{"id":4705,"date":"2023-06-14T12:13:47","date_gmt":"2023-06-14T11:13:47","guid":{"rendered":"https:\/\/marriott-stats.com\/nigels-blog\/?p=4705"},"modified":"2023-06-16T10:39:22","modified_gmt":"2023-06-16T09:39:22","slug":"cricket-donald-bradman-9-sigma-batsman","status":"publish","type":"post","link":"https:\/\/marriott-stats.com\/nigels-blog\/cricket-donald-bradman-9-sigma-batsman\/","title":{"rendered":"Cricket #1 – Sir Donald Bradman, the 9 Sigma GOAT"},"content":{"rendered":"

Sir Donald Bradman is the GOAT (Greatest of All Time<\/strong>) of sporting GOATs.\u00a0 All cricket lovers accept the great Australian is the greatest batsman of all time but how many are aware he was 9<\/strong> standard deviations<\/strong> better than the next best 166<\/strong> batsmen of all time? I can’t think any other sports person who comes close to this standard which is why I say this 9 Sigma GOAT<\/strong> is the greatest sports person of all time.<\/p>\n

<\/p>\n

This article was first published on 2nd January 2023 and updated on 14th June 2023 with latest data.<\/em><\/span><\/p>\n

Sir Donald Bradman in Statistics<\/strong><\/span><\/h5>\n

\"\"Bradman played 52<\/strong> test matches for Australia between the years of 1928<\/strong> and 1948<\/strong><\/a>.\u00a0 Over those matches he batted 80<\/strong> times, was dismissed 70<\/strong> times and scored a total of 6,996<\/strong> runs.\u00a0 A cricketer’s batting average is the number of runs scored divided by the numbers of dismissals so Sir Donald Bradman ended his career with an average of 99.94 <\/strong>(=6996\/70).\u00a0 Famously, he only needed 4<\/strong> runs in his very last innings against England at the Oval<\/a> to end his test career with a batting average of 100 but the entire cricketing world was stunned when he was bowled second ball for a duck.\u00a0 What is less well known is that Australia beat England by an innings in that match but had Australia batted again, Bradman may well have achieved this stunning feat.<\/p>\n

Over his 80<\/strong> innings, he scored 29<\/strong> Centuries (36%<\/strong> of all innings) making him the only test batsman to score a century in at least 1\/3<\/strong> of his innings.\u00a0 In addition, he scored 13<\/strong> Fifties which meant he scored 50+<\/strong> runs in over half of his innings (42<\/strong> or 53%<\/strong>), again the only test batsmen in history to do so.\u00a0 His 12<\/strong> Double Centuries have yet to be surpassed with only Sangakkara coming close with 11<\/strong> doubles in 3 times as many innings.\u00a0 Finally, Bradman is one of only 4<\/strong> test batsmen (Sehwag, Gayle & Lara being the others) to score 2<\/strong> Triple Centuries and could have been on his own with 3 had he not run out of partners when 299 not out<\/strong> <\/a>in a match against South Africa.<\/p>\n

He faced England in 65<\/strong> of his 80<\/strong> innings with the remainder spread evenly across series with India, South Africa and the West Indies.<\/p>\n

The 9 Sigma GOAT<\/strong><\/span><\/h5>\n

It’s obvious Bradman is the GOAT<\/strong> (Greatest Of All Time) when it comes to test batting but just how much better was he compared to his peers?<\/p>\n

The answer is his batting average of 99.94<\/strong> was an astonishing 9<\/strong> (Nine<\/strong>) standard deviations better than the mean batting average of 45.3<\/strong> recorded by the next best 166<\/strong> batsmen of all time.<\/p>\n

\"\"<\/p>\n

The chart here shows the distribution of batting averages of the next best 166<\/strong> batsmen is close to a normal distribution, perhaps with a slight positive skew.\u00a0 This means Bradman’s average of 99.94<\/strong>, differing from the next 166’s average of 45.3<\/strong> by 8.9<\/strong> times the next 166’s standard deviation of 6.1<\/strong> runs, can be interpreted in terms of a normal distribution.\u00a0 On that basis, to be 9<\/strong> standard deviations better than the best of the rest (note not all batsmen, just the best) is out of this galaxy let alone this world.\u00a0 Is there any other sports person that comes close to standing out like this?<\/p>\n

Who are the Top 167 Test Batsmen of all time?<\/strong><\/span><\/h5>\n

The full list of the top 167<\/strong> test batsmen I chose to use in this analysis can be downloaded here in Microsoft Excel format.<\/p>\n

All Time Greatest Test Batsmen – as of 2023-06-14<\/a><\/strong><\/h5>\n

All data was downloaded from ESPN’s Cricinfo<\/strong> database<\/a> and the downloadable spreadsheet gives you instructions on how you can download the data yourself from ESPN’s site.\u00a0 The data I’ve used here is up to date as of the end of 2022 and the 167<\/strong> batsmen I’ve included account for 5%<\/strong> of all 3,123<\/strong> men to have ever played test cricket.<\/p>\n

I spent many hours trying to identify the best of the rest for this blog.\u00a0 In the end, I decided the mark of a top class test batsmen is they score Centuries<\/strong> (100+ runs in a single innings<\/em>) and the mark of a top class test bowler is they take 5-Wicket Hauls<\/strong> (I will be writing a separate post about the top test bowlers of all time).\u00a0 From this I arrived at a simple criteria whereby any batsman who scores at least 10<\/strong> test centuries in their career is a top class test batsman.\u00a0 This criteria has the advantage of excluding batsmen with short careers who were hot for a couple of years.\u00a0 139<\/strong> batsman have achieved this feat since the first ever test match in 1877<\/a> but where did I get the other 28<\/strong>?<\/p>\n

You may have noticed earlier that Bradman’s career spanned 21<\/strong> years and consisted of only 52<\/strong> matches.\u00a0 Obviously, 6<\/strong> years lost to World War Two didn’t help but this still only works out as an average of 3.5<\/strong> ( =52\/(21-6) ) matches per year for Bradman.\u00a0 These days, plenty of players reach 100 matches in 10 years but of course they are helped by widespread air travel around the globe.\u00a0 This was not an option in Bradman’s day when teams travelled by boat.\u00a0 From my readings, it looks like the first time a team flew to its destination was around 1960.<\/p>\n

\"\"<\/p>\n

The above chart shows the trend in the average number of matches per year a test cricketer can expect to play during their career.\u00a0 The horizontal axis is the midpoint of a player’s career which in Bradman’s case was 1938<\/strong> (halfway between 1928 & 1948).\u00a0 That puts him firmly in the Inter-War era when players could expect to play just under 2<\/strong> matches a year so Bradman was clearly above average for this era.\u00a0 However, for the modern era from the late 60s onwards, Bradman’s experience is now the norm.<\/p>\n

To be fair to players from the earlier three eras, when global travel was by boat and there were fewer test playing nations, my criteria of at least 10<\/strong> centuries only applies to the modern era from 1968<\/strong> onwards.\u00a0 For the earlier eras, I prorated the threshold of 10<\/strong> by the average number of matches per year as shown in the chart above to arrive at the following thresholds –<\/p>\n

    \n
  1. At least 5<\/strong> centuries for the 19th century – Only 2<\/strong> players from this era meet this criteria<\/li>\n
  2. At least 6<\/strong> centuries for 1st half of 20th century – 24<\/strong> players including Bradman<\/li>\n
  3. At least 7<\/strong> centuries in the immediate post WW2 era – 24<\/strong> players<\/li>\n
  4. At least 10<\/strong> centuries for the modern era – 117<\/strong> players with Marnus Labuschagne of Australia the most recent player to join the list<\/li>\n<\/ol>\n

    Using these thresholds, I arrive at 167<\/strong> top class batsmen including Bradman broken down by era as above.\u00a0 One reason why I defined the modern era to start in 1968 was to be fair to South African cricketers before 1970.\u00a0 Due to apartheid, South Africa was kicked out of test cricket then which shortened the career of some very strong players.<\/p>\n

    As noted earlier, Bradman only just missed out on a test career batting average of 100<\/strong>.\u00a0 For more ordinary mortals, a test career batting average of 50<\/strong> is a prize worth having.\u00a0 Out of the 167<\/strong> in my list, 36<\/strong> ended their career or currently have a batting average of at least 50<\/strong>.\u00a0 Of these 36<\/strong>, four are still playing (Labuschagne, Root, Smith, Williamson).<\/p>\n

    \"\"<\/p>\n

    Donald Bradman V Herbert Sutcliffe<\/strong><\/span><\/h5>\n

    How did Bradman manage to be 9<\/strong> standard deviations better than his peers?\u00a0 The best way to answer this question is to compare him with the English batsman Herbert Sutcliffe whose career (1924-1938)<\/a> overlapped with Bradman’s (1928-1948)<\/a>.\u00a0 Sutcliffe played a similar number of innings (84<\/strong>) to Bradman (80<\/strong>) and he is number 4 in the all time list above for test career batting average.\u00a0 More than that Sutcliffe came closest to repeating Bradman’s feat of scoring 50+<\/strong> runs in at least half of his innings.\u00a0 As the chart below shows, Sutcliffe (46%<\/strong>) was 3<\/strong> standard deviations and Bradman (53%)<\/strong> was 4<\/strong> standard deviations above the overall average of 30%<\/strong> so clearly both were outstanding test batsmen.<\/p>\n

    \"\"<\/p>\n

    Both had similar records in getting to their Fifty.\u00a0 The difference came afterwards.\u00a0 Sutcliffe went on to convert only 16\"\" <\/strong>(41%<\/strong>) of his 39<\/strong> Fifties into centuries whereas Bradman converted 29<\/strong> (69%<\/strong>) of his 42<\/strong> Fifties into centuries.\u00a0 More than that, Bradman converted 62%<\/strong> of his 100s into 150s and 67%<\/strong> of his 150s into 200s.\u00a0 In other words, he just did not slow down and was remorseless. It won’t surprise you to hear that yet again Bradman had the highest ever conversion rate from 50 to 100 with only Headley coming close at 67%<\/strong>.<\/p>\n

    Sutcliffe however, only converted 25%<\/strong> of his 100s into 150s and never scored a double hundred which suggests an inability to really punish the bowlers.\u00a0 Remember Sutcliffe was no slouch, he had the 4th best test career batting average of all time, the best ever for an English player and was second only to Bradman in scoring Fifties.\u00a0 It is the gulf between their conversion rates that explains why Sutcliffe was only(!) a 2.5<\/strong> Sigma GOAT and Bradman was an unsurpassable 9 Sigma<\/strong> GOAT<\/strong>.<\/p>\n

     <\/p>\n

    — Would you like to comment on this article? —-<\/span><\/strong><\/h5>\n

    Please do leave your comments on these LinkedIn<\/strong><\/span><\/a> and Twitter<\/strong><\/span><\/a> threads.<\/p>\n

    I also wrote this Twitter thread<\/a> on 16th June 2023, the day the 2023 Ashes started.<\/p>\n

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    Sir Donald Bradman is the GOAT (Greatest of All Time) of sporting GOATs.\u00a0 All cricket lovers accept the great Australian is the greatest batsman of all time but how many are aware he was 9 standard deviations better than the next best 166 batsmen of all time? I can’t think any other sports person who […]<\/p>\n","protected":false},"author":3,"featured_media":5180,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[4],"tags":[279,278,60,56,280,13,276,277],"class_list":{"0":"post-4705","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-sport","8":"tag-average","9":"tag-batting-average","10":"tag-cricket","11":"tag-goat","12":"tag-normal-distribution","13":"tag-rankings","14":"tag-standard-deviation","15":"tag-variance","16":"entry","17":"override"},"_links":{"self":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/4705","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/comments?post=4705"}],"version-history":[{"count":21,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/4705\/revisions"}],"predecessor-version":[{"id":5195,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/4705\/revisions\/5195"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media\/5180"}],"wp:attachment":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media?parent=4705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/categories?post=4705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/tags?post=4705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}