<p><div><div><div><div data-show-faces="false" data-height="21" data-width="100" data-layout="button_count" data-send="true" data-href="https://www.r-bloggers.com/sankey-diagram-for-the-2018-fifa-world-cup-forecast/"></div></div><div></div></div><div></div></div>
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(This article was first published on <strong><a href="https://eeecon.uibk.ac.at/~zeileis/news/fifa2018sankey/"> Achim Zeileis</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>The probabilistic forecast from the bookmaker consensus model for the 2018 FIFA World Cup is visualized in an interactive Sankey diagram, highlighting the teams’ most likely progress through the tournament.</p>
<h2>Bookmaker consensus model</h2>
<p>Two weeks ago we published our <a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/news/fifa2018/" target="_blank">Probabilistic Forecast for the 2018 FIFA World Cup</a>: By adjusting quoted bookmakers’ odds for the profit margins of the bookmakers (also known as overrounds), transforming and averaging them, a <a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/assets/posts/2018-05-30-fifa2018/p_win.html" target="_blank">predicted winning probability</a> for each team was obtained. By employing millions of tournament simulations in combination with a model for <a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/assets/posts/2018-05-30-fifa2018/p_pair.html" target="_blank">pairwise comparisons</a> (or matches) we could also obtain forecasted probabilities for each team to progress through the tournament. In our original study, we visualized these by <a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/assets/posts/2018-05-30-fifa2018/p_surv.html" target="_blank">“survival” curves</a>. See the <a rel="nofollow" href="http://econpapers.repec.org/RePEc:inn:wpaper:2018-09" target="_blank">working paper</a> for more details and references.</p>
<h2>Sankey diagram</h2>
<p>Here, we present another display that highlights the likely flow of all teams through the tournament simultaneously. Click on the image to obtain an <a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/assets/posts/2018-06-11-fifa2018sankey/p_sankey.html" target="_blank">interactive full-width version</a> of this Sankey diagram produced by <a rel="nofollow" href="https://plot.ly/r/" target="_blank">Plotly</a>.</p>
<p><a rel="nofollow" href="https://eeecon.uibk.ac.at/~zeileis/assets/posts/2018-06-11-fifa2018sankey/p_sankey.html" target="_blank"><img alt="Sankey diagram" src="https://i2.wp.com/eeecon.uibk.ac.at/~zeileis/assets/posts/2018-06-11-fifa2018sankey/p_sankey.png?w=456&ssl=1" data-recalc-dims="1"></a></p>
<p>Compared to the survival curves shown in our original study this visualization brings out more clearly at which stages of the tournament the strong teams are most likely to meet. Its usage was inspired by the nice working paper <a rel="nofollow" href="https://arxiv.org/abs/1806.01930" target="_blank">On Elo based prediction models for the FIFA Worldcup 2018</a> by <a rel="nofollow" href="https://www.researchgate.net/profile/Sebastian_Mueller10" target="_blank">Lorenz A. Gilch</a> and <a rel="nofollow" href="https://sites.google.com/site/drsebastianmueller/" target="_blank">Sebastian Müller</a>.</p>
<p>In a few days we will start learning which of these paths will actually come true. Enjoy the 2018 FIFA World Cup!</p>
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<div>To <strong>leave a comment</strong> for the author, please follow the link and comment on their blog: <strong><a href="https://eeecon.uibk.ac.at/~zeileis/news/fifa2018sankey/"> Achim Zeileis</a></strong>.</div>
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