Net Run Rate (NRR) is a statistical method used in analysing teamwork and/or performance in the sport of cricket. It is the most commonly used method of ranking teams with equal points in limited overs league competitions, analogous to goal difference in association football. (Source: Wikipedia)

#### The issues with the existing system

The net run rate method that is used currently does not consider the number of wickets a chasing team has lost in the equation, which is not the right indicator of the competitiveness of the match.  For instance, in the Champions Trophy tournament in 2013, New Zealand beat Sri Lanka by 1 wicket, but since they had utilised only a few overs, they ended up with a higher NRR than they ideally should have. The NRR difference suggested a comprehensive victory for the Kiwis, but in actuality it was not so.

Such is the case with several other matches, which necessitates the need to amend the current system that is used to calculate the NRR.

The net run rate in a single game is the average runs per over that a team scores, minus the average runs per over that is scored against them. The net run rate in a tournament is the average runs per over that a team scores across the whole tournament, minus the average runs per over that is scored against them across the whole tournament. (Source: Wikipedia)

Currently if a team loses all its wickets within the stipulated 50 overs, the runs it scored is considered to have been scored off all 50 overs. For instance, if a team scores 100 runs in 20 overs and loses all the wickets in the process, then the run rate is calculated to be 100/50 = 2 RPO and not 100/20 = 5 RPO.

But if a team chasing a score of 150 reaches the target within 25 overs at the cost of 9 wickets, then the run rate of that team would be computed as 150/25 = 6 RPO. But since the team has lost 9 wickets it is least likely to play out all 50 overs; therefore, the NRR does not reflect the margin of victory in this regard, as the number of wickets lost is not considered.

An alternate method can be employed here to calculate the margin of victory/defeat.

Just like the net run rate system that is already in place, the average runs per over against that team should be deducted from the average runs per over of that team.

• If the team batting first completes all its 50 overs without getting all out, then the total runs it scored should be divided by 50 to get the average runs per over.
• If the team batting first loses all 10 wickets before the completion of 50 overs, then the final score should be divided by 50 to get the average runs per over.
• If the team chasing loses all its wickets before the completion of 50 overs, then the total runs should be divided by 50 to get the average runs per over.
• If the team chasing bats out all 50 overs with wickets in hand, then their final score should be divided by 50 to get the average runs per over.
• If the team chasing completes the chase with wickets in hand and overs still left to play, then in contrast to the previous system where the final score is divided by the number of overs played, the following method can be used:

The average runs per wicket should be calculated. That average multiplied by the wickets in hand should be used as an upper limit for the total number of runs that can be scored off the allotted 50 overs.

The score with which the team finished should be divided by the number of overs played to get the average runs per over. This average runs per over should then be multiplied by the remaining number of overs and added to the actual score with which the team ended up to calculate the possible final score. If the calculated score is less than the upper limit, this score should be considered for calculating the actual average runs per over.

If this score exceeds the upper limit, then the upper limit should be considered as the final score.

(Here both the upper limit and probable final score based on RPO act as mutual limiting factors)

#### Example 1:

In a tournament, the NRR is calculated by dividing the total number of runs scored by the total number of overs played. For out convenience, though, let’s take a single match here: the Pool A World Cup 2015 match between New Zealand and Scotland.

Scotland 142/10 in 36.2 overs

New Zealand 146/7 in 24.5 overs

According to the current NRR system, this is what we get:

Scotland’s average runs per over: 142/50 = 2.84

New Zealand’s average runs per over: 146/24.5 (actually 24.8333) = 5.8791

So New Zealand’s net run rate after that game = 5.8791-2.84 = 3.0391

An NRR of 3.0391 does not represent how close the game was.

#### It can be made accurate by the NRR system that I propose:

Scotland’s average runs per over: 142/50 = 2.84

New Zealand’s average runs per over:

NZ’s average runs per wicket: 146/7 = 20.857 runs per wicket

Upper limit = 146 + (3 x 20.857) = 146 + 62.571 runs = 208.571

New Zealand’s average runs per over: 146/24.5 (actually 24.8333) = 5.8791

Their probable score after 50 overs: 5.8791 x 50= 293.955

Since the probable score is greater than the upper limit, the upper limit should be considered as the final score. (New Zealand will have lost all their wickets for 208.571 runs, hence they are unlikely to get a score of 293.955)

Hence, NZ’s actual average runs per over = 208.571/50 = 4.171

So New Zealand’s NRR is: 4.171-2.84 = 1.331

#### Example 2:

Let us consider the Pool B World Cup 2015 match between England and Sri Lanka, the 22nd match of the tournament:

England 309/6 in 50 overs

Sri Lanka 312/1 in 47.2 overs

England’s average runs per over: 309/50 = 6.18

Sri Lanka’s average runs per over:

Sri Lanka’s average runs per wicket: 312

Upper limit: 312+ (9*312) = 312+2808 = 3120

Sri Lanka’s average runs per over: 312/47.2 (actually 47.333) = 6.591

Sri Lanka’s probable score in 50 overs: 50*6.591 = 329.55

Since their probable score is less than the upper limit, 329.55 can be considered as their final score. (Sri Lanka will lose its 10th wicket at 3120th run, but they will exhaust their 50 overs when they reach 329.55 runs)

Hence, Sri Lanka’s actual runs per over: 329.55/50 = 6.591

So Sri Lanka’s NRR: 6.591-6.18 = 0.411

In the unlikeliest of circumstances where the chasing team gets over the target losing all ten wickets, the final score of that team should be divided by 50 to get the average runs per over.

#### When DLS method is used

If the match is abandoned and the result is decided through Duckworth-Lewis-Stern method, the number of overs faced by the team batting second will be taken into account to decide the par score of the team batting first.

If DLS method is applied at an earlier point in the match to decide on a target for the team chasing, the team batting first should be accredited with 1 run less than the target for the chasing team. And then the NRR can be calculated using the above method.

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