{"id":2393,"date":"2009-10-01T17:21:27","date_gmt":"2009-10-01T22:21:27","guid":{"rendered":"http:\/\/www.howderfamily.com\/blog\/?p=2393"},"modified":"2022-02-18T07:28:59","modified_gmt":"2022-02-18T12:28:59","slug":"the-danger-of-a-small-sample-size","status":"publish","type":"post","link":"https:\/\/www.howderfamily.com\/blog\/the-danger-of-a-small-sample-size\/","title":{"rendered":"The Danger of a Small Sample Size"},"content":{"rendered":"\n<p>Fair warning, little geographic content makes it onto Twelve Mile Circle today. Mostly I\u2019ll focus on statistics. No, no, don\u2019t go running for the door quite yet. It will be <i>fun<\/i> and actually the statistical slant will be relatively mild, grossly overly simplified with sweeping generalizations and involve no actual mathematics.<\/p>\n\n\n\n<p>I went to a Washington Nationals baseball game yesterday evening. If you&#8217;re a baseball fan I already know what you\u2019re thinking, but actually this is a happy story.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"final-home-game-of-the-2009-season\">Final Home Game of the 2009 Season<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/www.howderfamily.com\/graphics\/blog\/nationals_park_september_2009.jpg\" alt=\"Nationals Park. Photo by howderfamily.com; (CC BY-NC-SA 2.0)\"\/><figcaption>Nationals Park on September 30, 2009; a crappy image taken with my mobile phone. Check out the size of the crowd<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p>Imagine the Nats down 3-4 at the bottom of the ninth inning, bases loaded, two outs, a batter facing a full count, and BAM, a walk-off grand slam homer with the Nationals taking the game 7-4 over the Mets.<b><sup>(<a href=\"#footnote\">1<\/a>)<\/sup><\/b> The Post declared &#8220;<a href=\"https:\/\/www.washingtonpost.com\/wp-dyn\/content\/article\/2009\/09\/30\/AR2009093004557.html\" target=\"_blank\" rel=\"noreferrer noopener\">the last scene of the 81st and final home game of the season was unlike any moment that preceded it, perfect and delirious<\/a>\u2026&#8221;<\/p>\n\n\n\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.google.com\/maps\/embed?pb=!1m10!1m8!1m3!1d1269.993797397541!2d-77.007363!3d38.873051!3m2!1i1024!2i768!4f13.1!5e1!3m2!1sen!2sus!4v1605975013822!5m2!1sen!2sus\" style=\"border:0;\" allowfullscreen=\"\" aria-hidden=\"false\" tabindex=\"0\" width=\"600\" height=\"450\" frameborder=\"0\"><\/iframe><\/p>\n\n\n\n<p>This was the last home game of the year, a final chance to catch a ballgame in Washington until next April. I\u2019m not a huge fan of any given team. I have no loyalties. However, I do enjoy attending live sporting events. I love being part of the crowd, soaking up the atmosphere, participating in the pageantry, and drinking a couple of beers with friends. Buy me some peanuts and cracker jacks, and all that. I\u2019d only been to one other game the entire season so I figured I should fit this last opportunity into my schedule when it was offered to me.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"earlier-that-season\">Earlier That Season<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/www.howderfamily.com\/graphics\/blog\/ryan_zimmerman_nationals_11.jpg\" alt=\"Ryan Zimmerman Washington Nationals 2009. Photo by howderfamily.com; (CC BY-NC-SA 2.0)\"\/><figcaption>Ryan Zimmerman on May 24, 2009; when I remembered to bring a much better camera<\/figcaption><\/figure>\n\n\n\n<p>Oddly, the only other game that I\u2019d happened to attend this year also featured a grand slam home run. That time, on May 24, 2009, it came off the bat of Adam Dunn. He put the Nats out front in the seventh inning. They left the field with a <a href=\"https:\/\/www.washingtonpost.com\/wp-dyn\/content\/article\/2009\/05\/24\/AR2009052402740.html\" target=\"_blank\" rel=\"noreferrer noopener\">victory over the Orioles<\/a>, 8-5.<\/p>\n\n\n\n<p>Getting back to the title of this article, the Danger of Small Sample size, if one were to examine only these two instances one might conclude that the Washington National are a fantastic team producing a grand slam home run every game as they cruised to another victory.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"not-as-it-seems\">Not As it Seems<\/h2>\n\n\n\n<p>Let\u2019s get real. Grand slams don\u2019t happen often. The chance of seeing one occur in two separate pseudorandom games &#8212; the only two games attended in an entire season &#8212; has to be considerably less than one percent. I\u2019m sure the baseball statisticians out there could find the actual number of grand slams, the actual number of games, and the joint probability of two such occurrences. If there are any baseball math nerds out there who\u2019d like to take this on as a challenge and post the calculation\/results in the comments below, it would be a truly outstanding contribution. Until then I\u2019m going to forgo precision and guess &#8220;it is fairly remote.&#8221;<\/p>\n\n\n\n<p>Let\u2019s look at the other improbable thought. This one is easy to dispel because the entire population is well known, and in fact is published widely every day. As of October 1, 2009, the Nationals have won 55 games and lost 103, with four games remaining in the regular season. This isn\u2019t good. In fact it\u2019s the worst in major league baseball. Any season with a hundred or more losses is considered pretty dismal, and the Nationals have accomplished this dubious achievement two years in a row.<\/p>\n\n\n\n<p>Sample size of two: the Nationals are a great team.<br>Larger sample: well, not so much.<\/p>\n\n\n\n<p>Either way, I\u2019ll be out at the ballpark next spring. Maybe I\u2019ll bring them some luck.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12mc-loves-footnotes\">12MC Loves Footnotes!<\/h2>\n\n\n\n<p><span style=\"font-size: xx-small;\"><a name=\"footnote\"><\/a><sup>(1)<\/sup>My apologies to those of you who live in parts of the world not familiar with this sport. It\u2019s probably best to simply note that this was &#8220;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Grand_slam_(baseball)\" target=\"_blank\" rel=\"noreferrer noopener\">an exciting and somewhat rare event<\/a>&#8220;<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fair warning, little geographic content makes it onto Twelve Mile Circle today. Mostly I\u2019ll focus on statistics. No, no, don\u2019t go running for the door quite yet. It will be fun and actually the statistical slant will be relatively mild, grossly overly simplified with sweeping generalizations and involve no actual mathematics. I went to a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,501,4],"tags":[1762,1759,102,1761,1952,101,1760],"class_list":["post-2393","post","type-post","status-publish","format-standard","hentry","category-cities","category-event","category-misc","tag-100-losses","tag-baseball","tag-district-of-columbia","tag-grand-slam","tag-probability","tag-washington-dc","tag-washington-nationals"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Danger of a Small Sample Size - Twelve Mile Circle - An Appreciation of Unusual Places<\/title>\n<meta name=\"description\" content=\"I went to only two baseball games during the entire season and saw a Grand Slam in each of them. 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