# How do the top Test batters compare to Don Bradman?

A new measure, the Z-Score, gives us a more complete picture of the gap between the greatest batter and the rest

## Population standard deviation

SD = Population standard deviation

Σ means 'sum of'

N = Population size

x? = each value from the population

x? = population mean

- The Mean works out to
**47.73**

- The SD for this distribution is
**27.08**

- The CoV for this distribution is
**0.567**. This is quite high and represents a widely distributed population. It can be seen that the scores are distributed across the spectrum

- Each of these values has a Z-Score, which represents how many SDs away from the Mean the value is. The Z-Score for 85 is 1.376 ((85-47.73)/27.08) and for 20 is -1.024 ((20-47.73)/27.08). Z-Scores can be positive or negative. By definition, the sum of the Z-Scores for any distribution is always 0.0.

- The median is the value of the middle entry. The median here is
**45**, which is the sixth entry (out of 11)

**Batting**

A reasonable cut-off of 2000 runs has been set for all the batting measures. It is true that a few late-order batters get in, however, it is also true that these batters have performed well often and it allows for certain top batters, like Graeme Pollock and George Headley, who didn't have long careers, to be part of the population.

**Bowling**

Now for the bowlers. To start with, the bowling average. A reasonable cut-off of 75 wickets has been set for all the bowling measures. A few casual bowlers will get in; however, these bowlers have performed well often to even reach this number, and it also allows for certain top bowlers, like Shane Bond and Frank Tyson, to be part of the population.

**Fielding: dismissals per Test**

I wanted to do two analysis segments: one for wicketkeepers and one for fielders. There are no problems with dedicated wicketkeepers. However, I have many grey areas in my database when it comes to players like Sangakkara, Walcott, Mushfiqur Rahim, who donned the wicketkeeping gloves for only part of their careers. I am not 100% certain as to when a catch was taken with the gloves or without. Hence, I decided to have one consolidated fielding segment, taking the total number of dismissals as the base. I am aware that this favours wicketkeepers, but I will make sure that fielders also get enough coverage. The cut-off is 50 dismissals. This will require around 15 Tests for keepers and 40 Tests for fielders.

**Team: Innings Scoring Rate**

Finally, we come to the team-based metric. After going through various options, I decided that the only true performance-based measure I can consider for a team is the scoring rate. That too, the innings scoring rate is the cleanest of measures since it can be derived from the scorecard for all Tests. I have set up a cut-off of 30 overs (a session and some) merely to add significance to the values available. Still, over 8600 innings qualify, making this the most represented population sample. The CoV is a comfortable 0.236, making this an evenly distributed population.

**Longevity-based landmarks**

Sachin Tendulkar has scored 15,921 runs in 200 Tests. Currently Ricky Ponting is in second position with 13,378 runs (84%). Jacques Kallis, with 13,289 runs (83%) is in third position. Among the active players, Joe Root is currently at 11,736 runs (74%). In my last

*Cricket Monthly*article, I had projected that Root is likely to end at 14,531 runs (91%), close to Tendulkar, but not close enough. So, it is almost certain that Tendulkar's record will never be broken.

**The quirky stats section**

In each article, I present a numerical/anecdotal outlier relating to Test and/or ODI cricket. This time the outlier query is: What are the least number of runs scored or wickets lost while securing Test wins?

**Wins after scoring very few runs**

- The Oval, 1882: Australia won after scoring only 185 runs, against England

- Lord's, 1888: Australia won after scoring only 176 runs, against England

- Manchester, 1888: England won after scoring only 172 runs, against Australia

- Melbourne, 1931-32: Australia won after scoring only 153 runs, against South Africa

- Bridgetown, 1934-35: England won after scoring only 156 runs, against West Indies

**Wins after losing very few wickets**

- Lord's, 1924: England won after losing only two wickets, against South Africa

- Leeds, 1958: England won after losing only two wickets, against New Zealand

- Birmingham, 1974: England won after losing only two wickets, against India

- Chittagong, 2003: South Africa won after losing only two wickets, against Bangladesh

- The Oval, 2012: South Africa won after losing only two wickets, against England

**Talking Cricket Group**

Any reader who wishes to join my general-purpose cricket-ideas-exchange group of this name can email me a request for inclusion, providing their name, place of residence, and what they do.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems