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Building on research that often targets winner prediction and betting spreads, the work studies score outcomes using a Poisson-based framework and demonstrates shortcomings of a stationary approach. Using extensive play-by-play data, it develops a non-stationary, state-dependent Poisson process that better matches observed scoring behavior, then applies the model to simulate future Scorigamis and forecast their likely occurrence.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/scorigami-simulating-the-distribution-and-assessing-the-rarity-of-national-football-league-scores/565173/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/scorigami-simulating-the-distribution-and-assessing-the-rarity-of-national-football-league-scores/565173.png","ImageObject",442,249,{"name":88,"@type":89},"Muffet","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-22","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What is an NFL Scorigami?","Question",{"text":109,"@type":110},"An NFL Scorigami occurs whenever a game ends in a final score that has not previously happened in the league’s history.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"Why does the paper criticize a stationary Poisson approach?",{"text":114,"@type":110},"The analysis shows that a stationary Poisson model fails to incorporate important game dynamics reflected in real score outcomes.",{"name":116,"@type":107,"acceptedAnswer":117},"How does the proposed model improve realism and what is it used for?",{"text":118,"@type":110},"The paper extends to a non-stationary, state-dependent Poisson process that better fits play-by-play scoring data, then uses it to simulate and forecast likely future Scorigamis.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},565173,1792171492,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":15,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":79},962090768927,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","SCORIGAMI: SIMULATING THE DISTRIBUTION AND ASSESSING THE RARITY OF  \nNATIONAL FOOTBALL LEAGUE SCORES  \nLiam Moyer 1 , Jameson Railey2 , Andrew Daw3 , and Samuel C. Gutekunst4  \n1Dept. of Computer Science, Bucknell University, Lewisburg, PA, USA  \n2Dept. of Computer Science, Stevens Institute of Technology, Hoboken, NJ, USA  \n3Dept. of Data Sciences and Operations, University of Southern California, Los Angeles, CA, USA  \n4Depts. of Computer Science and Mathematics, Bucknell University, Lewisburg, PA, USA  \nABSTRACT  \nNFL Scorigamis have a cult-like following, and occur whenever a game ends in a new, never-before-seen score. While substantial research has gone into simulating and predicting NFL game scores, most work has been in relation to winner prediction and betting spreads. We analyze a Poisson random variable model for the distribution of NFL game scores and show that it fails to incorporate important game dynamics. Through an analysis of extensive play-by-play data, we extend this to a non-stationary, state-dependent Poisson process model. This latter model more closely fits real NFL score data, and we use it in NFL score simulations to forecast likely future Scorigamis.  \n1 INTRODUCTION  \nOver the past decade, National Football League (NFL) Scorigamis have attracted a sizeable fanbase. AScorigami occurs in the NFL whenever a game ends in a new score that has not previously happened in the league’s history. Most recently, on 12/31/2023, an NFL game ended 56-19 (Baltimore vs. Miami) . Since that score had never occurred in the 100+ year history of the NFL, it was dubbed a Scorigami and reported as such (Breech 2023, among others) .  \nIn many sports, scores that are “numerically close” occur with similar frequencies. For instance, of the 64 games in the 2022 World Cup, the most frequent final game score (not accounting for penalty kicks) was 2-0; 12 games ended 2-0 . The next two most frequent final scores were each one goal away: 2-1 (occurring 11 times) and 1-0 (occurring 10 times) . In contrast, American football’s scoring distribution is decidedly less regular. The most frequent NFL final score is 20-17, with 290 professional football games (of 17,665 in history) ending 20-17 . However, just eight games have ended 20-18, two games have ended 19-18, and zero games have ended 18-18 . Similarly, 177 different games have ended with a 24-17 score; 25-18 has never occurred. See Figure 1 for the full distribution of final scores.  \nThe term Scorigami was coined by sports journalist Jon Bois. The concept rose to prominence in a 2016 YouTube video (Bois 2016), and it quickly took on a cult-like following: the original YouTube video now has almost 4 million views, the @NFL_Scorigami X (formerly Twitter) account has over 450,000 followers, the nine new Scorigamis in the 2023-24 season were each reported by press, and DraftKingseven offered a prop bet on the Super Bowl ending in a Scorigami (Roush 2024) . Jon Bois used the Scorigami distribution to identify a “good game” region of competitive games with a good balance of scoring events. The Scorigami concept has since been extended to baseball (Bennett 2018) and even weather via daily minimum/maximum temperatures (Kahl 2023) . “Scorigami” itself is a portmanteau of “score”and “origami,” which Bois proposed because of the way the sport’s unique point values fold together to create the disparate rarity among game outcomes that might otherwise appear similar. In the NFL, a team can only score 1 point if they had scored 6 points immediately before; the other base scoring events are worth 2 and 3 points. Hence, NFL scores are typified by strange sums.  \nFigure 1: The distribution of NFL final scores (by winning and losing team’s score) from the 1920 season through the 2023 season, from [https://nflscorigami.com/](https://nflscorigami.com/. The winning team)[. The winning team](https://nflscorigami.com/. The winning team)’s score corresponds to the column, and the losing team’s score, t","cbCaiiJaaeBxqkfh","https://ap.wps.com/l/cbCaiiJaaeBxqkfh","pdf",1059089,"English","# Introduction\n## Scorigamis definition and background\n## Observed scoring irregularities\n## Prior related simulation work\n## Paper motivation and approach","[{\"question\":\"What is an NFL Scorigami?\",\"answer\":\"An NFL Scorigami occurs whenever a game ends in a final score that has not previously happened in the league’s history.\"},{\"question\":\"Why does the paper criticize a stationary Poisson approach?\",\"answer\":\"The analysis shows that a stationary Poisson model fails to incorporate important game dynamics reflected in real score outcomes.\"},{\"question\":\"How does the proposed model improve realism and what is it used for?\",\"answer\":\"The paper extends to a non-stationary, state-dependent Poisson process that better fits play-by-play scoring data, then uses it to simulate and forecast likely future Scorigamis.\"}]","SCORIGAMI - Simulating the Distribution and Assessing the Rarity of National Football League Scores | PDF",1791847795]