{"id":111977,"date":"2020-02-18T09:51:49","date_gmt":"2020-02-18T09:51:49","guid":{"rendered":"https:\/\/staging.wingify.com\/blog\/better-understand-and-optimize-your-average-basket-size\/"},"modified":"2020-02-18T09:51:49","modified_gmt":"2020-02-18T09:51:49","slug":"better-understand-and-optimize-your-average-basket-size","status":"publish","type":"post","link":"https:\/\/wingify.com\/blog\/better-understand-and-optimize-your-average-basket-size\/","title":{"rendered":"Better Understand (And Optimize) Your Average Basket Size"},"content":{"rendered":"<p><strong>When it comes to using <a href=\"https:\/\/wingify.com\/blog\/ab-vs-multivariate-test\/\" target=\"_blank\" rel=\"noopener noreferrer\">A\/B testing<\/a> to improve the user experience, the end goal is about increasing revenue. However, we more often hear about improving conversion rates (in other words, changing a visitor into a buyer).\u00a0<\/strong><\/p>\n<p><strong>If you increase the number of conversions, you\u2019ll automatically increase revenue and increase your number of transactions. But this is just one method among many&#8230;another tactic is based on increasing the \u2018average basket size\u2019. This approach is, however, much less often used. Why? Because it\u2019s rather difficult to measure the associated change.<\/strong><\/p>\n<h2>A Measurement and Statistical Issue<\/h2>\n<p>When we talk about statistical tests associated with average basket size, what do we mean? Usually, we\u2019re referring to the <a href=\"https:\/\/wingify.com\/blog\/ab-vs-multivariate-test\/\" target=\"_blank\" rel=\"noopener noreferrer\">Mann-Whitney-U test<\/a> (also called the Wilcoxon), used in certain A\/B testing software, including AB Tasty.\u00a0 A \u2018must have\u2019 for anyone who wants to improve their conversion rates. This test shows the probability that variation B will bring in more gain than the original. However, it\u2019s impossible to tell the <em>magnitude<\/em> of that gain &#8211; and keep in mind that the strategies used to increase the average basket size most likely have associated costs.\u00a0 It\u2019s therefore crucial to be sure that the gains outweigh the costs.<\/p>\n<p>For example, if you\u2019re using a product recommendation tool to try and increase your average basket size, it\u2019s imperative to ensure that the associated revenue lift is higher than the cost of the tool used\u2026.<\/p>\n<p><strong>Unfortunately, you\u2019ve probably already realized that this issue is tricky and counterintuitive&#8230;<\/strong><\/p>\n<p><strong>Let\u2019s look at a concrete example:<\/strong> the beginner&#8217;s approach is to calculate the average basket size directly. It\u2019s just the sum of all the basket values divided by the number of baskets. And this isn\u2019t wrong, since the math makes sense. However, it\u2019s not very precise! The real mistake is comparing apples and oranges, and thinking that this comparison is valid. Let\u2019s do it the right way, using accurate average basket data, and simulate the average basket gain.<\/p>\n<p><strong>Here\u2019s the process:<\/strong><\/p>\n<ul>\n<li>Take P, a list of basket values (this is real data collected on an e-commerce site, not during a test).<\/li>\n<li>We mix up this data, and split them into two groups, A and B.<\/li>\n<li>We leave group A as is: it\u2019s our reference group, that we\u2019ll call the \u2018original\u2019.<\/li>\n<li>Let\u2019s add 3 euros to all the values in group B, the group we\u2019ll call the \u2018variation\u2019, and which we\u2019ve run an optimization campaign on (for example, using a system of product recommendations to website visitors).<\/li>\n<li>Now, we can run a Mann-Whitney test to be sure that the added gain is significant enough.<\/li>\n<\/ul>\n<p>With this, we\u2019re going to calculate the average values of lists A and B, and work out the difference. We might naively hope to get a value near 3 euros (equal to the gain we \u2018injected\u2019 into the variation). But the result doesn\u2019t fit. We\u2019ll see why below.<\/p>\n<h2>How to Calculate Average Basket Size<\/h2>\n<p>The graph below shows the values we talked about: 10,000 average basket size values. The X (horizontal) axis represents basket size, and the Y (vertical) axis, the number of times this value was observed in the data.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41221 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image1-13-300x219.png\" alt=\"\" width=\"300\" height=\"219\" \/><\/p>\n<p>It seems that the most frequent value is around 50 euros, and that there\u2019s another spike at around 100 euros, though we don\u2019t see many values over 600 euros.<\/p>\n<p>After mixing the list of amounts, we split it into two different groups (5,000 values for group A, and 5,000 for group B).<\/p>\n<p>Then, we add 3 euros to each value in group B, and we redo the graph for the two groups, A (in blue) and B (in orange):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41223 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image3-10-300x219.png\" alt=\"\" width=\"300\" height=\"219\" \/><\/p>\n<p>We already notice from looking at the chart that we don\u2019t see the effect of having added the 3 euros to group B: the orange and blue lines look very similar. Even when we zoom in, the difference is barely noticeable:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-41222 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image2-13.png\" alt=\"\" width=\"200\" height=\"148\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-41225 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image5-10.png\" alt=\"\" width=\"200\" height=\"146\" \/><\/p>\n<p><strong>However, the Mann-Whitney-U test &#8216;sees&#8217; this gain:<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41224 size-full\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image4-14.png\" alt=\"\" width=\"640\" height=\"61\" \/><\/p>\n<p>More precisely, we can calculate pValue = 0.01, which translates into a confidence interval of 99%, which means we\u2019re very confident there\u2019s a gain from group B in relation to group A. We can now say that this gain is &#8216;statistically visible.\u2019<\/p>\n<p>We now just need to estimate the size of this gain (which we know has a value of 3 euros).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-41229 size-full\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image7-11.png\" alt=\"\" width=\"200\" height=\"167\" \/><\/p>\n<p>Unfortunately, the calculation doesn\u2019t reveal the hoped for result! The average of group A is 130 euros and 12 cents, and for version B, it\u2019s 129 euros and 26 cents. Yes, you read that correctly: calculating the average means that average value of B is smaller than the value of A, which is the opposite of what we created in the protocol and what the statistical test indicates. This means that, instead of gaining 3 euros, we lose 0.86 cents!<\/p>\n<p><strong>So where\u2019s the problem? And what\u2019s real? A &gt; B or B &gt; A?<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41221 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image1-13-300x219.png\" alt=\"\" width=\"300\" height=\"219\" \/><\/p>\n<h2>The Notion of Extreme Values<\/h2>\n<p>The fact is, B &gt; A! How is this possible? It would appear that the distribution of average basket values is subject to \u2018extreme values\u2019. We do notice on the graph that the majority of the values is &lt; 500 euros.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41230 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image8-6-300x214.png\" alt=\"\" width=\"300\" height=\"214\" \/><\/p>\n<p>But if we zoom in, we can see a sort of \u2018long tail\u2019 that shows that sometimes, just sometimes, there are values much higher than 500 euros. Now, calculating averages is very sensitive to these extreme values. A few very large basket size values can have a notable impact on the calculation of the average.<\/p>\n<p>What\u2019s happening then? When we split up the data into groups A and B, these \u2018extreme\u2019 values weren\u2019t evenly distributed in the two groups (neither in terms of the number of them, nor their value). This is even more likely since they\u2019re infrequent, and they have high values (with a strong variance).<\/p>\n<p>NB: when running an A\/B test, website visitors are randomly assigned into groups A and B as soon as they arrive on a site. Our situation is therefore mimicking the real-life conditions of a test.<\/p>\n<p><strong>Can this happen often?<\/strong> Unfortunately, we\u2019re going to see that yes it can.<\/p>\n<h2>A\/A Tests<\/h2>\n<p>To give a more complete answer to this question, we\u2019d need to use a program that automates creating A\/A tests, i.e. a test in which no change is made to the second group (that we usually call group B). The goal is to check the accuracy of the test procedure. Here\u2019s the process:<\/p>\n<ol>\n<li>Mix up the initial data<\/li>\n<li>Split it into two even groups<\/li>\n<li>Calculate the average value of each group<\/li>\n<li>Calculate the difference of the averages<\/li>\n<\/ol>\n<p>By doing this 10,000 times and by creating a graph of the differences measured, here\u2019s what we get:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41233 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image11-3-300x215.png\" alt=\"\" width=\"300\" height=\"215\" \/><\/p>\n<p>X axis: the difference measured (in euros) between the average from groups A and B.<\/p>\n<p>Y axis: the number of times this difference in size was noticed.<\/p>\n<p>We see that the distribution is centered around zero, which makes sense since we didn\u2019t insert any gain with the data from group B.\u00a0 The problem here is how this curve is spread out: gaps over 3 euros are quite frequent. We could even wager a guess that it\u2019s around 20%. What can we conclude? Based only on this difference in averages, we can observe a gain higher than 3 euros in about 20% of cases &#8211; even when groups A and B are treated the same!<\/p>\n<p>Similarly, we also see that in about 20% of cases, we think we\u2019ll note a loss of 3 euros per basket\u2026.which is also false! This is actually what happened in the previous scenario: splitting the data \u2018artificially\u2019 increased the average for group A. The gain of 3 euros to all the values in group B wasn\u2019t enough to cancel this out. The result is that the increase of 3 euros per basked is \u2018invisible\u2019 when we calculate the average. If we look only at the simple calculation of the difference, and decide our threshold is 1 euro, we have about an 80% chance of believing in a gain or loss&#8230;that doesn\u2019t exist!<\/p>\n<h2>Why Not Remove These \u2018Extreme\u2019 Values?<\/h2>\n<p>If these \u2018extreme\u2019 values are problematic, we might be tempted to simply delete them and solve our problem. To do this, we\u2019d need to formally define what we call an extreme value. A classic way of doing this is to use the hypothesis that the data follow \u2018Gaussian distribution\u2019. In this scenario, we would consider \u2018extreme\u2019 any data that differ from the average by more than three times the standard deviation. With our dataset, this threshold comes out to about 600 euros, which would seem to make sense to cancel out the long tail. However, the result is disappointing. If we apply the A\/A testing process to this \u2018filtered\u2019 data, we see the following result:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41231 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image9-7-300x221.png\" alt=\"\" width=\"300\" height=\"221\" \/><\/p>\n<p>The distribution of the values of the difference in averages is just as big, the curve has barely changed.<\/p>\n<p>If we were to do an A\/B test now (still with an increase of 3 euros for version B), here\u2019s what we get (see the graph below). We can see that the the difference is being shown as negative (completely the opposite of the reality), in about 17% of cases! And this is discounting the extreme values. And in about 18% of cases, we would be led to believe that the gain of group B would be &gt; 6 euros, which is two times more than in reality!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41232 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image10-4-300x223.png\" alt=\"\" width=\"300\" height=\"223\" \/><\/p>\n<h2>Why Doesn\u2019t This Work?<\/h2>\n<p>The reason this doesn\u2019t work is because the data for the basket values doesn\u2019t follow Gaussian distribution.<\/p>\n<p>Here\u2019s a visual representation of the approximation mistake that happens:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-41234 aligncenter\" src=\"https:\/\/static.wingify.com\/gcp\/uploads\/abtasty\/image12-2-300x214.png\" alt=\"\" width=\"300\" height=\"214\" \/><\/p>\n<p>The X (horizontal) axis shows basket values, and the Y (vertical) axis shows the number of times this value was observed in this data.<\/p>\n<p>The blue line represents the actual basket values, the orange line shows the Gaussian model. We can clearly see that the model is quite poor: the orange curve doesn\u2019t align with the blue one. This is why simply removing the extreme values doesn\u2019t solve the problem.<\/p>\n<p>Even if we were able to initially do some kind of transformation to make the data &#8216;Gaussian\u2019, (this would mean taking the log of the basket values), to significantly increase the similarity between the model and the data, this wouldn\u2019t entirely solve the problem. The variance of the different averages is just as great.<\/p>\n<p>During an A\/B test, the estimation of the size of the gain is very important if you want to make the right decision. This is especially true if the winning variation has associated costs. It remains difficult today to accurately calculate the average basket size. The choice comes down soley to your confidence index, which only indicates the existence of gain (but not its size). This is certainly not ideal practice, but in scenarios where the conversion rate and average basket are moving in the same direction, the gain (or loss) will be obvious. Where it becomes difficult or even impossible to make a relevant decision is when they aren\u2019t moving in the same direction.<\/p>\n<p>This is why A\/B testing is focused mainly on ergonomic or aesthetic tests on websites, with less of an impact on the average basket size, but more of an impact on conversions. This is why we mainly talk about \u2018conversion rate optimization\u2019 (CRO) and not \u2018business optimization&#8217;. Any experiment that affects both conversion and average basket size will be very difficult to analyze. This is where it makes complete sense to involve a technical conversion optimization specialist: to help you put in place specific tracking methods aligned with your upsell tool.<\/p>\n<p>To understand everything about A\/B testing, check out our article: <a href=\"https:\/\/wingify.com\/blog\/ab-vs-multivariate-test\/\" target=\"_blank\" rel=\"noopener noreferrer\">The Problem is Choice.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>How can you increase your revenue? By increasing conversions&#8230;and average basket size. But it&#8217;s easier said than done! Read on to learn why. <\/p>\n","protected":false},"author":1432,"featured_media":114953,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"post_read_time":0,"footnotes":""},"categories":[10783,10806],"tags":[10809,10836],"feature":[],"industry-type":[],"product":[],"role":[],"region":[],"class_list":["post-111977","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ab-testing","category-conversion-optimization","tag-e-commerce","tag-statistics"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How to Increase Your Average Basket Size the Right Way<\/title>\n<meta name=\"description\" content=\"How can you increase your revenue? By increasing conversions...and average basket size. But it&#039;s easier said than done! 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