# Date’s proposal to make the World cup fairer- A relook

A couple of days ago, Kartikeya Date wrote an interesting proposal on cricinfo about how to handle a 14 team World cup tournament. His idea is a a noble one in light of the reduced playing field in the 2019 World cup which has been pilloried and supported with differing points of view. Kartikeya himself has made a case for inclusion of the associates on cricinfo earlier and this blog too has advocated their inclusion, albeit in a different route- breaking free from the nexus of an Old Boys’ club. While his idea to make the 14 team world cup fairer is certainly interesting, the execution is less than ideal. Here’s why:

1) Inconsistency in approach: He proposes to split the points obtained by the teams in a match based on batting and bowling performances. Assuming two teams A and B play each other with A batting first, as explained by him,

Batting points for team A= (Runs scored by A/ Deliveries consumed by A).

Let us call Runs scored by A as x. Since A has batted first, using the formula and logic for NRR calculations, this value is always x/300, unless it is a rain- curtailed match.

Bowling points for team A= (No. of wickets captured by team A)* (Total no. of runs scored by A & B/ Total wickets lost by A & B)* (1/ Balls faced by team B)

This can be reworked as:

Bowling points of team A= (Total runs scored in match/ Balls faced by team B)*(Fraction of wickets taken by team A w.r.t total).

If the balls faced by team B is y and the fraction of wickets taken by team A is f, we can work this as f*(total runs scored in the match)/y. There are three unknowns- x, y and f. The total runs scored in the match is not an unknown if B is assumed to win the match- it can range from (2x+1) to (2x+6), the latter occurring if team B wins the match after scoring a 6 post tying the scores.

He proceeds to add batting and bowling points for each team to get a total for and against score. Plus, the winning team gets a bonus which is the average of the two scores. Many commenters have struggled with application of the method and have also thrown in two scenarios- one, where the losing team tries ends up with the higher points than the winner; two, where teams conspire to get a higher set of points and lose the match which is not very different from NRR farcical situations we’ve seen before. Let us ignore the second one from the time being.

If team A’s points are A and team B’s points are B, then the mathematical condition that team A gets more points than B in spite of B winning is,

A> B+(A+B)/2 which implies that A> 3B.

Now, plugging this into the formulae that Kartikeya has provided,

(x/300) + f(2x+1)/y > 3 [ {(x+1)/y} – {(1-f)*(2x+1)/300}]

Rearranging, we get,

[x- 3 (1-f) (2x+1)]/300 > [3(x+1)- f (2x+1)]/ y ———— (1)

As x is very large compared to 1 (since x is the score made by team A), we can ignore 1 next to x and as a first order approximation, present this equation after eliminating x as:

y (6f-5) > 300 (3- 2f) ———— (2)

This shows that in order for the losing team to get higher points than the winning team, the winning team has to play the full 50 overs (to maximize y) and the f for team A must be greater than 0.9 (which implies that the LHS is positive). In the worst case scenario of y= 300 and f= 1 (i.e. team B does not capture any wickets during the match), LHS= RHS for total runs scored in the match = 2x+1. Even if this were to increase all the way to 2x+6, for f=1, the first term in the RHS 3(x+6) would increase at a faster rate compared to the second (2x+6) and this would result in the RHS being higher. So, mathematically speaking, the calculations seem sound even when equation (1) is used. But philosophically speaking, there is a problem with this calculation as batting points depend only on the team’s run rate but the bowling points depend on the performance of the other team also. This leads to a very inconsistent yardstick applied even though the output of both these factors are runs/ball.

Rain of terror: D/L system would make the implementation of the system more difficult. Image source: 1

2) The dreaded Duckworth Lewis: What would happen in a rain curtailed match? Teams used to scramble for cover and reach out to the D/L tables when rain interrupted. You don’t want that scenario to happen at every ball to compute instantaneous values and haranguing the authorities to stop play at the right time & swing the numbers in your favour.

The eliminator is not a knockout idea: The possibilities of repeat matches are rife and the top 2 teams can lose 2 matches and still win the World cup.

3) The eliminator “I’ll be back” syndrome : My biggest problem with his proposal is the way the eliminators are structured around the maximum number of matches a team can play (5). If I understand this correctly, if the teams were to progress as per seedings, Rank 1 would go all the way to the final. But Rank 2 would face Rank 1 thrice en route! If you needed a plot for a Bollywood reincarnation drama, this one would fit the bill a little too well with the Ghost of Christmas past thrown in for good measure (I shudder to think what the fans would have felt if it was India vs Sri Lanka a few years ago!). The top 2 teams can afford to lose twice- they need to win 3 matches to win the cup. The lower ranked teams have a shorter rope (Ranks 3 & 4 need to win 4 matches and the bottom 2 need to win 5 in a row). Plus, multiple face-offs and transplants tend to dilute the seriousness of the competition. A parallel that I would invoke is the UEFA Europa league where in the knockout phase, where the third placed teams from the prettier sister tournament, the UEFA Champions league, are parachuted into the draw. This causes an uncomfortable situation where the team usually considers it below their dignity to participate in the tournament and only causes showcasing the league as second rate.

An alternative

The best way to resolve this conundrum is to consider all three factors which are important in a one day match- runs, wickets and balls. A product of average and strike rate/ economy rate (corrected for teams getting all out prematurely, of course) for a team is usually a good indicator of how the team has done (This is how S Rajesh has compared batsmen & bowlers across eras on cricinfo). These measures take all factors into consideration while applying the same yardsticks and are much easier to compute.

How do we solve the knockout phase? If we have to borrow from football, a league structure with a home-away format ensures that the teams are judged over a season in the fairest manner possible. Considering all countries traditionally have a 6 month long cricket season (which don’t coincide with each other unlike most of the UEFA football season) and 14 teams have to be accommodated, this option is clearly unviable.  Broadcasters prefer to have the artificial imposition of a knockout format to ensure pressure and a sudden- death scenarios. The finale, however anti-climactic it turns out to be, is always billed as the mother of all matches and is a marketer’s dream. The knockout phase is a necessary evil and is here to stay. I would suggest to leave it unperturbed, much like how the other major tournaments are conducted across the sporting world.

Disclaimer: Some images used are not property of this blog. The copyright, if any, rests with the respective owners.

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