Playing To Win

Surfaces Concave & Convex

Contrasting Strategy Challenges

Roger Martin
8 min readMay 27, 2024


Source: Roger L. Martin, 2024

I was talking to my wife, Marie-Louise, about our book project (more on that at some later point) and we got into a way of distinguishing between types of business strategy issues. I thought it was a sufficiently interesting subject about which to write a Playing to Win/Practitioner Insights piece. It is called Surfaces Concave & Convex: Contrasting Strategy Challenges.

Concave and Convex Surfaces in Golf

At some risk, I am going to start with a golf metaphor. I know far from everyone is a golfer, but hopefully the metaphor will even work for non-golfers (for whom I provide added explanations that golfers won’t need).

In golf, placement of the flagstick (or pin, which marks the 4.25” diameter cup that is the final target of the golfer who attempts to hit the golf ball from the tee-off area into this cup in the fewest strokes possible) on the putting surface (or green) has a big impact on scoring. The very same hole (of the 18 holes on a golf course) can play much harder or easier depending on pin placement. Greens are never entirely flat. There will always be flat parts and sloped parts. Let’s think of the pin being situated on a flat part of the green. In that position, it will generate a certain average score across all the players who play that hole with that pin placement. Consider that average, the baseline score.

Then consider the pin instead placed at or near the lowest point in a bowl-shaped depression in the green. Average scoring on that very same hole will be considerably lower than the baseline scoring above because any approach shot from off the green that lands anywhere in the vicinity of the pin will funnel towards the pin — making for a shorter (and therefore, easier) put. And any put will also funnel towards the hole and not be in danger of racing past the pin because the upward slope on the other side of the pin will stop its momentum.

That is a concave context in which there is natural momentum toward a positive, desirable outcome — in this case, getting the golf ball into the hole using the fewest strokes. It is like the red ball on the left above — the shape of the surface on which it lies causes the ball to get to the desired resting place.

But sometimes the pin is placed at or near the top of a crested part of the green — think inverted bowl. Scoring with this pin placement is considerably higher than baseline because approach shots will funnel away from the pin resulting in longer and harder puts. Those puts also will funnel away from the pin when they miss rather than towards the hole — making for harder puts — and generally more of them.

That is the convex context in which there is natural momentum away from a positive, desirable outcome. It is like the red ball on the right above — currently, it is sitting precariously at the right spot, but is ready to roll down and away in any direction.

Convex and Concave Surfaces in Business

In business, many situations are vexatious because they are convex, and the natural energy funnels away from the desired outcome — like the red ball above right. An example is worklife/homelife balance, a subject for which many young consultants came to me for advice when I was one of the leaders of Monitor Company. They wanted to know how to solve the problem. My counsel was that there is no solution. If they achieved a happy balance at a given point in time, chances are it would just go on to get unbalanced in one direction or another. Hence, they should not think about ‘solving’ worklife/homelife balance but rather continuously managing it. The ball will forever threaten to roll done from the apex, and energy must continuously be applied to get it back up — because it is a convex surface.

The same holds for pricing between consumer packaged goods companies and their retailers. While they might come to an optimal agreement on pricing at a given point in time, both sides will attempt to improve their own situation at the expense of the other, and it will require energy to get it back closer to optimal. The same holds for managing expectations in the equity markets. CEOs and CFOs can work with analysts to guide expectations to a level that best matches with reality. But left to their own devices, analysts are likely to get overly excited or overly depressed about prospects for the company. So, energy needs to be constantly applied to get expectations back in line with reality.

These are but a few examples of convex surfaces in business. There are many more — maintaining optimal staffing levels, balancing short-term and long-term priorities, investing in current products vs. new products. In all cases, it takes great energy to get the ball to the optimal position — but when it is there, it is not stable; it is ready to role down the slope at any moment.

The enjoyable business contexts are concave — where outcomes naturally roll toward optimal.

For example, habit (which I have written about) creates a concave surface for a company whose products or services are the object of the habit. Unless some roadblock in put in their way, customers naturally buy based on their habit — the ball rolls to the bottom of the bowl. Platforms that successfully harness network effects are concave surfaces. Customers naturally come to them because it is the easiest and most efficient thing to do. Fame on Instagram or TikTok is concave — having more followers makes it more likely that still more followers will arrive. A situation in which switching costs are high is a concave surface with respect to existing customers — they are inclined to buy more.

Recognition and Tailoring

It is essential to its prosperity for a company to discern whether it is operating on a convex or concave surface when it is considering its strategic choices. For convex surfaces, eternal vigilance is — literally — the price of freedom. You must keep investing to push the ball back to the peak. If you ever stop, it will roll down. Don’t spend 10 years not worrying about accumulating overhead count and then realize that you have to fire 10,000 white collar workers. Don’t assume that worklife/homelife balance will take care of itself. It won’t. Don’t assume that equity market expectations will stay consistent with reality. They won’t.

For concave surfaces: Do not get in the way. The worst thing you can do is to slow the ball — or worse, stopping it — from getting where you want it to get. Instead, grease the surface. If you are Marvel Studios and have a bevy of beloved superhero characters, tie them all together into the Marvel Cinematic Universe and make it easy and natural for the fans of each character to go to them all — and end up with four of the top ten grossing movies of all time. If you are Ford and have the market leading commercial van, Transit, you develop relationships with the ‘upfitters’ that customize the vans for the customer’s desired use (e.g. electrician or plumber) and make the process of upfitting as seamless as possible for customers.

Turning Convex to Concave

Tailoring your strategy choices cleverly to the shape of the surface on which you operate is extremely valuable. But the biggest and most valuable trick is to turn a convex surface into a concave one.

To do so, you need to understand the forces that cause outcomes to roll away from optimal and ask how you could flip those forces. Sometimes it can be a tiny thing.

Let’s imagine you installed a new furnace (or air conditioner, or water heater) in your house — or more likely bought a house that already had its equipment installed by the previous owner. From the perspective of the company that installed and wants to service the furnace over time, that business is inherently a convex surface. The installer is at the apex when it did the installation, but typically a long time will pass before the equipment needs to be serviced or repaired, during which time the customer forgets entirely (or never knew) who installed the furnace. Because the service & repair business tends to be a fragmented with lots of competitors, winning that service/repair business is tough. The tiny companies don’t have the scale to advertise. They don’t know when customers are in a buying situation — so direct mail/email marketing has low efficacy. Basically, the original installer rolls down to the bottom edge of the convex surface along with the rest of the competitors.

But imagine instead, during the installation, you put a sticker prominently on the furnace that informs the customer that you installed the furnace and will provide an automatic discount on service & repairs to the owner of this furnace — with your phone, email, QR code. That turns what would otherwise be a convex surface into a concave one in which outcomes are inclined to funnel towards optimal. Regardless of when the buying situation arrives or why, you will get the first call, and it is yours to lose.

I learned the trick of turning convex to concave from my dad, an entrepreneur who created an animal feed manufacturing company, which grew to be #1 in its market, and still is 65 years later. To him, sales calls (which were in-person at the farmer’s location) were (in my terms) a convex surface. Dad wanted the outcome to be the salesperson spending the entire call selling the company’s feed quality and service — because we had competitive advantage in both. However, farmers were inclined to spend as much of the call as possible negotiating price — crowding out time for selling the company’s differentiating features. It seemed impossible to push the outcome up the slope to optimal.

But he flipped the surface. He published a price list every week and declared that the company would never sell at a price not on the published price list — and has kept that promise for over half of a century without a single deviation. Because farmers ceased to gain any utility whatsoever from negotiating on price, salespeople could use the sales call to discuss the desired topics — feed quality and service. And farmers were happier because they could be confident that no other farmer would get a better deal, enabling them to spend time on other things about which they cared — the quality of the feed they were buying and the service level they could expect. The surface was flipped to concave. Actions funneled themselves toward the desired outcome.

Practitioner Insights

It is critical to recognize the shape of the surface on which you are operating. The strategic imperatives are different for each. If you treat one accidently as the other — or flat — you will at best be ineffective and at worst, make terrible strategic mistakes.

If it is a concave surface, you mainly need to get out of the way. Do nothing that will slow things from their natural progress. Don’t reinvent. Don’t ‘refresh our look and feel.’ Make it easier for players in your system to do what they were already inclined to do.

If it is a convex surface, you have two productive paths. You can manage it optimally as a convex surface, or you can flip it to concave. To pursue the former, you need to build an Enabling Management System that keeps applying resources to push the outcome back up the desired place. You have a chance of winning on a convex surface by having systems in place that push you back up more expeditiously and effectively than competitors, who might not appreciate that it is a convex surface.

But even better, if you can figure out a clever way, flip your convex surface to concave. It takes imagination and fortitude. But the payoff is well worth it.



Roger Martin

Professor Roger Martin is a writer, strategy advisor and in 2017 was named the #1 management thinker in world. He is also former Dean of the Rotman School.