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 in limited overs league competitions, analogous to the goal difference in association football.

The net run rate in a single game is the run rate per over that a team scores, minus the run rate per over that is scored against them.

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. ${\mbox{net run rate }}={\frac {\mbox{total runs scored}}{\mbox{total overs faced}}}-{\frac {\mbox{total runs conceded }}{\mbox{total overs bowled}}}$

The only complication is that 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).

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:

${\mbox{tournament net run rate }}={\frac {\mbox{total runs scored in match 1 + total runs scored in match 2 + ...}}{\mbox{total overs faced in match 1 + total overs faced in match 2 + ...}}}$

                           $-{\frac {\mbox{total runs conceded in match 1 + total runs conceded in match 2 + ...}}{\mbox{total overs bowled in match 1 + total overs bowled in match 2 + ...}}}$

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 for the loss of four wickets off 25.5 overs, scoring a single to win the game and end with 128 runs.
Despite Team A's runrate for the balls they faced being 127 / 25.667 = 4.95 (2dp) 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, however they managed to protect their wickets. Thus, only the 25 .(5/6) overs are added to the seasonal tally.

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

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 rate at which total 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. South Africa's listing in the Group A points table published in the group stages was as follows:

South Africa
P	W	L	NR	T	Pts	Net-RR	For	Against
3	3	0	0	0	6	+1.362	678/147.2	486/150

The columns we are looking at here are the last three: "Net-RR", "For" and "Against". The figure in the "Net-RR" column is achieved by subtracting the answer of the division in the "Against" column from the answer to the division in the "For" column.

To use this example:

FOR

South Africa had scored, so far in the tournament:

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

Across the three games, South Africa scored 678 runs in a total of 147 overs and 2 balls (actually 147.333 overs), a rate of 678/147.333 or 4.602 RPO (runs per over).

AGAINST

Teams opposing South Africa scored: India, 243 (for 5 wkts) from 50 overs. Sri Lanka, 110 all out from 35.2 overs. England, 133 all out from 41 overs.

In the case of Sri Lanka and England, because they 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, the run-rate scored against South Africa across the first three games is calculated on the basis of 486 runs in a total of 50 + 50 + 50 = 150 overs, a rate of 486/150 or 3.24 RPO.

NET-RR

The net run-rate is therefore + 4.602 - 3.24 = + 1.362 as shown in the table above.