The 2019 ICC Cricket World Cup - A Quick Analysis

Ten teams played a total of 45 matches at the round-robin stage, i.e. each team played the other once. The four "best" teams at the end of this stage went into the playoff rounds: India, Australia, England and New Zealand. 

We will tabulate the matrix positions of all the teams at the end of the round-robin stage. The row-totals or row-sums (let us call this P) give an idea of the “power” of each team and the column-totals or column-sums (we will call this W) give the “weakness” of each team.  Note that ICC uses only row-sums and disregards the column-sums and in that sense is an incomplete assessment of the relative merits of the teams when they play each other – in simpler words, while the attacking (offensive) record is rewarded, the defensive role is not credited.

The P values (i.e. the row-totals) and the W values (the column-totals) now measure the “power” and “weakness” of each team. The P/W ratio (we call this the Power-Weakness Ratio) and the ratio (P-W)/(P+W) (we shall call this the Normalized Power-Weakness Difference) are dimensionless measures of the “quality” of the team. Note that PWD is a one-to-one monotonic transformation of PWR. PWD has the attractive feature that it is always bounded between -1 and 1 but this is not true of PWR which has no upper bound. 

At this stage, we should understand that the simple row-sums and column-sums assume that each team is given the same weight. Thus, India gets the same 2 points for a win against Australia as it would for a win against Afghanistan. For example Ramanujacharyulu pointed out that the weightage can be changed iteratively, taking consideration of the “quality” of the team, leading to an eigen-value problem. Effectively, this is done by multiplying the citation matrix by itself recursively until convergence is reached in both the power and weakness dimensions. This yields the weighted values of P and W and the ratio of these values is PWR. This graph-theoretical procedure has considerable mathematical elegance: it handles the rows (power) and columns (weakness) symmetrically although the matrix, to start with, was necessarily asymmetrical. 

The final match between New Zealand and England ended in a perfect tie even after the Super Over was bowled. We shall assign 1 point each to the two teams for the purpose of our calculations. Further tabulation shows how the 96 points are shared. England and India are tied on 15 points on a power basis but India has a superior record on the weakness basis (5 points against 7 points). Also it must be remembered that India’s 15 points came from 10 matches while England had to play 11 matches to collect its 15 points. After recursive iteration, it is still India on top. The ICC system, as is now practiced, has robbed India of its rightful place of power and glory! The second figure shows the two-dimensional dispersion of Power-Weakness Ratio (PWR) and Normalized Power-Weakness Difference (PWD) for the weighted tournament matrix at the end of the tournament.

Full details can be found here:

https://www.researchgate.net/publication/334458320_The_2019_ICC_Cricket_World_Cup