{"id":177799,"date":"2024-02-13T15:37:38","date_gmt":"2024-02-13T14:37:38","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=177799"},"modified":"2024-02-08T17:29:30","modified_gmt":"2024-02-08T16:29:30","slug":"expected-goals-understand-the-math-behind-it","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/expected-goals-understand-the-math-behind-it","title":{"rendered":"Expected goals: Understand the math behind it"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"177799\" class=\"elementor elementor-177799\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fc6122b e-flex e-con-boxed e-con\" data-id=\"fc6122b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-5a32872 e-con-full e-flex e-con\" data-id=\"5a32872\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-522bebc elementor-widget elementor-widget-heading\" data-id=\"522bebc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">The number of expected goals is a new performance indicator that has recently appeared in soccer analysis. This statistic is increasingly used to interpret the physiognomy of a match, but do we really know how to interpret it?<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f6fbb9f elementor-widget elementor-widget-text-editor\" data-id=\"f6fbb9f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>The aim of this article is to present the mathematical realities behind <strong>expected goals (xG)<\/strong> as simply as possible. The results presented are taken from a simulation carried out by David Sumpter on the Friends of Tracking youtube channel on Premier League data over an entire season.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5eaeae4 e-flex e-con-boxed e-con\" data-id=\"5eaeae4\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-e2ffa1b e-con-full e-flex e-con\" data-id=\"e2ffa1b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-92dccbb elementor-widget elementor-widget-heading\" data-id=\"92dccbb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is an expected goal? <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e8f7cd3 elementor-widget elementor-widget-text-editor\" data-id=\"e8f7cd3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>What is<strong> xG? What does a score of 2.71 to 0.78 in xG correspond to?<\/strong><\/p><p>For each shot taken in a match, it is possible to assign a probability of the ball finding the back of the net.<\/p><p>For example, a shot from 35 meters will have a very low probability of success (perhaps 5%, i.e. 0.05 xG), whereas a penalty kick will have a good chance of deceiving the goalkeeper (76%, i.e. 0.76 xG). By adding up the <strong>expected goals<\/strong> of all the shots in a match, we obtain an xG score.<\/p><p>Compared with the classic score, which only counts goals, the advantage of xGs is that they are calculated over a greater number of events. As a result, they often reflect the physiognomy of a match, and make it possible to identify which team has had the biggest chances.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d7d5a43 e-flex e-con-boxed e-con\" data-id=\"d7d5a43\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-1524df3 e-con-full e-flex e-con\" data-id=\"1524df3\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ce8fb5b elementor-widget elementor-widget-heading\" data-id=\"ce8fb5b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">But how is the expected goals probability calculated? \n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c9e9b62 elementor-widget elementor-widget-text-editor\" data-id=\"c9e9b62\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>To understand this, let&#8217;s build a simple model of <strong>expected goals.<\/strong> Let&#8217;s start with the following intuition: the further you are from the goal, the harder it will be to score. In our model, the probability of scoring will be established by considering only the position of the shot.<\/p><p>So we&#8217;re going to visualize the distribution of shots in 2-dimensional space.<\/p><p>Here&#8217;s what we get over a full Premier League soccer season:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-91bfa12 elementor-widget elementor-widget-image\" data-id=\"91bfa12\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-126.png\" class=\"attachment-large size-large wp-image-62903\" alt=\"Number of shot\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-126.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-126-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-126-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">This visualization and all the graphics that follow are the work of David Sumpter, Professor of Applied Mathematics at Uppsala University. David co-founded the Friends of Tracking channel, where you'll find a wealth of content on soccer analytics:<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3adb5ec elementor-widget elementor-widget-text-editor\" data-id=\"3adb5ec\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Now let&#8217;s compare the number of goals scored:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9d0f106 elementor-widget elementor-widget-image\" data-id=\"9d0f106\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-127.png\" class=\"attachment-large size-large wp-image-62912\" alt=\"Number of goals\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-127.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-127-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-127-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c9d37d7 elementor-widget elementor-widget-text-editor\" data-id=\"c9d37d7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>We can see that the number of shots outside the box seems to be proportionally much higher than the number of goals.<\/p><p>Now let&#8217;s remember that our aim is to establish a goal probability for each shot. To do this, we calculate the ratio number of goals\/number of shots number of goals number of shots for each gridded area of space. This ratio is our probability of scoring. We then display this probability for each zone of the space, and here&#8217;s the result:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3cb667a elementor-widget elementor-widget-image\" data-id=\"3cb667a\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-142.png\" class=\"attachment-large size-large wp-image-63104\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-142.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-142-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-142-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f1945f elementor-widget elementor-widget-image\" data-id=\"0f1945f\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-128.png\" class=\"attachment-large size-large wp-image-62904\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-128.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-128-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-128-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c3f3efe elementor-widget elementor-widget-text-editor\" data-id=\"c3f3efe\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>This image is an initial model of expected goals. But as you can see, it&#8217;s far from perfect and has many limitations.<\/p><p>The first observation we can make is that the result obtained seems to present anomalies.<\/p><p>Indeed, some very distant areas of space seem to have a very high probability of scoring.<\/p><p>This is due to the fact that the example considered only takes into account shots over a single season, in a single league. Sometimes, there&#8217;s just one shot in a very remote area, and that shot is scored &#8211; and that&#8217;s what we call the magic of soccer. However, if we had carried out our calculations with much more data (several championships over several seasons), the result obtained would have presented less pronounced anomalies.<\/p><p>From this generated visualization, we&#8217;re now going to try and <a href=\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\">build a mathematical model<\/a> that best fits the observed goal frequency. To do this, we&#8217;ll study two parameters separately: shot angle and distance to goal.<\/p><p>Shooting angle represents the angle between the two posts at the point of shooting.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-dd6ed42 e-con-full e-flex e-con\" data-id=\"dd6ed42\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-43a28cb e-con-full e-flex e-con\" data-id=\"43a28cb\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-694d5de elementor-widget elementor-widget-image\" data-id=\"694d5de\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-129.png\" class=\"attachment-large size-large wp-image-62913\" alt=\"L\u2019angle de tir\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-129.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-129-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_template_blog-129-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f1a093b e-con-full e-flex e-con\" data-id=\"f1a093b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0bde492 elementor-widget elementor-widget-image\" data-id=\"0bde492\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-130.png\" class=\"attachment-large size-large wp-image-62905\" alt=\"L\u2019angle de tir\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-130.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-130-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-130-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4899996 elementor-widget elementor-widget-image\" data-id=\"4899996\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-131.png\" class=\"attachment-large size-large wp-image-62906\" alt=\"L\u2019angle de tir\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-131.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-131-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-131-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c2ecbb elementor-widget elementor-widget-text-editor\" data-id=\"9c2ecbb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>This time, we plot the scoring probability obtained previously in each zone of space, as a function of the shooting angle of that zone. We obtain the following point cloud:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ff9ccb elementor-widget elementor-widget-image\" data-id=\"8ff9ccb\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-132.png\" class=\"attachment-large size-large wp-image-62907\" alt=\"Nuage de points\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-132.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-132-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-132-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-90adc90 elementor-widget elementor-widget-text-editor\" data-id=\"90adc90\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>These points can then be approximated by logistic regression using the formula: P(theta) = . We&#8217;ve chosen logistic regression rather than linear regression, because the<a href=\"https:\/\/datascientest.com\/en\/quantitative-analysis-what-is-it-and-how-do-i-become-a-quant\"> probability of scoring<\/a> is 1 when the angle approaches 180\u00b0 and 0 when the angle is 0\u00b0.\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b3338f5 elementor-widget elementor-widget-image\" data-id=\"b3338f5\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-143.png\" class=\"attachment-large size-large wp-image-63105\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-143.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-143-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-143-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e36e4b8 elementor-widget elementor-widget-text-editor\" data-id=\"e36e4b8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Now we can do exactly the same thing with the distance :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c2c00f2 elementor-widget elementor-widget-image\" data-id=\"c2c00f2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-134.png\" class=\"attachment-large size-large wp-image-62909\" alt=\"Nuage de points\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-134.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-134-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-134-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7164faa elementor-widget elementor-widget-text-editor\" data-id=\"7164faa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Once again, we run a logistic regression and obtain a probability of scoring as a function of distance:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ecabecb elementor-widget elementor-widget-image\" data-id=\"ecabecb\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-144.png\" class=\"attachment-large size-large wp-image-63103\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-144.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-144-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-144-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d353b8 elementor-widget elementor-widget-text-editor\" data-id=\"5d353b8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The model isn&#8217;t ideal, as the probability of scoring at 0 meters should be equal to 1. It could be improved (for example, by adding a d2to the exponential), but let&#8217;s start with this first approximation.<\/p><p>These 2 mathematical models, one based on angle and the other on distance, predict our experimental scoring probability quite correctly. However, they are not ultra-precise.<\/p><p>To improve the accuracy of our mathematical model, this time we take into account the impact of these 2 dimensions simultaneously.<\/p><p>We do this by means of a multivariate regression, but this is a little beyond the theoretical scope of this article. The result that emerges from this bivariate regression is as follows:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dd4db2d elementor-widget elementor-widget-image\" data-id=\"dd4db2d\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-136.png\" class=\"attachment-large size-large wp-image-62911\" alt=\"probalit\u00e9 de goals\" srcset=\"https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-136.png 1024w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-136-300x165.png 300w, https:\/\/datascientest.com\/en\/files\/2021\/04\/illu_expected_goals_blog-136-768x422.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56a0b5a elementor-widget elementor-widget-text-editor\" data-id=\"56a0b5a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The model isn&#8217;t ideal, as the probability of scoring at 0 meters should be equal to 1. It could be improved (for example, by adding a d2to the exponential), but let&#8217;s start with this first approximation.<\/p><p>These 2 mathematical models, one based on angle and the other on distance, predict our experimental scoring probability quite correctly. However, they are not ultra-precise.<\/p><p>To improve the accuracy of our mathematical model, this time we take into account the impact of these 2 dimensions simultaneously.<\/p><p>We do this by means of a multivariate regression, but this is a little beyond the theoretical scope of this article. The result that emerges from this bivariate regression is as follows:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-990cb02 elementor-widget elementor-widget-text-editor\" data-id=\"990cb02\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>This mathematical model takes into account both the angle and distance of the shot. It is designed to be as close as possible to the reality of observed goals. It is now much more general, has fewer anomalies and seems to be closer to reality. Based on this model, it is now possible to assign a probability of scoring to the next shots taken, depending on the area of the shot.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-713be71 e-con-full e-flex e-con\" data-id=\"713be71\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-25754ef elementor-widget elementor-widget-heading\" data-id=\"25754ef\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ede6d4 elementor-widget elementor-widget-text-editor\" data-id=\"4ede6d4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>You&#8217;ve seen how to<strong> build an expected goals model<\/strong> using angle and distance. This model can be used to draw initial conclusions for players. For example, we realize that it&#8217;s difficult to score when the shot is off-center, and that a backward pass might be more appropriate.<\/p><p>On the other hand, our <strong>model is far from perfect.<\/strong> Its first flaw is that it is based on data from a single championship in a single season. Its second flaw is that we&#8217;ve only taken angle and distance into account. More elaborate models will take into account the contact zone of the shot (head or foot), the position of the defenders at the moment of the shot, the type of action (placed attack, counter-attack), the choice of foot (good or bad) and many other parameters.<\/p><p>If there&#8217;s one thing to remember from this article, it&#8217;s that expected goals are constructed to best match the frequency of goals observed as a function of a multitude of parameters.<strong> A probability of scoring remains a probability.<\/strong> It will prove true on average over the long term if correctly constructed, but in a single match anything is possible, and that&#8217;s what makes this sport so magical.<\/p><p>If you&#8217;re interested in football-related data analysis, we recommend you look at the &#8220;MPG, le soccer dans toute sa data&#8221; , a project developed in the DataScientest studio.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b476f7b elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"b476f7b\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/appointment\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Find out more about our training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The number of expected goals is a new performance indicator that has recently appeared in soccer analysis. This statistic is increasingly used to interpret the physiognomy of a match, but do we really know how to interpret it? The aim of this article is to present the mathematical realities behind expected goals (xG) as simply [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":177803,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2421],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Expected goals: Understand the math behind it<\/title>\n<meta name=\"description\" content=\"Expected goals (xG) is a statistical metric used in sports analytics, particularly in soccer (football). 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