 3, 2007
01:54 AM

The method is not that complicated. My explanation leaves a lot to be desired though :)

You're quite right. You could have hypothetical scenarios where something like that happens. Your calculation is correct.

The way i have dealt with that is that i don't normalize individual games on the scale of 1. Given how the rating is determined, what would go forward is that the "performance per ball" for Team A in the first instance would be 4.42, while the performance against would be 2.083. In the other instance (200/3), the performance for would be 3.92 and the performance against would be 1.83

The reason this works is that teams winning close games tend to get higher win bonuses (because both teams tend to stack up points) than teams winning one sided games.

The normalization is done only once at the end - and it is done only to offer a comparable scale of measurement.

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