Net run rate (NRR) is a statistical method used in analysing teamwork and/or performance in cricket.[1] It is the most commonly used method of ranking teams with equal points in limited overs league competitions, similar to goal difference in football.
The NRR in a single game is the average runs per over that team scores, minus the average runs per over that is scored against them. The NRR 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.[2] [3] This is the same as the weighted average of the run rates scored in each match (weighted by the lengths of the innings batted compared to the other innings batted), minus the weighted average of the run rates conceded in each match (weighted by the lengths of the innings bowled compared to the other innings bowled). This is not usually the same as the total or average of the NRRs from the individual matches in the tournament.
A positive NRR means a team is scoring faster than its opposition overall, while a negative NRR means a team is scoring slower than the teams it has come up against.[4] It is therefore desirable for the NRR to be as high as possible.
NRR has been criticised as hard to understand. Also, while it measures how quickly teams score and concede runs, this is not at all the same as how big the teams' margins of victory or defeat are (as it ignores wickets lost), and so ranking sides by NRR does not rank them by size of victory. This means a team which progresses in a tournament at the expense of another team, due to a higher NRR, may not have truly performed better than their opponents.[5]
In the Cricket World Cup, the first use of NRR was in the 1992 tournament.[6] Earlier tournaments used run rate instead as the tie-breaker.[7]
A team's run rate (RR), or runs per over (RPO), is the average number of runs scored per over by the whole team in the whole innings (or the whole innings so far), i.e.
| runrate= | totalrunsscored |
| totaloversfaced |
So if a team scores 481 runs off 50 overs then their RR is
| 481 | |
| 50 |
=9.62
| 481 | |||
|
=9.986
The concept of net run rate involves subtracting the opponents' run rate from the team's run rate, i.e.
| matchnetrunrate= | totalrunsscored | - |
| totaloversfaced |
| totalrunsconceded | |
| totaloversbowled |
For two teams which have just played, the winning side will have a positive Match NRR, and the losing side will have the negative of this (i.e. the Match NRRs will be additive inverses, summing to zero). A single match's NRR is used very rarely, perhaps only after a team has played one match in a tournament, so their tournament NRR is the same as the match NRR.
Usually, runs and overs are summed together throughout a season to compare teams in a league table. A team's overall NRR for a tournament is not defined as the sum or average of the NRR's from the individual matches, but as:
| tournamentnetrunrate= | totalrunsscoredinallmatches |
| totaloversfacedinallmatches |
-
| totalrunsconcededinallmatches | |
| totaloversbowledinallmatches |
The exceptions to this are:
All scenarios assume One Day International rules with 50 overs per side.
| 287 | |
| 50 |
=5.74
| 243 | |
| 50 |
=4.86
| 265 | |
| 50 |
=5.30
| 267 | |||
|
=5.64
| 287+265 | - | |
| 50+50 |
| 243+267 | |||
|
=
| 552 | - | |
| 100 |
| 510 | |||
|
=5.52-5.24=0.28
| 127 | - | |
| 50 |
| 128 | |||
|
=-1.61
| 128 | - | ||
|
| 127 | |
| 50 |
=+1.61
=
| 149 | |
| 44 |
≈ 3.39
| 150 | |
| 26.33 |
≈ 5.70
| = | ParScoreforTeamB |
| OversfacedbyTeamB |
=
| 140 | |
| 30 |
≈ 4.67
| = | RunsscoredbyTeamB |
| OversfacedbyTeamB |
=
| 172 | |
| 30 |
≈ 5.73
Most of the time, in limited overs cricket tournaments, there are round-robin groups among several teams, where each team plays all of the others. Just as explained in the scenarios above, the NRR is not the average of the NRRs of all the matches played, it is calculated considering the overall rate at which runs are scored for and against, within the whole group.
Here is an example South Africa's net run rate in the 1999 World Cup.
FOR
South Africa scored:
In the case of Zimbabwe, because South Africa were all out before their allotted 50 overs expired, the run rate is calculated as if they had scored their runs over the full 50 overs. Therefore, across the five games, South Africa scored 1016 runs in a total of 238 overs and 2 balls (i.e. 238.333 overs), an average run rate of 1016/238.333 = 4.263.
AGAINST
Teams opposing South Africa scored:
Again, with Sri Lanka, England and Kenya counting as the full 50 overs as they were all out, the run rate scored against South Africa across the five games is calculated on the basis of 851 runs in a total of 250 overs, an average run rate of 851/250 = 3.404.
NET RUN RATE
South Africa's final tournament NRR is therefore 4.263 − 3.404 = +0.859.
After match one
In the above example of South Africa at the 1999 World Cup, after their first match their tournament NRR was
| 254 | |
| 47.33 |
-
| 253 | |
| 50 |
.
As Run Rate = Runs scored/Overs faced, the runs scored by and against South Africa in each innings can be replaced in this formula by Run Rate x Overs faced. They scored 254 runs from 47.33 overs, a rate of 5.37 runs per over. Therefore, the total of 254 runs can be replaced by 5.37 runs per over x 47.33 overs. Similarly, the total of 253 runs conceded can be replaced by 5.06 runs per over x 50 overs:
| \left(5.37 x | 47.33 |
| 47.33 |
\right)-\left(5.06 x
| 50 | |
| 50 |
\right)=\left(5.37 x 100\%\right)-\left(5.06 x 100\%\right).
After match two
After their second match, tournament NRR was
| 254+199 | |
| 47.33+50 |
-
| 253+110 | |
| 50+50 |
,
| 254 | |
| 97.33 |
+
| 199 | |
| 97.33 |
-
| 253 | |
| 100 |
-
| 110 | |
| 100 |
.
Making the same replacements for 254 and 253 as before, and replacing 199 runs scored in match two with 3.98 runs per over x 50 overs, and 110 runs conceded in match two with 2.20 runs per over x 50 overs, this becomes:
| \left(5.37 x | 47.33 |
| 97.33 |
\right)+\left(3.98 x
| 50 | |
| 97.33 |
\right)-\left(5.06 x
| 50 | |
| 100 |
\right)-\left(2.20 x
| 50 | |
| 100 |
\right)
=\left(5.37 x 48.6\%\right)+\left(3.98 x 51.4\%\right)-\left(5.06 x 50\%\right)-\left(2.20 x 50\%\right).
After match three
After their third match, tournament NRR was
| 254+199+225 | |
| 47.33+50+50 |
-
| 253+110+103 | |
| 50+50+50 |
,
| 254 | |
| 147.33 |
+
| 199 | |
| 147.33 |
+
| 225 | |
| 147.33 |
-
| 253 | |
| 150 |
-
| 110 | |
| 150 |
-
| 103 | |
| 150 |
.
Making the same replacements for 254, 253, 199 and 110 as before, and replacing 225 runs scored in match three with 4.50 runs per over x 50 overs, and 103 runs conceded in match three with 2.06 runs per over x 50 overs, this becomes:
| \left(5.37 x | 47.33 |
| 147.33 |
\right)+\left(3.98 x
| 50 | |
| 147.33 |
\right)+\left(4.50 x
| 50 | |
| 147.33 |
\right)-\left(5.06 x
| 50 | |
| 150 |
\right)-\left(2.20 x
| 50 | |
| 150 |
\right)-\left(2.06 x
| 50 | |
| 150 |
\right)
=\left(5.37 x 32.1\%\right)+\left(3.98 x 33.9\%\right)+\left(4.50 x 33.9\%\right)-\left(5.06 x 33.3\%\right)-\left(2.20 x 33.3\%\right)-\left(2.06 x 33.3\%\right).
Tournament NRR as a weighted average
Therefore, tournament NRR can alternatively be thought of as the weighted average of the run rates scored in each match (weighted by the lengths of the innings batted compared to the other innings batted), minus the weighted average of the run rates conceded in each match (weighted by the lengths of the innings bowled compared to the other innings bowled). Each time another match is played, the weights of the previous innings reduce, and so the contributions of the previous innings to overall NRR reduce.
For example, the 5.37 run rate achieved in match one had 100% weighting after match one, 48.6% weighting after match two, and 32.1% weighting after match three.
In the language of Duckworth-Lewis-Stern, teams have two resources with which to score runs − overs and wickets. However, NRR takes into account only one of these − overs faced; it takes no account of wickets lost. Therefore, a narrow victory can produce a higher NRR than a comfortable victory.[8] For example, in the 2013 Champions Trophy Group A:
This fact can encourage a team to play in an overly aggressive manner, to maximise NRR by batting with next to no regard for preserving wickets, when the required run rate alone seems low, which can then put the team in danger of losing.[9]
A team may choose to artificially reduce their margin of victory, as measured by NRR, to gain an additional advantage by not disadvantaging their opponent too much. For example, in the final round of matches in the 1999 World Cup Group B, Australia needed to beat West Indies to progress to the Super Six stage, but wanted to carry West Indies through with them to the Super Six, rather than New Zealand. This is because Australia would then have the additional points in the Super Six stage from beating West Indies in the group stage, whereas they had lost to New Zealand in the group stage. It was therefore to Australia's advantage to reduce their scoring rate and reduce their margin of victory, as measured by NRR, to minimise the negative impact of the match on West Indies' NRR, and therefore maximise West Indies' chance of going through with them.[10]
However, this is also likely to be a possibility with alternatives to NRR.
This is similar to the way a narrow victory for one side in a game of football may enable both sides to progress to the next stage, e.g. West Germany v Austria in the 1982 World Cup.
A number of alternatives or modifications done to NRR is suggested below as following -
Duckworth Lewis Stern method in used Tournament NRR as present, but when a side batting second successfully completes the run chase, use the Duckworth-Lewis method to predict how many runs they would have scored with a full innings. This means the calculation would be done on the basis of all innings being complete, and so would remove the criticisms of NRR penalising teams which bat second, and NRR not taking into account wickets lost. However, this does nothing to alter the fact that when matches are rain-affected, different matches and even two complete innings in one match, can be different lengths long (in terms of overs), and so does nothing about some of the other criticisms above.
Therefore, alternatively, use Duckworth–Lewis–Stern to predict the 50-over total for every innings less than this,[11] even, for example, if a match is reduced to 40 overs each, and a side completes their 40 overs. This would make every innings in the tournament the same length, so would remove all the criticisms above. However, a side will bat differently (less conservatively) in a 40-over innings compared to a 50-over innings, and so it is quite unfair to use their 40-over total to predict how many runs they could have scored in 50 overs.
Calculate tournament NRR as the total or average of the individual match NRRs. This would mean all matches have equal weighting, no matter how long they were, (rather than all batted overs across the tournament having equal weighting, and all bowled overs across the tournament having equal weighting). This would remove the criticisms under the 'Tournament NRR calculation' subheading above. For example, the different teams' tournament NRRs would always sum to zero if the total of the individual match NRRs were used, or if the average of the individual match NRRs were used and all teams had played the same number of games.
An example of when using this would have made a difference was the 1999 Cricket World Cup Group B. New Zealand and West Indies finished level on points. Having scored a total of 723 runs from 201 overs, and conceded 746 runs from 240.4 overs, West Indies' tournament NRR was (723/201) − (746/240.6667) = 0.50. However, New Zealand had scored 817 runs from 196.1 overs, and conceded 877 runs from 244.2 overs, so their tournament NRR was (817/196.167) − (877/244.333) = 0.58. Therefore, New Zealand progressed to the Super Six stage and West Indies were eliminated. However, with individual match NRRs of −0.540, 0.295, 0.444, 5.525 and −0.530, the West Indies' average match NRR was 1.04, and with individual match NRRs of 1.225, 0.461, −0.444, −1.240 and 4.477, New Zealand's average match NRR was 0.90. Therefore, West Indies' average NRR was better than New Zealand's.
Split teams level on points using the results from the matches between them. However, this unfairly increases the importance of that one match and reduces the importance of other matches in the league, when all matches in a league should be of equal value − the team with the better head-to-head record will have a worse record against other teams. Also, the head-to-head record will not decide it if the game between them was a No result, or if they played each other twice, and won one game each.[12] [13] An example of where a team progressed further because of a head-to-head result taken into account, was in the 1999 World Cup semi-finals when South Africa vs Australia played to a tie but Australia progressed due to them beating South Africa in the group stages, even though South Africa won more matches.
Alternatively, stage a play-off match between the teams level on points. However, organising this at very short notice may be difficult, or the teams may be in the middle of a league table with no promotion or relegation or progression at stake, so there may be no appetite for a play-off match.
These two methods both also run into difficulties when three or more teams are level on points.