When An Actuary Helped Cricket Survive!!

When An Actuary Helped Cricket Survive!!

Call for help, Comes an Actuary!!

South Africa needed 22 off 13 balls to beat England in Sydney on March 22,1992 when rain stopped play. Ten minutes later the players were back on... and South Africa needed 21 off one ball. Blame the lowest-scoring-over rain rules, which ruined a cracking contest and chances of a WC Final.

South Africa Team was out of the competition, but they left with a question hanging amongst every cricket fan….

What if this happens again???

That day Mr. Christopher Martin Jenkins said on the radio… "Surely someone somewhere could come up with something better” and soon Mr. Duckworth realized that it was a mathematical problem that required a mathematical solution."

And then came the revolution!!

…….

Since then, Mr. Duckworth – An Actuary, and Mr. Tony Lewis, a renowned Statistician worked together for years, just to bring out an effective method of calculating target score in 1997, officially recognized by ICC in 1999...

They developed an easy way by which one can calculate the score with the help of a Calculator, Paper and of course a Pen unless you are great at Mental Math….!!

So, let's dig out how did Duckworth-Lewis Duo gave the cricketing world, a tool that is remembered whenever rain stops play!!

Basis of DLS Method:

When a match is shortened after it has begun, a revised target is set using the The D/L method.

The DL method is based on two things

1. Number of overs left

2. The number of wickets they have in hand.

A Resource Table was created, Over by Over and for each wicket remaining.

1.] It was a table with % of resources that are available to the Team Batting based on the number of Overs Left to bat and wickets in Hand…

2.] For a 50 Over or 20 Over, match, at the start resources were 100% as all balls and wickets are available

One may seem, that this method is as complex as Einstein’s Theory of Relativity….

Surprisingly, it doesn’t need a degree in mathematics to understand it or to use it!

Working of the Method:

Just when the play stops or gets suspended temporarily, the resource percentage still available to the team is to be noted from the Resource Percentage Table. We name it R(a).

After the suspension, when the play resumes, again, we are to make a note of the resource percentage available to the team then.

This can be done similarly to the above. We name it R(b).

Subtracting, we get R(L1) = R(a) – R(b).

R(L1) means the Resource Percentage Lost due to interruption or suspension of play.

Now, in case the innings do not resume after the suspension. In that case, Since R(b) = 0, R(L1) = R(a).

If there happens to be more than one suspension, then all the resource percentage losses are taken in the order R(L1), R(L2), R(L3), and so on.

The final Resource Loss Percentage, R(L) = R(L1) + R(L2) + R(L3) ……

In the initial stage, the Resource Percentage Available to any team at the start of the innings is 100%.

Firstly, we need to evaluate Thus, R1 = [ 100 – R(L) ]%

Now, we are to evaluate R2, which can be estimated simply by looking at the table.

If Team2 gets a full 50 overs, R2 will be 100%.

If not, it has to be read from the table based on the number of overs remaining and 0 wickets lost.

Now, the values of R1 and R2 are to be compared next.

If R1 = R2, NO alterations are made to the target i.e., no revised target for Team2.

T = S + 1

1.] If R1 > R2, Team2’s revised target is made by reducing Team1’s total, S, in the ratio R2/R1

Any decimal figures should be neglected and the result should be obtained in integer form. T = (S x R2/R1) + 1

2.] If R2 > R1, Team2’s revised target is calculated and it is greater than Team1’s total, owing to the excess of resources.

The excess resources are calculated by R2 – R1 and it is added to the total as a multiple of the average total, agreed by the two teams, i.e., G50.

T = S + (R2 – R1) x G50/100 + 1

However, the above method holds for Standard Edition. In the case of Professional Edition, there is no involvement of G50 or the average score.

Hence, T = (S x R2/R1) + 1

This is the algorithm.

With some modifications to the modern-day scoring rate by Steven Stern, this method was renamed as DLS Method!!

Too many variables?? Let's see an example!!

Example:

In an ODI match, Team 1 reaches 79/3 after 20 overs and then there is a suspension in play. It is decided that 20 overs of the match should be lost. Team 1 resumes reaching a final total of 180 in its revised allocation of 40 overs.

Solution :

Since 20 overs are lost, 10 overs are lost for each team.

S = 180

When play was suspended, Team1’s resource percentage available(30 overs left and 3 wickets lost), R(a) = 61.6

When play was resumed, Team1’s resource percentage available(20 overs left and 3 wickets lost), R(b) = 49.1

R(L) = R(a) – R(b) = (61.6 – 49.1)% = 12.5%

R1 =100 – R(L) = (100 – 12.5)% = R1 = 87.5%

Resource percentage available to Team2 at the start of the innings(40 overs left and 0 wickets lost), R2 = 89.3%

R2>R1

So, by Standard Edition, the revised target will be,

T = S + G50 x (R2 – R1)/100 + 1 = 180 + 245 x (89.3 – 87.5)/100 + 1 = 185 : [Target is 185]

By Professional Edition Method,

T = (S x R2/R1) + 1 = 180 x (89.3%/87.5%) + 1 = 185 : [Target is 185]

Outcome:

Isn't this very simple?? Yes, it is.....

This was good enough in 95 percent of matches, but in the 5 percent of matches with very high scores, the simple approach started to break down. To overcome the problem, an upgraded formula was proposed with an additional parameter whose value depends on the Team 1 innings. This became the Professional Edition.

Mr. Lewis and Duckworth were appointed MBEs in the 2010 British honors for their services to cricket and mathematics.