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The Innovation Equation for Managers

Updated: Apr 25, 2019

Stanford physicist (and former CEO of a publicly-traded company) Safi Bahcall, in an article in the most recent edition of the Harvard Business Review, lays out an algebraic formula describing how to manage people towards innovation. In providing this comprehensive, MBA-school summarizing, management formula, Dr. Bahcall provides several strategies to optimize the parameters of this formula for any organization so that you can structure your organization to be innovative at a larger scale.

Introduction, Premise, and Formula

Having studied several prominent companies that failed to continue to innovate, Dr. Bahcall theorized that there is a certain size, call it “M” (for magic number), at which that company undergoes a phase transition from an innovative company to a company that is hostile to innovation.

In studying the reasons for these phase transitions, he posited that there is an interplay of several factors that, if successfully managed, can increase the size M to which a company can grow and maintain a culture of innovation. This interplay, he reduced to the following formula:


M (magic number)

E (equity fraction)

S (management span)

F (fitness ratio)

G (salary growth)

This equation implies that to keep your organization innovative at greater scale (aka to increase M), you have to increase E, S, F, and reduce G.

What do the variables mean?

E (equity fraction)

This variable represents the fraction of project-outcome-based compensation as opposed to rank-based-compensation. Thus, the higher the project-outcome based compensation is relative to total compensation, the higher the value of E.

Special Note: This project-outcome-based compensation (or equity) can come in two forms:

1. Hard equity: stock options, grants, commissions, bonuses, etc.

2. Soft Equity: non-financial stakes, such as peer recognition, awards, visibility within the company and with clients.

Why a higher E affects innovation…

Where compensation depends on successful outcomes, rather than successful interactions with management, employees are incentivized to be more innovative, ambitious, and efficient in handling problems and coming up with solutions that will improve their own bottom line and payout.

S (Management Span)

This variable represents the average number of direct reports that executives of the company have. A smaller average number of direct reports implies more layers of management and thus, greater draw (and distraction) for employees to climb the ladder.

Why a higher S affects innovation…

Where there is a flatter management hierarchy (less mini-managers), “[p]romotions occur so rarely that no one thinks about them; instead they focus on their work.”

“The large group of equal-level colleagues provides ‘a continuous form of peer review,’ [Internet Pioneer Bob] Taylor said. ‘Projects that are exciting and challenging obtain more than financial or administrative support; they receive help and participation from other…researchers. As a result, quality work flourishes; less interesting work tends to wither.’

F (Fitness Ratio)

This variable represents the ratio between the project-skill fit (PSF) and the marginal return on politics (ROP). F=(PSF)/(ROP)

PSF, in turn, represents the marginal return of an employee’s investment of an additional unit of time on a project. Thus, where employees work on projects for which their skills are well suited and on which they can have a significant impact, the marginal return of the additional time spent on the project will be high, resulting in a high value of PSF.

ROP represents the marginal return of an employees investment of an additional unit of time on lobbying, networking, and self-promoting. Thus, more an employee can affect her or his standing in the organization through spending time on schmoozing a particular manager or influencer within the organization, the higher the value of ROP.

Why a higher F affects innovation…

Where an employee is better served spending an extra hour on a project that s/he is well-suited to master than on spending that extra hour networking with management, that employee can spend the time necessary to come up with innovative, ambitious, and efficient solutions.

G (Salary Growth)

This variable represents the average step-up in base salary (and other executive perks) that employees receive as they ascend the hierarchy. Thus, the more employees can aspire to (and invest time and resources in) increasing their salary through ascending the hierarchy, the greater the value of G.

Why a lower G affects innovation…

Where moving up the management ladder only nominally affects salary, there is an incentive to spend more time crafting innovative, ambitious, and efficient solutions to project tasks (whose success will result in higher compensation if E has been properly optimized) and less time on finessing the political levers necessary to climb the corporate ladder.

How to Optimize these Variables for Innovation

1. Appoint a Chief Incentives Officer: “Organizations need top-level executives who are well trained in the subtleties of aligning incentives and solely focused on achieving a state-of-the-art compensation system. A good incentives officer can identify wasteful bonuses (such as blanket stock options and bonuses based on companywide, rather than group or individual, performance), reduce the risks of perverse incentives (for example, when an auto dealer’s sales goals for service reps lead to overcharging customers), and tap thoughtfully into the power of nonfinancial rewards (peer recognition, choice of assignments, freedom to work on a passion project, and so on). The goal of achieving the most motivated employees for a given compensation budget is as important and strategic to companies as is the goal of achieving the best sales for a given marketing budget (the province of a chief revenue officer) or the best IT systems for a given technology budget (a chief information officer’s terrain).”

2. Optimize Management Spans: “Companies should widen management spans and design looser controls for groups in which radical innovation is the goal. Those structures encourage experimentation, peer-to-peer problem solving, and engagement in project work.” Your authors contribution: Use soft, informal management positions and delegate more authority to the employee with the skillset that is most important to project outcome.

3. Perfect Employee Placement: “Designate a person or a small central team to regularly scan the organization for project-skill fit, ensuring that everyone, from new hires to old-timers, is in the right job at the right time.”

4. Reduce office-political considerations: “Employees need to see that lobbying for pay and promotions will not help them. One way to do this is to have those decisions depend less on an employee’s manager and more on impartial assessments by neutral parties. When promotions are considered at McKinsey, for example, a partner from a different office and preferably a different functional practice interviews candidates’ colleagues and clients and then reports back to a group of partners who make the decision.”

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