# How Can We Use the Risk-to-Return Ratio in Cricket?

Can we adjust the average to reflect lean patches and unusually big scores using concepts in portfolio theory?

Cricketing community has relied on test average to benchmark players’ performances for decades. Its simplicity and convenience has become the cornerstones of its popularity. Although it gives us a perfect picture of the mean runs scored per inning, the results are easily distorted by some basic concepts in statistics. A mean score is distorted by outliers. In other words sporadic big scores inflate the average while obscuring the low scores. An average tricks us to believe the player delivers the arithmetic mean  on a consistent basis. A team planner would prefer an alternative measurement which accounts for these “big surprises” and low scores and gives a better picture of a players consistency.

There are more traditional measurements of player performances which we can clearly get out of the way. The total number of runs only keeps ballooning no matter how much a player scores. The number of centuries and man of the match awards too suffer from the same problem. While I acknowledge that there is a lot to admire of a player who has labored a 100 plus test career, in a statistical standpoint they render useless.

The measurement I suggest is inspired by the Sharpe Ratio which is widely used in portfolio theory and was developed by William F. Sharpe.  It is calculated by adjusting the excess return on the portfolio to the risk of the asset.  It follows a simple notion that a rational investor desires more return with a low risk. And if an asset comes with more risk, the investor requires better compensation. Therefore any return the asset carries should be adjusted to the variability of return. The same theory could be applied to benchmark test cricket players.

Unlike the other forms of cricket, test cricket places much emphasis on consistency. A batsmen’s ability to deliver good scores steadily and absorb pressure is a trait of a dependable player. We need to factor in the volatility that comes with the surprisingly good scores that a mere average fails to demonstrate. If a player has great averages the team manager would want to know how much he can depend on the player’s ability to produce the impressive numbers that the average suggests. The results produced are interesting and can be used to benchmark players. The following table shows the reward to variability (risk-return) ratio of some notable players.

 Player Risk-Return ratio Average Allen Border 1.11 50.56 Jacques Kallis 1.06 55.37 Don Bradman 1.06 99.94 Rahul Dravid 1.02 52.43 Sachin Tendulkar 0.99 53.96 Garfield Sorbers 0.98 57.74 Ricky Ponting 0.98 52.5 Viv Richards 0.98 50.23 Jawed Miandad 0.97 54.65 Kumar Sangakkara 0.92 57.4 Mahela Jayawardena 0.87 49.84 Brian Lara 0.84 52.89

(Table 1:risk-return ratio of notable players )

Having the risk-return ratios and averages make very good comparison as to the dependability on a player on producing good scores consistently. Brian Lara is considered as an all-time great having cracked the long-elusive 400 mark and with an impressive average. However, my calculations suggest that his big scores have come at a cost of comparatively high rate of low scores and his high scores masquerades the lean patches he has gone through. The record of Don Bradman too is insightful. While his jaw-dropping average certainly speaks for his caliber, the risk to variability ratio suggests the runs have come at a rate almost equal to the variability. An average of 100 may trick you to think that the great scored almost a century in every match and makes you feel bad about the English bowlers who used to bowl at him. The new ratio makes you realize Bradman also has gone through lean patches like anyone else but also scored big scores.

The table also makes you appreciate the record of some players who deserve better recognition. Jacques Kallis is more known as an all rounder and his batting prowess is often overlooked. His great average and a reward-to-variability ratio goes on to show how formidable he was in the middle order delivering good scores reliably. Coupled with his exceptional skills with the ball, he deserved to be spoken in the same breath as some of the all-time greats.

The Case of Mahela and Thilan

 Player Risk-Return ratio Average Thilan Samaraweera 0.99 49.13 Kumar Sangakkara 0.92 57.4 Mahela Jayawardena 0.87 49.84

(Table 2: risk-to-return ratio of 3 Sri Lankan players)

A perfect example can be drawn from Sri Lanka where the ratio can be put to use to better identify a worth of a player.  The table 2 shows the average and the risk-to-return ratio of three Sri Lankan contemporaries. The two persons in comparison here are Mahela Jayawardena and Thilan Smaraweera. While Mahela Jayawardena needs no introduction, Thilan Samaraweera does. Thilan played for Sri Lanka in 80 tests for approximately 11 years. He was a consistent middle-order player with a robust technique and a resilient mindset. The selection committee is largely to blame for his inconsistent selection and finally resulting in an abrupt ending of the career. The average of 49 itself speaks for the consistency of the player and his ability to absorb pressure. His worth is showcased by his remarkable risk-to-return ratio of 0.99. Having a very similar average, Mahela Jayawardena has a considerably lower risk-to-return ratio while Thilan touches the score of 1 showing his ability to deliver consistently and suggesting that he should have been better utilized by Sri Lanka cricket. Such juxtaposition using the reward-to-variability ratio gives a clear view of the capacity of a player that the average says nothing about.

What the ratio cannot do

In cricket it is absolutely impossible to create a perfect indicator to mirror the ability of a player. It is notable that the risk-to-return ratio should be used alongside the average in order to get a clearer idea of a player profile. It also says nothing about the strike-rate the player possesses although in test cricket it matters less. The part of the world the match is played invariably plays a part in player performance. If a heavy majority of tests were scored in familiar pitches, then a player tends to have a better average. It overlooks the quality of the opposition too.

Despite all the weaknesses the ratio helps the team planner to select the best players, assign positions of the players in the side and manage them. The worth of a player will be better recognized and will help to manage them. Cricket is still in pursuit of the best indicator of player performance and it would be silly on my part to say this is the best predictor. But it is no denying that the return-to-variability ratio is a one step ahead.