Over the years, many investigators have examined possible factors which might have led to the breakup of The Beatles, but Professor Tadashi Yagi (Faculty of Economics, Doshisha University, Kyoto, Japan) is one of the few* scholars to have approached the subject from a mathematical standpoint. The professor takes the view that incentives for collaborating within a team tend to decrease as the knowledge of each member is shared over time. Thus the breakup of the band was “an inevitable consequence of the superstar collaboration.”
His formula for the quality of music produced by the group is as follows:
[see full paper for definitions of variables]
“Based on this equation, one can finally understand why the final album recorded by the Beatles, Abbey Road, is critically acclaimed as a masterpiece, even though it was recorded when the group was on the verge of breaking up: the period during which the album was recorded coincided with the creative peak of each member of the band.”
See: Nonlinear Effects of Superstar Collaboration: Why the Beatles Succeeded but Broke Up, Applied Economics and Finance, Vol. 2 , No. 2 ; May 2015
*Note [1]: Few, but not the only. See, for example: ‘Assortative Matching, Reputation, and the Beatles Breakup’ (University of Michigan Economics Department, 2001)
Note [2]: For copyright reasons, we are not permitted to reproduce any Beatles music on this website, so instead the video above shows The Rutles performing ‘Cheese and Onions’ from ‘Yellow Submarine Sandwich’ (Soundtrack 1/17/1969).