The paper proposes a novel concept called the Net Relative Run Ratio (NRRR) as an alternative to the currently

used Net Run Rate (NRR) for evaluating the "degree of authority" of match wins in limited-over cricket. It aims

to provide a more nuanced assessment of team performance. In essence, the paper proposes that NRRR offers a

more comprehensive and fairer evaluation of team performance in limited-over cricket by accounting for aspects

that NRR overlooks, ultimately leading to a more authoritative ranking of teams.

Key words: NRR, RRR, NRRR, Resources, Par-score

also as a major parameter in their calculations, surprisingly, this parameter is yet to find a place in the NRR

calculation. In the case of chasing a fixed targets, if team-2 achieves it with quite a lot of overs and balls to

spare, NRR invariably ends up giving awful results. This is because, whether the team achieves it without losing

any wickets or by losing 9 wickets, NRR value does not have an effect on it. The proposed method is based on

the resources team-2 had to surrender in achieving the target and hence there are significant changes in RRR

values consistent with the wickets they lose in the process of achieving the target.

Team-A is all out for 150 runs. Team-B wins in 25 overs but only by losing 9 wickets that is by scoring 151/9.

Team-A scores 275 runs and Team-C just makes 200 runs in reply.

Team-C scores 245 runs and team-B gets all out for 200 runs.

Here, one can easily make out even without any calculation that Team-A though lost marginally with team-B

posted a massive win over team-C and deserves qualification. Team-B gets a just technical win over team-1 in

net run rate, despite just a marginal win against team-A, protects their position as number one, even when they

lost fair and square to team-C in their second match.

As per the proposed method NRRR values for the teams would be +0.699, -0.399 and -0.300. That means team-

A and team-C qualify, which makes the true sense.

In NRR method, the overall NRR value of a team is found not by adding individual NRR values of each match.

Instead the total runs scored (adding all the values in the numerator) is divided by the total overs played (adding

all values in the denominator). This is mathematically incorrect as the denominators are not the same. But this

is not a slip but is an intentionally introduced error. Some of the very high individual values of NRR, as we have

seen in the examples cited above cannot be compensated at all, if the individual values are added. When the

denominator. But the difficulty is that, these values are not publically available. Hence, if it is required to utilize

these values for calculation, the method has to be developed as an integral part of these programs and it will be

a complicated affair. But, fortunately the par-score tables which are the outputs of these methods does the help.

These par-score tables are readily available with the scorers, as in every match, when team-2 starts their innings;

these tables are to be issued mandatorily. Revised par score table are also to be issued when matches restart

after interruptions. Here what we need is only the final par score table.

Before discussing the theory behind the proposed method, it will be interesting to see, mathematically what the

most correct approach is. If RRR denotes the relative run ratio, mathematically:

In this approach, the central value will be “1” instead of “0” like in the NRR method and the method to be

proposed in this paper. Winning team gets a value more than one and losing team gets a value between one and

zero. There will be no negative values. NRRR value will be the average of the RRR values). This means, if

there are three games, and the RRR values are say a, b and c for a team, the NRRR value will be (a + b + c)/3.

If we consider the example of triangular series above:

RRR values for team-A will be 0.94 and 1.375 for their two matches and their NRRR value will be

(0.94+1.375)/2 = 1.1575.

RRR for team-B will be 1.06 and 0.816 and NRRR value will be (1.06+0.816)/2 = 0.9380

RRR for team-C will be 0.72 and 1.225 and NRRR value will be (0.72+1.225)/2 = 0.9725

formula, one can presume that the ICC is looking forward to a method giving significance to high scoring than

relying just on the ratio between the scores. Under this circumstance, staying in the same line of thought of the

NRR method, a new method giving credence to high scoring is proposed here.

How the equation for the parameter, relative run ratio (RRR), is derived and how the net relative run ratio

(NRRR) is calculated etc., are explained below. It is also felt that, Performance Index (PI) could perhaps be a

better name for RRR and Overall Performance Index (OPI) for NRRR. However, in this paper, the names RRR

and NRRR are made use of.

RRR for Team-1=

(1)

(3)

Also, the resources used_Team-1 will be 100% when the score of team-1 is the final value in the par-score

table.

Applying these conditions in Eq.1, it becomes:

RRR for team-1 =

Where:

Score of Team1 is the last value in the final par-score table.

Score of Team-2 is the final score of Team2 at the end of the match and

Parscore_Team2 is the required par-score for team-2 corresponding to the overs and balls played and wickets

lost. If team-2 gets all out, this value will be the final value in the par score table.

The net relative run rate (NRRR) of a team is calculated as the sum of all their RRR values in individual matches.

This calculation is very simple. If the final par score table of the match is available, the RRR values can be

calculated in a time less than a minute.

Fig-1: Work sheet for RRR and NRRR calculations