--- title: Factor Analysis and the Best Super Bowl Quarterback Ever description: Factor Analysis and the Best Super Bowl Quarterback Ever image: https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/superbowlxxiiilombarditrophy-3.jpg --- English - [English](https://blog.minitab.com/en/?hsLang=en) - [Français](https://blog.minitab.com/fr/?hsLang=en) - [Deutsch](https://blog.minitab.com/de/?hsLang=en) - [Português](https://blog.minitab.com/pt/?hsLang=en) - [Español](https://blog.minitab.com/es/?hsLang=en) - [日本語](https://blog.minitab.com/ja/?hsLang=en) - [한국어](https://blog.minitab.com/ko/?hsLang=en) - [中文（简体）](https://blog.minitab.com/zh/?hsLang=en) - [![Icon Partners](https://blog.minitab.com/hubfs/WCM/Partners.png) Partners](https://www.minitab.com/en-us/company/partners/) - [![Icon Contact](https://blog.minitab.com/hubfs/WCM/Contact.png) Contact](https://www.minitab.com/en-us/company/contact-us/) - [![Icon Talk to Minitab](https://blog.minitab.com/hubfs/WCM/Phone.png) Talk to Minitab](https://www.minitab.com/en-us/talk-to-minitab/) - [![Icon My Account](https://blog.minitab.com/hubfs/WCM/MyAcct.png) My Account](https://licensing.minitab.com/account/manage) [![Minitab](https://blog.minitab.com/hubfs/WCM/minitab-corp-logo.svg)](https://www.minitab.com/en-us/) - Products Back [Products](https://www.minitab.com/en-us/products/) [All Products](https://www.minitab.com/en-us/products/) - [Minitab Solution Center](https://www.minitab.com/en-us/products/minitab-solution-center/) - [Minitab Statistical Software](https://www.minitab.com/en-us/products/minitab/) - [Minitab Connect](https://www.minitab.com/en-us/products/connect/) - [Minitab Model Ops](https://www.minitab.com/en-us/products/model-ops/) - [Minitab Education Hub](https://www.minitab.com/en-us/products/education-hub/) - [Minitab Engage](https://www.minitab.com/en-us/products/engage/) - [Minitab Workspace](https://www.minitab.com/en-us/products/workspace/) - [Real-Time SPC](https://www.minitab.com/en-us/products/real-time-spc/) - [Prolink Data Collection & SPC](https://www.minitab.com/en-us/products/prolink) - [Simul8 Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en) - [SPM](https://www.minitab.com/en-us/products/spm/) - Solutions Back [Solutions](https://www.minitab.com/en-us/solutions/) [All Solutions](https://www.minitab.com/en-us/solutions/) - [Analytics](https://www.minitab.com/en-us/solutions/analytics/) - [Statistics & Predictive Analytics](https://www.minitab.com/en-us/solutions/analytics/statistical-analysis-predictive-analytics/) - [Data Science & Machine Learning](https://www.minitab.com/en-us/solutions/analytics/data-science-machine-learning/) - [Business Analytics & Intelligence](https://www.minitab.com/en-us/solutions/analytics/business-analytics-intelligence/) - [Statistical Process Control](https://www.minitab.com/en-us/solutions/analytics/statistical-process-control/) - [Quality Analytics](https://www.minitab.com/en-us/solutions/analytics/quality-analytics/) - [Live Analytics](https://www.minitab.com/en-us/solutions/analytics/live-analytics/) - [Reliability & Life Data Analysis](https://www.minitab.com/en-us/solutions/analytics/reliability/) - [Discrete Event Simulation](https://info.minitab.com/en/new-to-simul8?hsLang=en) - [Process Mining](https://info.minitab.com/en/new-to-simul8?hsLang=en) - [Key Capabilities](https://www.minitab.com/en-us/solutions/key-capabilities/) - [Continuous Improvement](https://www.minitab.com/en-us/solutions/key-capabilities/continuous-improvement/) - [Data Integration & Data Prep](https://www.minitab.com/en-us/solutions/key-capabilities/data-integration-data-prep/) - [Diagramming & Mind Mapping](https://www.minitab.com/en-us/solutions/key-capabilities/diagramming-mind-mapping/) - [Digital Twins](https://info.minitab.com/en/new-to-simul8?hsLang=en) - [Model Deployment & ML Ops](https://www.minitab.com/en-us/solutions/key-capabilities/model-deployment-ml-ops/) - [Innovation & Project Management](https://www.minitab.com/en-us/solutions/key-capabilities/innovation-project-management/) - [Process Excellence: Detect, Correct & Prevent](https://www.minitab.com/en-us/solutions/key-capabilities/process-excellence/) - [Featured Industries](https://www.minitab.com/en-us/solutions/industry/) - [Academic](https://www.minitab.com/en-us/solutions/industry/academic/) - [Energy & Natural Resources](https://www.minitab.com/en-us/solutions/industry/energy-resources/) - [Government & Public Sector](https://www.minitab.com/en-us/solutions/industry/government/) - [Healthcare](https://www.minitab.com/en-us/solutions/industry/healthcare/) - [Insurance](https://www.minitab.com/en-us/solutions/industry/insurance/) - [Manufacturing & Industrial](https://www.minitab.com/en-us/solutions/industry/manufacturing-industrial/) - [Services](https://www.minitab.com/en-us/solutions/industry/service-industries/) - [Software & Technology](https://www.minitab.com/en-us/solutions/industry/software-technology/) - [Construction](https://www.minitab.com/en-us/solutions/industry/construction/) - [Featured Roles](https://www.minitab.com/en-us/solutions/role/) - [Engineering](https://www.minitab.com/en-us/solutions/role/engineering/) - [Business Analysis](https://www.minitab.com/en-us/solutions/role/business-analysts/) - [Information Technology](https://www.minitab.com/en-us/solutions/role/information-technology/) - [Supply Chain](https://www.minitab.com/en-us/solutions/role/supply-chain/) - [Customer Service & Contact Center](https://www.minitab.com/en-us/solutions/role/customer-service-contact-center/) - [Human Resources](https://www.minitab.com/en-us/solutions/role/human-resources/) - [Marketing](https://www.minitab.com/en-us/solutions/role/marketing/) - [Research and Development](https://www.minitab.com/en-us/solutions/role/research-and-development/) - Resources & Services Back [Resources & Services](https://www.minitab.com/en-us/resources-services/) [All Resources & Services](https://www.minitab.com/en-us/resources-services/) - [Resources](https://www.minitab.com/en-us/resources-services/resources/) - [Case Studies](https://www.minitab.com/en-us/resources-services/resources/case-studies/) - [eBooks & White Papers](https://www.minitab.com/en-us/resources-services/resources/ebooks-and-white-papers/) - [Blog](https://blog.minitab.com/blog/?hsLang=en) - [Data Sets](https://www.minitab.com/en-us/resources-services/resources/data-set/) - [Webinars & Events](https://www.minitab.com/en-us/resources-services/resources/events/) - [Education Hub](https://www.minitab.com/en-us/resources-services/resources/education-hub/) - [Services](https://www.minitab.com/en-us/resources-services/services/) - [Training](https://www.minitab.com/en-us/resources-services/services/training/) - [Deployment](https://www.minitab.com/en-us/resources-services/services/deployment/) - [Consulting](https://www.minitab.com/en-us/resources-services/services/statistical-consulting/) - [Self-Paced Learning](https://www.minitab.com/en-us/resources-services/services/self-paced-learning/) - [Continuing Education](https://www.minitab.com/en-us/resources-services/services/continuing-education/) - Support Back [Support](https://www.minitab.com/en-us/support/) [Technical Support](https://www.minitab.com/en-us/support/) - [Subscriptions & Activation](https://www.minitab.com/en-us/support/subscriptions-and-activation/) - [Minitab Quick Start](https://www.minitab.com/en-us/support/quick-start/) - [Training](https://www.minitab.com/en-us/resources-services/services/training/) - [Installation Support](https://www.minitab.com/en-us/support/installation/) - [Support Videos](https://www.minitab.com/en-us/support/videos/) - [Support Documentation](https://www.minitab.com/en-us/support/documents/) - [Software Updates](https://www.minitab.com/en-us/support/software-updates/) - [Product Downloads](https://www.minitab.com/en-us/support/downloads/) - [Support Policy](https://www.minitab.com/en-us/support/policy/) - Company Back [Company](https://www.minitab.com/en-us/company/) [Company](https://www.minitab.com/en-us/company/) - [About Us](https://www.minitab.com/en-us/company/our-company/) - [Leadership Team](https://www.minitab.com/en-us/company/leadership-team/) - [Partners](https://www.minitab.com/en-us/company/partners/) - [Careers](https://www.minitab.com/en-us/company/careers/) - [Contact](https://www.minitab.com/en-us/company/contact-us/) - [News](https://www.minitab.com/en-us/company/press-releases/) [Try/Buy](https://www.minitab.com/en-us/try-buy/) - [Statistics](https://blog.minitab.com/en/blog/tag/statistics) - [Data Analysis](https://blog.minitab.com/en/blog/tag/data-analysis) - - [Quality Improvement](https://blog.minitab.com/en/blog/tag/quality-improvement) - [Subscribe](https://info.minitab.com/blog/subscribe?hsLang=en) ![Minitab](https://20853177.fs1.hubspotusercontent-na1.net/hubfs/20853177/minitab-corp-logo.svg?t=1755011311618) ## Notice You are now leaving minitab.com. Click Continue to proceed to: Continue Go Back # Factor Analysis and the Best Super Bowl Quarterback Ever [Cody Steele](https://blog.minitab.com/en/blog/author/cody-steele) | 12/9/2015 - [Share](https://www.linkedin.com/shareArticle?mini=true&url=https://blog.minitab.com/en/blog/statistics-and-quality-improvement/the-best-super-bowl-quarterback-ever) - [Share](https://www.facebook.com/sharer.php?u=https://blog.minitab.com/en/blog/statistics-and-quality-improvement/the-best-super-bowl-quarterback-ever) [![The Lombardi Trophy from Super Bowl XXIII](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/superbowlxxiiilombarditrophy-3.jpg)Last time](https://blog.minitab.com/blog/statistics-and-quality-improvement/terry-bradshaw-might-be-the-best-super-bowl-quarterback-ever?hsLang=en), we used [factor analysis](http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/multivariate/principal-components-and-factor-analysis/what-is-factor-analysis/) to come up with factors we could use to describe the performances of Super Bowl-winning quarterbacks. Now, we’ll try to use those factors to compare the performance of our [candidate quarterbacks](https://blog.minitab.com/blog/statistics-and-quality-improvement/tom-brady-is-the-best-super-bowl-quarterback-ever?hsLang=en) who won at least 3 Super Bowls. Recall that one purpose of factor analysis is to identify underlying factors that you *can't measure directly*. For example, the members of a committee at a hospital design a survey with questions that assess 3 underlying factors: timeliness of service, accuracy of service, and courteousness of service. The committee members can use factor analysis to combine the responses for many different questions into 3 factors. For the analysis of quarterbacks who have won at least 3 Super Bowls, we came up with three factors from 7 variables: - **Factor 1:** How well the winning quarterback played. Higher is better. - **Factor 2**: Competitiveness of matchup. Far from 0 is better, either low or high. - **Factor 3:** How impressive the victory was. More negative is better. The most typical statistical analysis for describing a group, like the data points for Joe Montana, would be to measure their distance from the average factor point. (In this case, the average factor point would be where every factor equals 0). Because our factors are directional, a quarterback could be far from the average point, but in the wrong direction. Instead of looking at the distance, I’m going to measure the distance from a hypothetical great performance where each factor has its best value attained so far. Because either high or low values are good for factor 2, I’ll check the distances for 2 different points. For factor 1, the best possible point was 1.773 by Jim Plunkett. For factor 2, the best possible point is either Joe Montana’s 2.322 or Tom Brady’s -0.386, depending on whether we take the low side or the high side. For factor 3, the best value is Tom Brady’s -2.144. This 3-D scatterplot shows the mean value for each candidate quarterback, the mean value for all other performances by quarterbacks who won Super Bowls, and the 2 ideal values. ![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/scatterplot_of_ideal-3.png) A rough guess from the graph assures me only that Aikman is probably further from the ideal points than the other 3. Here are the actual Euclidean distances between the mean factor scores for each candidate quarterback and the ideal games. (Want to see how to calculate Euclidean distance? In Minitab, Click **Help > Methods and Formulas**. Then, use the Search tab to look for "Euclidean.") | **Quarterback** | **Distance from ideal with factor 2 high** | **Distance from ideal with factor 2 low** | | --- | --- | --- | | Aikman | 4.08328 | 3.53594 | | Bradshaw | 3.51415 | 2.15082 | | Brady | 4.15049 | 2.31167 | | Montana | 2.98226 | 2.36892 | Among the quarterbacks with 3 or more victories, Montana’s factor means are the closest to the best factor values ever achieved when you value how thoroughly a team dominated the other. Montana’s distance is a half unit closer to this ideal game than Terry Bradshaw is. Interestingly, although Tom Brady has the lowest value of factor 2 among all quarterbacks, it’s Terry Bradshaw who is the closest to the ideal point when you consider the ideal game to be winning a competitive matchup. The difference in the means is not as striking here. Bradshaw is within 0.22 of both Tom Brady and Joe Montana. ## Conclusion Terry Bradshaw deserves a lot of credit for beating Roger Staubach-led Cowboys teams twice. Tom Brady's achievement in beating the highest-rated loser ever is noteworthy. But Joe Montana comes away with credibility for beating the Ken Anderson-led Bengals and the Boomer Esiason-led Bengals in competitive Super Bowls, as well as blowing out John Elway and Dan Marino in less-competitive matchups. With these data, and these criterion, I'll turn to Joe Montana as the best superbowl quarterback ever. ###### The image of the Lombardi Trophy from the 49ers victory in Super Bowl XXIII is by [youraddresshere](https://www.flickr.com/photos/youraddresshere/6620253) and is licensed under [this Creative Commons License](https://creativecommons.org/licenses/by-sa/2.0/). --- - [Careers](https://www.minitab.com/en-us/company/careers/) - [Trust Center](https://www.minitab.com/en-us/trust-center/) - [Suppliers](https://www.minitab.com/en-us/suppliers/) - [Site Map](https://www.minitab.com/en-us/site-map/) - [![linkedin](https://blog.minitab.com/hubfs/WCM/linkedin-1.png)](https://www.linkedin.com/company/minitab/) - [![facebook](https://blog.minitab.com/hubfs/WCM/facebook.png)](https://www.facebook.com/Minitab/) - [![youtube](https://blog.minitab.com/hubfs/WCM/youtube.png)](https://www.youtube.com/user/MinitabInc) - [![instagram](https://blog.minitab.com/hubfs/WCM/instagram.png)](https://www.instagram.com/minitab/) --- © 2025 Minitab, LLC. All Rights Reserved. - [Terms of Use](https://www.minitab.com/en-us/legal/terms-of-use/) - [Privacy Policy](https://www.minitab.com/en-us/legal/privacy-policy/) - [Legal](https://www.minitab.com/en-us/legal/) - Cookies Settings