Expert Blog

The idea of the par score

If you have wondered how the Duckworth-Lewis method makes or breaks a game, look no further. Our expert tells you more.

Let’s suppose that India score 275/5 in 50 overs in an ODI game against England at Leeds. Suppose England have reached 98/2 after 22 overs in their chase when run (or even snow!) stops the game.

Who’s winning at this stage?

This is where we use the idea of the par score, now used by the Duckworth-Lewis method. The par score is the score that England must make to tie the match. England win if they score at least one run more than this par score.

To be sure, the par score is not unique. It depends on how much the team batting first has scored, the overs remaining in the innings and the wickets lost by the chasing team. For the same number of overs remaining, the par score is lower if fewer wickets are lost, and higher if more wickets are lost. In our example if 98/2 is the par score, then 88/1 or 121/3 may also be par scores (they are not actual D/L par scores, I’m just guessing).

On most English grounds, the par score is displayed on the score board – well, sort of … what score boards actually display are numbers like +11 or -5. The display ‘+11’ means that the side batting second is now 11 runs ahead of the D/L par score; ‘-5’ would mean that the side chasing is five runs behind the D/L par score.

Remember that the par score is not static. It keeps changing from ball to ball. Let’s suppose that, in our example, England’s 98/2 was the par score after 22 overs. Let’s suppose that the first ball of over 23 is a dot ball … and then it starts raining or snowing! Then in all probability, England have lost the match because that dot ball may have pushed the par score up to 99/2.

Amazingly enough this was how South Africa probably got knocked out of the 2003 World Cup that they were hosting. Chasing Sri Lanka’s 268/9, South Africa were 216/6 when Muralitharan started bowling the 45th over – which was almost certain to be the last with rain turning heavier. The par score at the end of that over was 229/6; so the batsmen in the middle – Boucher and Klusener – were told that they had to get to 229 by the end of the over without losing their wicket. Boucher hit a six off Murali’s fifth ball to take South Africa to 229/6. Happy to reach 229, and perhaps not wanting to take a risk and get out, Boucher quietly defended Murali’s last ball.

When the match was called off after over 45, a jubilant South African team thought that they had won! They hadn’t! They had merely tied the match because South Africa needed to score one run more than the par score to win. The loss of two points because of the tie finished off SA’s World Cup campaign. The story could have been very different if Boucher had played the last ball for a single. Sadly, the South African team management confused the par score with the winning score.

Some six years later, it was again some confusion around the par score that gave England a shock victory over West Indies. With light fading at Guyana, West Indies were ahead of the D/L par score at 244/6 when Broad trapped Ramdin lbw. The loss of the 7th wicket meant that 244 was no longer the par score; it had gone up to 245!

Not realizing this, the West Indies coach John Dyson called his team in when the umpires offered lights. West Indies could have won if they had walked off after the new batsman had scored a single or two off the next ball.

The par score is an interesting idea: it measures the difference between two teams after every ball in terms of runs. In the Bangladesh-India ODI on January 11, 2010, India overtook Bangladesh’s score of 247 in 43 overs. The record books will say that India won by 6 wickets with 7 overs to spare. But what was India’s victory target in terms of runs? Let us suppose that the D/L par score while chasing 247 with four wickets lost and seven overs remaining was 187/4 (again, just guessing). We could then say that India won by 60 runs.

The par score can also be used to define an interesting concept called the ‘pressure index’. We will talk about the pressure index in the next blog.