Relative Advantage: Quantifying Performance in Noisy Competitive Settings

Relative Advantage: Quantifying Performance in Noisy Competitive Settings | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Relative Advantage: Quantifying Performance in Noisy Competitive Settings Rowan Brown, Georgia Scott, Liam Kilduff This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6428535/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Performance measurement in competitive domains is frequently confounded by shared environmental factors that obscure true performance differences. For instance, absolute metrics can be heavily influenced by factors as varied as weather conditions in sports, prevailing economic climates in business evaluations, or the socioeconomic background of student populations in education. This paper develops a unified mathematical framework for relative performance metrics that systematically eliminates shared environmental effects through a principled transformation that will help improve interpretation of performance metrics. We formalise the mechanism of environmental noise cancellation using signal-to-noise ratio analysis and establish theoretical bounds on metric performance. Through comprehensive simulations across diverse parameter configurations, we demonstrate that relative metrics consistently outperform absolute ones under specified conditions, with improvements up to 28\% in classification accuracy when environmental noise dominates individual variations. As an example, we validate the mathematical framework using real-world rugby performance data, confirming that relativised metrics provide substantially better predictive power than their absolute counterparts. Our approach offers both theoretical insights into the conditions governing metric effectiveness and practical guidance for measurement system design across competitive domains from sports analytics to financial performance evaluation and healthcare outcomes research. Applied Mathematics relative performance key-performance indicators noise cancellation competition Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6428535","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":441693884,"identity":"591303cc-6bb9-4673-9b29-ab9ad19d2f1b","order_by":0,"name":"Rowan Brown","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYJACZjDJ3oAimECEFp4DJGuRQFWEW4tuA+8D5sI9NonbJZ8/k/i5o06Ov4H54QfGtjScWswOsBswz3iWlrhzdo6ZZO+Zw8YSB9iMJRjbcvBoYWNg5jlwOHfD7Ry2G7xtBxIbDjCYMTC2VRCh5ebxZzf/ttXVzz/A/o1ILTcYzG7ztjEnGBzgAdmCx2GH2RgOzziQVr/hTI75b9m2w4YbD/MUSyScw+P9422MjwsO2BgbHD/+2PBtW5283PH2jR8+lCXj1AKKlAMYIgQichSMglEwCkYBIQAAUGRTXXR7hQYAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-3628-2524","institution":"Swansea University","correspondingAuthor":true,"prefix":"","firstName":"Rowan","middleName":"","lastName":"Brown","suffix":""},{"id":441693885,"identity":"8de26cf9-daa5-4602-9e9a-bdd0bcc2b4f9","order_by":1,"name":"Georgia Scott","email":"","orcid":"","institution":"Swansea University","correspondingAuthor":false,"prefix":"","firstName":"Georgia","middleName":"","lastName":"Scott","suffix":""},{"id":441693886,"identity":"c305ee3e-6f20-498f-96ca-03d98cccec05","order_by":2,"name":"Liam Kilduff","email":"","orcid":"","institution":"Swansea University","correspondingAuthor":false,"prefix":"","firstName":"Liam","middleName":"","lastName":"Kilduff","suffix":""}],"badges":[],"createdAt":"2025-04-11 12:54:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6428535/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6428535/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81597166,"identity":"2131e499-0c25-4bfb-95a7-527512af11a6","added_by":"auto","created_at":"2025-04-29 02:59:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1269194,"visible":true,"origin":"","legend":"","description":"","filename":"Paper1Version6AxiomRestructurePreprintsarXiv.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6428535/v1_covered_dfb869b9-4969-434d-8e9a-24707b17e875.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eRelative Advantage: Quantifying Performance in Noisy Competitive Settings\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[{"identity":"0bbce5b0-f5f2-49ea-96f5-2f79b791560c","identifier":"10.13039/501100000266","name":"Engineering and Physical Sciences Research Council","awardNumber":"EGF1069","order_by":0}],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Swansea University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"relative performance, key-performance indicators, noise cancellation, competition","lastPublishedDoi":"10.21203/rs.3.rs-6428535/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6428535/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePerformance measurement in competitive domains is frequently confounded by shared environmental factors that obscure true performance differences. For instance, absolute metrics can be heavily influenced by factors as varied as weather conditions in sports, prevailing economic climates in business evaluations, or the socioeconomic background of student populations in education. This paper develops a unified mathematical framework for relative performance metrics that systematically eliminates shared environmental effects through a principled transformation that will help improve interpretation of performance metrics. We formalise the mechanism of environmental noise cancellation using signal-to-noise ratio analysis and establish theoretical bounds on metric performance. Through comprehensive simulations across diverse parameter configurations, we demonstrate that relative metrics consistently outperform absolute ones under specified conditions, with improvements up to 28\\% in classification accuracy when environmental noise dominates individual variations. As an example, we validate the mathematical framework using real-world rugby performance data, confirming that relativised metrics provide substantially better predictive power than their absolute counterparts. Our approach offers both theoretical insights into the conditions governing metric effectiveness and practical guidance for measurement system design across competitive domains from sports analytics to financial performance evaluation and healthcare outcomes research.\u003c/p\u003e","manuscriptTitle":"Relative Advantage: Quantifying Performance in Noisy Competitive Settings","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-29 02:50:59","doi":"10.21203/rs.3.rs-6428535/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"243b89d8-ed9b-4442-b244-dbe8f8a5c2a5","owner":[],"postedDate":"April 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47033186,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2025-04-29T02:50:59+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-29 02:50:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6428535","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6428535","identity":"rs-6428535","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}