# Net run rate

Net Run Rate (NRR) is a statistical method used in analyzing team work 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.

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.[1]

## Step by step explanation

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), ie. $\mbox{run rate }=\frac{\mbox{total runs scored}}{\mbox{total overs faced}}$.

So if a team scores 250 runs off 50 overs then their RR is $\frac{250}{50} = 5$. Note that as an over is made up of six balls, each ball is 1/6 of an over, despite being normally written in cricket's notation as .1 of an over. So if they got that same score off 47.5 overs, their RR would be $\frac{250}{47\frac{5}{6}} \approx 5.226$.

The concept of net run rate involves taking the opponents' final run rate away from the team's run rate, ie. $\mbox{net run rate }=\frac{\mbox{total runs scored}}{\mbox{total overs faced}}-\frac{\mbox{total runs conceded }}{\mbox{total overs bowled}}$.

Usually, runs and overs bowled are summed together throughout a season to compare teams in a league table. A team's overall NRR for a tournament is not the sum or average of the NRR's from the individual matches, but is:

$\mbox{tournament net run rate }=\frac{\mbox{total runs scored in all matches}}{\mbox{total overs faced in all matches}} - \frac{\mbox{total runs conceded in all matches}}{\mbox{total overs bowled in all matches}}$

The exceptions to this are:

• if a team is bowled out, it is not the overs faced which their score is divided by; instead the full quota of overs is used (e.g. 50 overs for a One Day International and 20 overs for a Twenty20 match).
• if a match is interrupted and Duckworth-Lewis revised targets are set, the revised targets and revised overs are used to calculate the net run rate for both teams (see below).
• if a match is abandoned as a No Result, none of the runs scored or overs bowled count towards this calculation.

## Scenarios

All scenarios assume One Day International rules with 50 overs per side.

### 1. Side that bats first wins

• Team A bat first and score 287-6 off their full quota of 50 overs. Team B fail in their run chase, early losses causing them to struggle to 243-8 in their 50 overs.
• Team A's Run Per Over is $\frac{287}{50} = 5.74$
• Team B's Run Per Over is $\frac{243}{50} = 4.86$
• Team A's NRR for this game is 5.74 − 4.86 = 0.88. If this was the first game of the season, their NRR for the league table would be +0.88.
• Team B's NRR for this game is 4.86 − 5.74 = −0.88. If this was the first game of the season, their NRR for the league table would be −0.88.

### 2. Side that bats second wins

• Team A bat first and score 265-8 off their full quota of 50 overs. Team B successfully chase, getting their winning runs with a four with sixteen balls (2.4 of the 50 overs) remaining, leaving them on 267-5.
• Team A's rpo is $\frac{265}{50} = 5.30$
• Team B faced 47.2 overs, so their rpo is $\frac{267}{47\frac{2}{6}} \approx 5.64$
• Assuming that Team A and Team B had previously played as in the game in scenario one, the new NRR for Team A would be $\frac{287+265}{50+ 50}-\frac{243+267}{50+47.33} = \frac{552}{100}-\frac{510}{97.33} \approx 0.28$

### 3. Side that bats first is bowled out, side batting second wins

• Team A bat first and are skittled out for 127 off 25.4 overs. Team B reach the target off 30.5 overs, ending with 128/4.
• Despite Team A's runrate for the balls they faced being 127 / 25.667 = 4.95, because they were bowled out the entire 50 overs are added to their total overs faced tally for the tournament, and Team B are credited with having bowled 50 overs.
• Team B actually scored at a slower pace (128/30.833 = 4.15), however they managed to protect their wickets and win. Thus, only the 30.833 overs are added to the seasonal tally.
• Team A's NRR for this game is (127/50) − (128/30.833) = −1.61.
• Team B's NRR for this game is (128/30.833) − (127/50) = +1.61.
• If 25.667 had been used for Team A's overs total rather than 50, Team A would have finished the match with a positive match NRR, and improved tournament NRR, despite losing. (Similarly Team B with a worsened NRR, despite winning.)

### 4. Side that bats second is bowled out, side batting first therefore wins

• Team A bat first and set a formidable 295/5 off their complement of 50 overs. Team B never get close, being bowled out for 116 off 35.4 overs.
• As in scenario 2, 295 runs and 50 overs are added to Team A's tally.
• However, Team B, despite facing only 35.4 overs, have faced 50 overs according to the NRR calculations, and Team A have bowled 50 overs.

### 5. Both sides are bowled out, side batting first therefore wins

• Team A bat first, and manage 117 off 24 overs on a difficult playing surface. Team B fall agonizingly short, reaching 112 off 23.3 overs.
• In this case, both teams get 50 overs both faced and bowled in the overs column for the season, just as in example 1.

### 6. The game ends in a tie

• Runs and overs are added as in the examples above, with teams bowled out being credited with their full quota of overs. Thus, the net run rate will always be zero for both teams.

### 7. Interrupted games with revised targets

• In matches where Duckworth-Lewis revised targets are set due to interruptions which reduce the number of overs bowled, those revised targets and revised overs are used to calculate the net run rate for both teams.
• For example, in a 50-over World Cup first-round group match, Team A are dismissed for 165 in 33.5 overs.
• Team B progresses to 120-0, but play is halted after 18 overs due to rain.
• Six overs are lost, and the target is reset to 150, which Team B reach comfortably after 26.2 overs with only 2 wickets lost.
• Because the target was revised, 6 overs were lost and Team A were bowled out, Team A's total is reset to 149 from 44 overs, thus their RR $= \frac{149}{44} \approx 3.39$. Team B's RR, however, is computed as normal: $\frac{150}{26.33} \approx 5.70$.
• Computing the match NRR for Team A gives us 3.39 - 5.70 = -2.31. Team B's NRR is: 5.70 - 3.39 = 2.31.

### 8. Abandoned games recorded as No-Result

• Abandoned games are not considered, whatever the stage of the game at stoppage may be, and the scores in such games are immaterial to NRR calculations.

## Net Run Rate within a tournament

### Basic example

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.

Let's take as an example South Africa's net run rate in the 1999 World Cup.

FOR

South Africa scored:

• Against India, 254 runs (for 6 wkts) from 47.2 overs.
• Against Sri Lanka, 199 runs (for 9 wkts) from 50 overs.
• Against England, 225 runs (for 7 wkts) from 50 overs.
• Against Kenya, 153 runs (for 3 wkts) from 41 overs.
• Against Zimbabwe, 185 runs (all out) from 47.2 overs.

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 (ie. 238.333 overs), an average run rate of 1016/238.333 = 4.263.

AGAINST

Teams opposing South Africa scored:

• India, 253 (for 5 wkts) from 50 overs.
• Sri Lanka, 110 (all out) from 35.2 overs.
• England, 103 (all out) from 41 overs.
• Kenya, 152 (all out) from 44.3 overs.
• Zimbabwe, 233 (for 6 wkts) from 50 overs.

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 tournament net run rate is therefore 4.263 − 3.404 = +0.859.

### Tournament Net Run Rate as weighted average of the run rates

Tournament net run rate 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).

For example, in Group D of the 2009 World Twenty20, New Zealand scored:

• Against Scotland, 90 runs from 6 overs, a run rate of 15.00.
• Against South Africa, 127 runs from 20 overs, a run rate of 6.35.

New Zealand conceded:

• Against Scotland, 89 runs from 7 overs, a run rate of 12.714.
• Against South Africa, 128 runs from 20 overs, a run rate of 6.40.

Using the formula above, this gives New Zealand:

$\mbox{tournament net run rate }=\frac{\mbox{90 + 127}}{\mbox{6 + 20}} - \frac{\mbox{89 + 128}}{\mbox{7 + 20}} = 0.31$

This can alternatively be calculated as the weighted average of the run rates as follows:

$\mbox{tournament net run rate }=\left(15.00\times\frac{\mbox{6}}{\mbox{6 + 20}}\right) +\left(6.35\times\frac{\mbox{20}}{\mbox{6 + 20}}\right) -\left(12.714\times\frac{\mbox{7}}{\mbox{7 + 20}}\right) -\left(6.40\times\frac{\mbox{20}}{\mbox{7 + 20}}\right)$

                          $=\left(15.00\times 23.1%\right)+\left(6.35\times 76.9%\right)-\left(12.714\times 25.9%\right)-\left(6.40\times 74.1%\right)$

                          $=0.31$


## Criticisms

• In the language of Duckworth-Lewis, 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 team regarded as having a narrow victory can have a higher NRR than a team regarded as having a comfortable victory. For example, a team which just manages to win a close game with many overs to spare but with only one wicket in hand is likely to have a higher NRR than a team which paces itself to win comfortably with only a few overs in hand but many wickets.[2]
• A team's NRR measures how many more runs it scores per over than it concedes, so the NRRs of all the teams in a league table should sum to zero. However, the way tournament NRR is calculated (total runs scored/total overs faced − total runs conceded/total overs bowled), means this rarely happens. If the sum is positive, this implies that overall more runs were scored per over than were conceded, which is obviously impossible. (And if the sum is negative that less were scored than conceded). The teams' tournament NRRs will all sum to zero if all the teams have played one or zero matches, or if every innings had exactly the same number of overs. This happens sometimes with small league tables. For example, Group B in the 2009 World Twenty20 featured three matches. Five of the six innings had the full complement of 20 overs, and in the sixth innings the team was bowled out, which counts as the full complement of 20 overs. If the teams' tournament NRRs were instead the sum of their individual match NRRs, then the teams' tournament NRRs would always sum to zero, or if the average of the individual match NRRs were used, then the tournament NRRs would sum to zero if all teams had played the same number of games.