{"id":1867,"date":"2026-06-27T15:28:04","date_gmt":"2026-06-27T15:28:04","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1867"},"modified":"2026-06-27T15:28:05","modified_gmt":"2026-06-27T15:28:05","slug":"greatest-goat-of-all-time","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/","title":{"rendered":"Greatest GOAT of All Time?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>A recent post claims that the \u201cmost statistically dominant athlete\u201d of all time was cricketer Don Bradman. It\u2019s a bold claim \u2013 let\u2019s see if it holds up.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In <a href=\"https:\/\/allendowney.github.io\/ProbablyOverthinkingIt\/lognormal.html#the-greatest-of-all-time\"><em>Chapter 4 of Probably Overthinking It<\/em><\/a>, I listed a few examples of athletes who are considered the Greatest Of All Time (GOAT), and noted that in many cases they are not just a little better than the second-best, but much better. That is, they are outliers among outliers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And I suggested that part of the explanation for this phenomenon is that the distribution of accomplishment in many fields (at least, the ones where accomplishment can be quantified) follows a lognormal distribution. That matters because the lognormal distribution has a long tail, which means that extreme values can be much farther from the mean than we would see in a Gaussian (normal) distribution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So I was intrigued by <a href=\"https:\/\/www.instagram.com\/reel\/DZ6anr1CjT2\/\">this post<\/a> about <a href=\"https:\/\/en.wikipedia.org\/wiki\/Don_Bradman#Statistical_summary\">Don Bradman<\/a>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">The most statistically dominant athlete ever isn\u2019t Jordan or Messi \u2014 and you\u2019ve probably never heard of him. \ud83c\udfcf<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I plotted the career batting averages of the greatest Test cricketers of all time. They make a clean bell curve. In cricket, averaging 50 makes you an immortal legend, and the all-time record holders top out around 60 \u2014 about 2 standard deviations above the mean.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Then there\u2019s Don Bradman: 99.94. More than 6 standard deviations out. The gap between him and the SECOND best player is bigger than the gap between #2 and the entire average. By the math, a batsman this good should appear about once in 7 billion.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To be this far ahead in basketball, Michael Jordan would\u2019ve had to average 43 points in every single game he ever played. No one in any sport \u2014 not Jordan, not Gretzky, not Messi \u2014 is this far from their peers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Not just the greatest. The single biggest outlier in the history of sport.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s see if that\u2019s true. In particular, I\u2019ll investigate the \u201cclean bell curve\u201d \u2013 it implies a Gaussian model of the data, which is where that \u201conce in 7 billion\u201d comes from.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To give away the ending, here\u2019s what I found:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The data don\u2019t fit a Gaussian particularly well, especially in the tail, so the \u201cone in 7 billion\u201d might not be right.<\/li>\n\n\n\n<li>I thought they might fit a lognormal better, but I was wrong.<\/li>\n\n\n\n<li>It turns out that the data fit a Weibull distribution <em>very<\/em> well, and from that we can get a revised estimate of how much of a GOAT Bradman was.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">As it turns out, he was a pretty goaty GOAT \u2013 but not quite one in 7 billion.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Load the data<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">I got the data from <a href=\"https:\/\/www.kaggle.com\/datasets\/udaytunguturi\/batsmen-career-runs-data-for-cricket-analytics\">Kaggle<\/a> (<code>runs_of_batsmen.csv<\/code>).<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">DATA_PATH = \"runs_of_batsmen.csv\"\n\ndf = pd.read_csv(DATA_PATH)\n\n# Convert to numeric, coercing errors to NaN\ndf['Batting Average'] = pd.to_numeric(df['Batting Average'], errors='coerce')\ndf['Innings'] = pd.to_numeric(df['Innings'], errors='coerce')\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">I select only batters with 10 or more innings.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">df = df.query('Innings >= 10')\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s what the distribution of batting averages looks like.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">import seaborn as sns\n\nsns.kdeplot(df['Batting Average'])\ndecorate()\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\" alt=\"_images\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\" class=\"wp-image-1873\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s not much of a bell curve. It\u2019s pretty clearly skewed to the right, even if we leave Bradman out of it. But let\u2019s fit a Gaussian to it anyway.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Gaussian Model<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">There are a lot of ways to fit a model to data. The one I like for applications like this is percentile matching \u2013 that is, finding a model that minimizes the average vertical distance between the empirical CDF of the data and the CDF of the model. That\u2019s what <code>fit_normal<\/code> does.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">avg_series = df[\"Batting Average\"].dropna()\ngaussian_model = fit_normal(avg_series)\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s what that looks like, plotting the tail distribution, which is the complement of the CDF. The shaded area shows the differences between the data and the model.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">tail_data = TailDist.from_seq(avg_series)\nplot_fit_with_area(tail_data, gaussian_model, kind=\"tail\")\ndecorate(xlabel=\"Batting Average\", title='Gaussian model')\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/4b2c95fa3fda1563ca2714d6361e97b106ed1984db9479b168798ca548a9d940.png\" alt=\"_images\/4b2c95fa3fda1563ca2714d6361e97b106ed1984db9479b168798ca548a9d940.png\" class=\"wp-image-1871\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/4b2c95fa3fda1563ca2714d6361e97b106ed1984db9479b168798ca548a9d940.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/4b2c95fa3fda1563ca2714d6361e97b106ed1984db9479b168798ca548a9d940-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/4b2c95fa3fda1563ca2714d6361e97b106ed1984db9479b168798ca548a9d940-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This is not a great fit. There are clear differences in the shapes of the tail distributions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And here\u2019s the average error, which is related to the area between the curves.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">mae_normal = average_error(avg_series, gaussian_model)\nmae_normal\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">0.017745997600540485\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">When we plot the tail distributions on linear scales, it looks like the model might be good enough. The problem is that we can\u2019t see what\u2019s happening in the tail. For that, it\u2019s useful to plot the tail distributions on a log-y scale.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">n = len(avg_series)\nqs = np.linspace(tail_data.qs.min(), tail_data.qs.max(), 200)\ntail_model = TailDist(gaussian_model.sf(qs), index=qs)\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">plot_model_bounds(gaussian_model, n=n, qs=qs, kind=\"tail\", color=\"gray\", alpha=0.2)\ntail_model.plot(label=\"model\")\ntail_data.plot(label=\"data\")\ndecorate(yscale=\"log\", title='Gaussian model (log-y scale)')\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b8bccf875d3216eb826852be8de578e37cbfb0909184ce61df747e79bef1db5e.png\" alt=\"_images\/b8bccf875d3216eb826852be8de578e37cbfb0909184ce61df747e79bef1db5e.png\" class=\"wp-image-1876\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b8bccf875d3216eb826852be8de578e37cbfb0909184ce61df747e79bef1db5e.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b8bccf875d3216eb826852be8de578e37cbfb0909184ce61df747e79bef1db5e-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b8bccf875d3216eb826852be8de578e37cbfb0909184ce61df747e79bef1db5e-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The model fits the left side of the distribution well enough, but after that, it diverges badly. Around 60, the difference between the model and the data is about an order of magnitude.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nevertheless, we can use the Gaussian model to compute the probability of a batting average as high as Bradman\u2019s 99.94.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">BRADMAN = 99.94\n\n\ndef probability_of_exceeding(model, x, n):\n    p = model.cdf(x)\n    one_in = 1 \/ (1 - p)\n    in_sample = 1 \/ (1 - p ** n)\n    return one_in, in_sample\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">In the fitted distribution, the probability of a single batter achieving Bradman\u2019s average is about one per 5.7 trillion.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">one_in, in_sample = probability_of_exceeding(gaussian_model, BRADMAN, n)\none_in \/ 1e12\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">5.71160383940456\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">And even if we account for the sample size, the probability that one of 3438 batsman reaches that level is one per 1.7 billion. So, according to the Gaussian model, this outcome is basically impossible.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">n, in_sample \/ 1e9\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">(3438, 1.6613158346144736)\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">But the Gaussian model doesn\u2019t fit the data well \u2013 and there\u2019s no reason it should. To see why not, let\u2019s think about the process that generates the distribution of batting averages.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As a simplifying assumption, suppose a batsman has the same probability of getting out at any time; in that case, the number of runs in an inning might follow a negative binomial (NB) distribution. As we add up innings (or average over them), the total would eventually converge to a normal distribution, but most batsmans don\u2019t have enough innings to converge. So for each batsman, the distribution of runs follows something between NB and normal. And when we combine them, we get a mixture of those hybrids. There\u2019s no obvious reason the results should fit a simple mathematical model.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But it turns out that they do.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Weibull Model<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Weibull distribution is not the first thing I thought of \u2013 I tried a lognormal distribution first. But a Weibull distribution fits the data really, really well. The <code>fit_scipy_dist<\/code> is a more general version of <code>fit_normal<\/code> that works with any of the SciPy distributions.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">weibull_model = fit_scipy_dist(avg_series, weibull_min)\nweibull_model.args\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">(1.8667199063293203, 0.9939717502596944, 22.486446489455503)\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s the result. Again, the gray area shows the difference between the data and the model.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">plot_fit_with_area(tail_data, weibull_model, kind=\"tail\")\ndecorate(xlabel=\"Batting Average\", title=\"Weibull model\")\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/2c9b224b40833eea766b5d0cd386fc20182601b3ae5245f8f68f7ffca163a4cf.png\" alt=\"_images\/2c9b224b40833eea766b5d0cd386fc20182601b3ae5245f8f68f7ffca163a4cf.png\" class=\"wp-image-1872\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/2c9b224b40833eea766b5d0cd386fc20182601b3ae5245f8f68f7ffca163a4cf.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/2c9b224b40833eea766b5d0cd386fc20182601b3ae5245f8f68f7ffca163a4cf-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/2c9b224b40833eea766b5d0cd386fc20182601b3ae5245f8f68f7ffca163a4cf-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The gray area is not visible. Here\u2019s the average error.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">mae_weibull = average_error(avg_series, weibull_model)\nmae_weibull\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">0.002555441381799216\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The average error of the Gaussian model is about 7x bigger.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">mae_normal \/ mae_weibull\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">6.944396270223196\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s what the tail looks like on a log-y axis.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">tail_model = TailDist(weibull_model.sf(qs), index=qs)\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">plot_model_bounds(weibull_model, n=n, qs=qs, kind=\"tail\", color=\"gray\", alpha=0.2)\ntail_model.plot(label=\"model\")\ntail_data.plot(label=\"data\")\ndecorate(yscale=\"log\", title=\"Weibull model (log-y scale)\")\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b42367fb1469d102aa278bd0b6f4c1a339ea7f78a8919fd2da3d27b61c2e3fc3.png\" alt=\"_images\/b42367fb1469d102aa278bd0b6f4c1a339ea7f78a8919fd2da3d27b61c2e3fc3.png\" class=\"wp-image-1875\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b42367fb1469d102aa278bd0b6f4c1a339ea7f78a8919fd2da3d27b61c2e3fc3.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b42367fb1469d102aa278bd0b6f4c1a339ea7f78a8919fd2da3d27b61c2e3fc3-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/b42367fb1469d102aa278bd0b6f4c1a339ea7f78a8919fd2da3d27b61c2e3fc3-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The model fits the data well \u2013 within the bounds of variability we expect for this sample size \u2013 except for Bradman, who is still an outlier.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Again, we can compute the probability that any batter exceeds Bradman\u2019s level:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">one_in, in_sample = probability_of_exceeding(weibull_model, BRADMAN, n)\none_in \/ 1e6\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">7.980438255436601\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">It\u2019s about one per 8 million. And in a sample of 3438 batsmen, the chance that any one of them reaches that level is one per 2,322.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">in_sample \/ 1e3\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">2.3217442928624186\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">So Bradman is still an outlier among outliers, but not quite the statistical anomaly that he would be in a normal distribution.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, let\u2019s think about why a Weibull distribution fits this dataset so well. In the data-generating process I suggested earlier, if a batsman has the same probability of getting out at any time, the number of runs in an inning might follow a negative binomial (NB) distribution. If we think of the run-generating process as continuous, the distribution of runs before an out would be exponential. And if we relax the assumption that the hazard rate is constant, the distribution of runs per inning would be Weibull.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I think that\u2019s an intriguing first step, but at best it explains the distribution of runs per inning \u2013 but not the distribution of batting averages across batsmen with, presumably, different hazard rates.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Appendix: The Lognormal Model<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Just for completeness, here\u2019s the lognormal model.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">log_series = np.log10(avg_series)\nlog_model = fit_normal(log_series, x0=norm.fit(log_series))\ntail_log_data = TailDist.from_seq(log_series)\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">plot_fit_with_area(tail_log_data, log_model, kind=\"tail\")\ndecorate(xlabel=\"log10(Batting Average)\", title=\"Lognormal model\")\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/6344bb082e43613d7cc8910ef8f34769e420045404b8d576f8382bc64b0c8bc2.png\" alt=\"_images\/6344bb082e43613d7cc8910ef8f34769e420045404b8d576f8382bc64b0c8bc2.png\" class=\"wp-image-1870\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/6344bb082e43613d7cc8910ef8f34769e420045404b8d576f8382bc64b0c8bc2.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/6344bb082e43613d7cc8910ef8f34769e420045404b8d576f8382bc64b0c8bc2-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/6344bb082e43613d7cc8910ef8f34769e420045404b8d576f8382bc64b0c8bc2-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The average error is slightly worse than the Gaussian model.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">mae_lognormal = average_error(log_series, log_model)\nmae_lognormal\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">0.01885918996726559\n<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">And it doesn\u2019t fit the tail well at all.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">log_qs = np.log10(qs)\ntail_model = TailDist(log_model.sf(log_qs), index=log_qs)\n<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">plot_model_bounds(log_model, n=n, qs=log_qs, kind=\"tail\", color=\"gray\", alpha=0.2)\ntail_model.plot(label=\"model\")\ntail_log_data.plot(label=\"data\")\ndecorate(xlabel=\"log10(Batting Average)\", yscale=\"log\", title=\"Lognormal model (log-y scale)\")\n<\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"470\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/5d0319f985ddb2ca9f541683b89a467e19b0e12c468c4c00b5a969111401be6b.png\" alt=\"_images\/5d0319f985ddb2ca9f541683b89a467e19b0e12c468c4c00b5a969111401be6b.png\" class=\"wp-image-1874\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/5d0319f985ddb2ca9f541683b89a467e19b0e12c468c4c00b5a969111401be6b.png 630w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/5d0319f985ddb2ca9f541683b89a467e19b0e12c468c4c00b5a969111401be6b-300x224.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/5d0319f985ddb2ca9f541683b89a467e19b0e12c468c4c00b5a969111401be6b-362x270.png 362w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/allendowney.github.io\/ProbablyOverthinkingIt\/chile.html\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A recent post claims that the \u201cmost statistically dominant athlete\u201d of all time was cricketer Don Bradman. It\u2019s a bold claim \u2013 let\u2019s see if it holds up. In Chapter 4 of Probably Overthinking It, I listed a few examples of athletes who are considered the Greatest Of All Time (GOAT), and noted that in many cases they are not just a little better than the second-best, but much better. That is, they are outliers among outliers. And I suggested&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[137,30,136,134,135],"class_list":["post-1867","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-cricket","tag-gaussian","tag-goat","tag-lognormal","tag-weibull"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Greatest GOAT of All Time? - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Greatest GOAT of All Time? - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"A recent post claims that the \u201cmost statistically dominant athlete\u201d of all time was cricketer Don Bradman. It\u2019s a bold claim \u2013 let\u2019s see if it holds up. In Chapter 4 of Probably Overthinking It, I listed a few examples of athletes who are considered the Greatest Of All Time (GOAT), and noted that in many cases they are not just a little better than the second-best, but much better. That is, they are outliers among outliers. And I suggested... Read More Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/\" \/>\n<meta property=\"og:site_name\" content=\"Probably Overthinking It\" \/>\n<meta property=\"article:published_time\" content=\"2026-06-27T15:28:04+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-27T15:28:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\" \/>\n\t<meta property=\"og:image:width\" content=\"630\" \/>\n\t<meta property=\"og:image:height\" content=\"470\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"AllenDowney\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:site\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"AllenDowney\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/\"},\"author\":{\"name\":\"AllenDowney\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#\\\/schema\\\/person\\\/4e5bfb2e9af6c3446cb0031a7bf83207\"},\"headline\":\"Greatest GOAT of All Time?\",\"datePublished\":\"2026-06-27T15:28:04+00:00\",\"dateModified\":\"2026-06-27T15:28:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/\"},\"wordCount\":1233,\"publisher\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\",\"keywords\":[\"cricket\",\"Gaussian\",\"GOAT\",\"lognormal\",\"Weibull\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/\",\"name\":\"Greatest GOAT of All Time? - Probably Overthinking It\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\",\"datePublished\":\"2026-06-27T15:28:04+00:00\",\"dateModified\":\"2026-06-27T15:28:05+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#primaryimage\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\",\"contentUrl\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png\",\"width\":630,\"height\":470},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2026\\\/06\\\/27\\\/greatest-goat-of-all-time\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Greatest GOAT of All Time?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#website\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/\",\"name\":\"Probably Overthinking It\",\"description\":\"Data science, Bayesian Statistics, and other ideas\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#organization\",\"name\":\"Probably Overthinking It\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/probably_logo.png\",\"contentUrl\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/probably_logo.png\",\"width\":714,\"height\":784,\"caption\":\"Probably Overthinking It\"},\"image\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/x.com\\\/AllenDowney\",\"https:\\\/\\\/www.linkedin.com\\\/in\\\/allendowney\\\/\",\"https:\\\/\\\/bsky.app\\\/profile\\\/allendowney.bsky.social\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/#\\\/schema\\\/person\\\/4e5bfb2e9af6c3446cb0031a7bf83207\",\"name\":\"AllenDowney\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g\",\"caption\":\"AllenDowney\"},\"url\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/author\\\/allendowney_6dbrc4\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Greatest GOAT of All Time? - Probably Overthinking It","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/","og_locale":"en_US","og_type":"article","og_title":"Greatest GOAT of All Time? - Probably Overthinking It","og_description":"A recent post claims that the \u201cmost statistically dominant athlete\u201d of all time was cricketer Don Bradman. It\u2019s a bold claim \u2013 let\u2019s see if it holds up. In Chapter 4 of Probably Overthinking It, I listed a few examples of athletes who are considered the Greatest Of All Time (GOAT), and noted that in many cases they are not just a little better than the second-best, but much better. That is, they are outliers among outliers. And I suggested... Read More Read More","og_url":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/","og_site_name":"Probably Overthinking It","article_published_time":"2026-06-27T15:28:04+00:00","article_modified_time":"2026-06-27T15:28:05+00:00","og_image":[{"width":630,"height":470,"url":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png","type":"image\/png"}],"author":"AllenDowney","twitter_card":"summary_large_image","twitter_creator":"@AllenDowney","twitter_site":"@AllenDowney","twitter_misc":{"Written by":"AllenDowney","Est. reading time":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#article","isPartOf":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/"},"author":{"name":"AllenDowney","@id":"https:\/\/www.allendowney.com\/blog\/#\/schema\/person\/4e5bfb2e9af6c3446cb0031a7bf83207"},"headline":"Greatest GOAT of All Time?","datePublished":"2026-06-27T15:28:04+00:00","dateModified":"2026-06-27T15:28:05+00:00","mainEntityOfPage":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/"},"wordCount":1233,"publisher":{"@id":"https:\/\/www.allendowney.com\/blog\/#organization"},"image":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#primaryimage"},"thumbnailUrl":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png","keywords":["cricket","Gaussian","GOAT","lognormal","Weibull"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/","url":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/","name":"Greatest GOAT of All Time? - Probably Overthinking It","isPartOf":{"@id":"https:\/\/www.allendowney.com\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#primaryimage"},"image":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#primaryimage"},"thumbnailUrl":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png","datePublished":"2026-06-27T15:28:04+00:00","dateModified":"2026-06-27T15:28:05+00:00","breadcrumb":{"@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#primaryimage","url":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png","contentUrl":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/06\/9e6e3e754fa48807f6d4f5b72552714ed01e3d2dec5cfb8bb37abb5ad845d7aa.png","width":630,"height":470},{"@type":"BreadcrumbList","@id":"https:\/\/www.allendowney.com\/blog\/2026\/06\/27\/greatest-goat-of-all-time\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.allendowney.com\/blog\/"},{"@type":"ListItem","position":2,"name":"Greatest GOAT of All Time?"}]},{"@type":"WebSite","@id":"https:\/\/www.allendowney.com\/blog\/#website","url":"https:\/\/www.allendowney.com\/blog\/","name":"Probably Overthinking It","description":"Data science, Bayesian Statistics, and other ideas","publisher":{"@id":"https:\/\/www.allendowney.com\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.allendowney.com\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.allendowney.com\/blog\/#organization","name":"Probably Overthinking It","url":"https:\/\/www.allendowney.com\/blog\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.allendowney.com\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/03\/probably_logo.png","contentUrl":"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/03\/probably_logo.png","width":714,"height":784,"caption":"Probably Overthinking It"},"image":{"@id":"https:\/\/www.allendowney.com\/blog\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/x.com\/AllenDowney","https:\/\/www.linkedin.com\/in\/allendowney\/","https:\/\/bsky.app\/profile\/allendowney.bsky.social"]},{"@type":"Person","@id":"https:\/\/www.allendowney.com\/blog\/#\/schema\/person\/4e5bfb2e9af6c3446cb0031a7bf83207","name":"AllenDowney","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/fb01b3a7f7190bea1bbf7f0852e686c2f8c03b099222df2ce4bc7926f15bcb43?s=96&d=mm&r=g","caption":"AllenDowney"},"url":"https:\/\/www.allendowney.com\/blog\/author\/allendowney_6dbrc4\/"}]}},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":1109,"url":"https:\/\/www.allendowney.com\/blog\/2023\/11\/21\/life-in-a-lognormal-world\/","url_meta":{"origin":1867,"position":0},"title":"Life in a Lognormal World","author":"AllenDowney","date":"November 21, 2023","format":false,"excerpt":"At PyData Global 2023 I will present a talk, \"Extremes, outliers, and GOATs: On life in a lognormal world\". It is scheduled for Wednesday 6 December at 11 am Eastern Time. [UPDATE: here is the video] https:\/\/youtu.be\/MhA5XWIWWys Here is the abstract: The fastest runners are much faster than we expect\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/log_vs_normal5-1.png?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":1210,"url":"https:\/\/www.allendowney.com\/blog\/2024\/02\/01\/extremes-outliers-and-goats\/","url_meta":{"origin":1867,"position":1},"title":"Extremes, outliers, and GOATS","author":"AllenDowney","date":"February 1, 2024","format":false,"excerpt":"The video from my PyData Global 2023 talk, Extremes, outliers, and GOATS, is available now: https:\/\/www.youtube.com\/watch?v=MhA5XWIWWys The slides are here. There are two Jupyter notebooks that contain the analysis I presented: Chapter 4 of Probably Overthinking It An exploration of Gaussian and lognormal models for anthropomorphic measurements Here's the abstract:\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/img.youtube.com\/vi\/MhA5XWIWWys\/0.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1646,"url":"https:\/\/www.allendowney.com\/blog\/2025\/11\/04\/its-levels\/","url_meta":{"origin":1867,"position":2},"title":"It&#8217;s Levels","author":"AllenDowney","date":"November 4, 2025","format":false,"excerpt":"A recent Reddit post asks \"Amateur athletes of Reddit: what's your 'There's levels to this shit' experience from your sport?\" Responses included: We have some good runners who can win local races ... And then you realise that if you put them in a 5000m race with Olympic-level athletes they'd\u2026","rel":"","context":"In \"lognormal distribution\"","block_context":{"text":"lognormal distribution","link":"https:\/\/www.allendowney.com\/blog\/tag\/lognormal-distribution\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/11\/212090bf9c6718b7d51f02945d3cb353d999e9243739e5c24535e8f5f36f013e.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1142,"url":"https:\/\/www.allendowney.com\/blog\/2023\/12\/06\/happy-launch-day\/","url_meta":{"origin":1867,"position":3},"title":"Happy Launch Day!","author":"AllenDowney","date":"December 6, 2023","format":false,"excerpt":"Today is the official publication date of Probably Overthinking It! You can get a 30% discount if you order from the publisher and use the code UCPNEW. You can also order from Amazon or, if you want to support independent bookstores, from Bookshop.org. I celebrated launch day by giving a\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":849,"url":"https:\/\/www.allendowney.com\/blog\/2023\/01\/28\/never-test-for-normality\/","url_meta":{"origin":1867,"position":4},"title":"Never Test for Normality","author":"AllenDowney","date":"January 28, 2023","format":false,"excerpt":"Way back in 2013, I wrote this blog post explaining why you should never use a statistical test to check whether a sample came from a Gaussian distribution. I argued that data from the real world never come from a Gaussian distribution, or any other simple mathematical model, so the\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/01\/anderson1-1.png?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":1122,"url":"https:\/\/www.allendowney.com\/blog\/2023\/11\/29\/superbolts\/","url_meta":{"origin":1867,"position":5},"title":"Superbolts","author":"AllenDowney","date":"November 29, 2023","format":false,"excerpt":"Probably Overthinking It is available to predorder now. You can get a 30% discount if you order from the publisher and use the code UCPNEW. You can also order from Amazon or, if you want to support independent bookstores, from Bookshop.org. Recently I read a Scientific American article about superbolts,\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/superbolt1-1.png?resize=1400%2C800&ssl=1 4x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/comments?post=1867"}],"version-history":[{"count":3,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1867\/revisions"}],"predecessor-version":[{"id":1877,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1867\/revisions\/1877"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=1867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=1867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=1867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}