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part eccentric ... part fun .... stubborn .. but not stuck up ... very open to different views, ideas and possibilities ... varied interests ... engineer ... mba ... trying-to-be-a-good-entrepreneur ... ex-software ... ex-quality ... ex-tobacco ... ex-alcohol ... trying-to-be-ex-cancer
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Saturday, September 23, 2006

Frank and Tony - Cricketing Gods

Here's one .....................When the "Rain Gods" shower their displeasure on cricket matches..............who saves the game ???

hint..... its not the players , neither the umpires, referees or the spectators

I must tell you......

The job is for two mathematician, statistician types.....whose abode is in the land of the English

Their names : "Frank Duckworth" and "Tony Lewis"

Their claim to fame: They have stated the cricketing "obvious" and then went on to give it a quantitative basis.

The obvious fact stated by Duckworth and Lewis :- The major resources needed by any team to score runs are 1) Overs, in which to score 2) The batsmen who can bat in these overs (wickets remaining)

Seems simple.. right???

Interestingly, This simple statement(and the attached tables and methods) have made Duckworth and Lewis an inalienable part of cricketing world. They decide the destiny of every team involved in an interrupted match.

This makes them "great men".. gods of the religion called cricket

History tells us this interesting fact about "great men". Most "great men" have not only stated the "obvious", but have also given some numbers and formula regarding the "obvious". Numerous people have become immortal by stating simple observations and then attaching confusing numbers to their observations. Take the case of Newton:- He first stated the obvious ("apples tend to fall on the earth") , he then went on to attach numbers/formulas with this "obvious" {9.8 m/sec,G, g, F=ma, v = ut+ 0.5 (at*at)..etc etc}

What Newton did for Physics, Duckworth/Lewis (D/L) have done for cricket. They have managed to confuse the common man.

D/L have given us formulas and tables that quantitatively link the two main batting resources- overs and wickets. They have reduced the two parameters into one - "Available run-scoring resources". Further, D/L have gone on to give the exact percentage of "available run-scoring resources" left with any team, at any stage of an innings ("stage" being defined by the remaining overs and the wickets in hand)

But how does D/L decide matches???

When rain interrupts matches, only parts of the initially available "run scoring resources" get used in the two innings (other parts get washed off).

While one team might get to use one fraction (say, only 75% of the resources) in their innings, the other team might get to use another fraction (say 50%).

It is unfair to compare the score of a team which used 50% of its resources to that of a team which used 75%.

This is where D/L come in, their method
1) Calculates the difference in available run scoring resources of the two teams
2) Adjusts for this difference, and
3) Gives a fair way of judging the winner.

Let me elaborate,

Take the example of "Team1" playing "Team2" in a one day match. Let there be two interruptions in Team1's batting and one Interruption in Team2 batting.

For Team1 -
Interruption 1 (9 overs washed when the team has played for 10 overs)
Status Interruption beginning - 1 wicket lost, 40 overs remaining - Resource avail - 84.2%
Status Interruption end - 1 wicket lost, 31 overs remaining - Resource avail - 73.2%
Resource loss = (84.2 -73.2) = 11%

Interruption 2 (i'll spare you the details) resource lost 9%

Total Resource loss (Team1) = 20%

Team1 Scores 160 Runs. As a result of rains, Team2 innings reduced to 39 overs

For Team 2

Resource loss due to shorter innings - 12%
Interruption 1 (I am sparing you the details) resources lost 18%

Total Resource loss (Team2) = 30%

Over all, Team1 had 80% resources at its disposal, while Team2 had 70% resources at its disposal.

D/L sets the new target for Team2 by reducing Team1's score in the proportion of the resources available

New Target = 160* (70/80) + 1 (plus one cause you need one more than the other team to win) = 141

If Team2 makes 141 by the end of the "reduced overs", then they win, else they lose.

This was a case when the team batting second had less resources at their disposal.

The other case is when the second batters have more resources than first batters. There is different calculation for this case - Team2 would need to score more than what Team1 scored

Lets take that case: Team1 has 70% available resources (and scores 160) while Team2 has 80% available resources

Warning: this formula has not resemblance to earlier formula
Now, Revised Target = 160 + (235(80-70)/100) + 1 = 184

Please note, in the first case, a proportionate reduction in target was done. But in the second case the "magic number" 235 was used.

D/L has funny ways.

Whatever you think of the confusing formulas, D/L have become a part of the cricketing history. A refined version of their method (which runs on computers) has been used for all interrupted international one day matches since 2002.

Congratulations Frank and Tony..

As for me.........I am looking for an "obvious" to state... I also want to find some confusing numbers behind it.

1 comment:

nothing spectacular said...

here is an obvious fact - less work with more pay leads to more happiness. perhaps you could find coefficients of work done and pay received and therefore calculate expected happiness distribution of a person over a period of time. you could then sell this information to credit card salesmen, so that they call up the guy only when he is very happy :-)