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Quantifying loss in cricket I: Net run rate

In the British Isles, losing a game of cricket has been elevated to a fine art, so it’s surprising that no more sophisticated technique exists to measure these losses than the net run rate (NRR). Football is a far cruder game than cricket, yet the NRR is but a second’s thought away from goal difference; when points from victories are level, the NRR is used as a tiebreaker. Why has it been given this privileged status when its deficiencies are so readily flaunted, and with what can it be replaced?

Principally, a game of one-day cricket will operate around three quantities: runs, overs and wickets. NRR measures just two of these, and in choosing to do so wilfully ignores available information. Ostensibly this is because it is far more often the case that a team runs out of overs than wickets when batting – but this is unsatisfactory. The term ‘net run rate’ is, to my ear, a small misnomer. Here is how I would guess it was calculated: let team A be the victorious team, and team B be England. The associated runs and overs batted for each team would be represented as RA, RB, OA and OB. The net run rate is the difference between the teams’ runs per over (the ‘run rate’),

NRR = RA/OA – RB/OB;

A will have this number added to their prior NRR total, if any; B will have it subtracted from theirs. When two teams are level on points, the team with the higher total NRR is judged better. In fact, the formula is slightly different. If the team batting second loses in less than the full fifty overs, their run rate is their total runs divided by 50, instead of OB. So in fact

NRR = RA/OA – RB/OB;
OB = OB (B batting first) or 50 (B batting second);

this is why it was necessary to specify which of A and B was the winner. This quirk has been introduced so that, if the team batting second judges that the game is lost, their best play is to maximise their score by batting with temperance rather than maximise their runs per over by throwing everything they have at the bowlers. This is pragmatic, and also implicit acknowledgment that wickets must play a role in deciding how a team has performed; as X. W. Halliwell has recently suggested to me [Halliwell (2007), pvt. comm.] “[it’s] essentially ‘if both teams batted out their allowed innings, what would the winning margin have been?’ using the simplest extrapolation technique available.” If such a concession to inclusion of wickets is allowed, why not a more rigorous statistic?

To motivate further your discontent, I submit the following examples from the 2007 World Cup:

• Ireland (221/8 from 50 overs) drew with Zimbabwe (221 all out from 50 overs)

Here both teams take a point for the draw and the NRR is zero. But hang on, Zimbabwe lost all ten wickets – the final one going on the last ball – while Ireland lost only eight. So Ireland have demonstrably performed better and are given nothing to show for it, though I suspect this will be overlooked by the lads in the Guinness-induced haze of their moral victory.

• Sri Lanka (321/6 from 50 overs) beat Bermuda (78 all out from 24.4 overs)

Sri Lanka takes full points and the NRR is 4.86, but once again their lost wickets are ignored. Luckily for NRR apologists, the previous day’s game

• Australia (334/6 from 50 overs) beat Scotland (131 all out from 40.1 overs)

doesn’t demonstrate the flaws as well as it could, but even so some problems are evident: the NRR is 4.06, comparable to the magnitude of Sri Lanka’s demolition, but Australia’s play was tepid – pundits would be hard pressed to say that they were even half as convincing.

Enough moaning – time for action. The aim is to create a statistic that quantifies performance taking runs, overs and wickets into account. Get your pens out and, as Luke would say, play along at home.

6 Responses

1. […] and Metrics and Sport Berian 7:02 pm A few days ago I penned a wee diatribe on the use of net run rate (NRR) as a tiebreaker in cricket. Today I will outline a few […]

2. dear sir,
i just read how to calculate nrr. i am confused can u explain me in detail along with example.
for example take srilanka and bermuda match, srilanka got +4.86 run rate how it was calculated

3. Hi b.anandan,

To calculate a team’s run rate, take the number of runs scored by a team and divide by the number of overs they faced. There is an exception to this, as I’ll mention below. For the Sri Lanka – Bermuda match, Sri Lanka score 321 from their 50 overs, so their run rate is

RR(SL) = 321 / 50 = 6.42;

if we apply this formula to Bermuda, we get

RR(Ber) = 78/24.67 = 3.16.

This is WRONG. The critical idea is that if the team batting second loses, having been bowled out in less than 50 overs – as happened with Bermuda – then their runs are divided by 50, *not* the number of overs bowled. So in fact,

RR(Ber) = 78/50 = 1.56.

The net run rate is the difference between the two teams’ individual run rates. So

NRR(SL) = RR(SL) – RR(Ber) = 6.42 – 1.56 = 4.68
NRR(Ber) = RR(Ber) – RR(SL) = 1.56 – 6.42 = -4.68

That’s all there is to it! But remember, NRR does not take wickets lost into account, so it is inadequate for judging how the teams performed.

Berian.

4. Hi Berian, a friend of mine came up with some more inadequacies of the NRR. Check it out.

http://www2b.abc.net.au/science/k2/stn/newposts/2857/topic2857000.shtm

5. Hi. I found this blog at random and found a cricket post. Hope I’m not too late into this discussion.

If the team batting second loses in less than the full fifty overs, their run rate is their total runs divided by 50, instead of OB.
According to the playing conditions for the World Cup (PDF link): “In the event of a team being all out in less than its full quota of overs, the calculation of its net run rate shall be based on the full quota of overs to which it would have been entitled and not on the number of overs in which the team was dismissed.”

This applies to both the team batting first and the team batting second.

I disagree that in the case of the Zim-Ireland tie, Ireland performed better. Each side should use whatever strategy it can to maximise the number of runs it scores. Some teams will have stronger lower-orders, and so they can afford to go harder early and lose more wickets. Other teams have to bat more carefully at the start and will try to lose fewer wickets. Only the number of runs matters.

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