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Three friends decide to bake a cake for a charity sale. Sarah brings the flour and sugar. Michael provides the eggs and butter. Lisa owns the oven and knows the recipe. They sell the cake for thirty dollars. Now comes the awkward part: splitting the money.
Sarah argues she should get more because baking is impossible without flour. Michael points out that nobody wants to eat flour soup, so his ingredients matter just as much. Lisa reminds everyone that raw batter won’t sell, and only she could actually bake it. Each person sees their own contribution as essential. Each person is absolutely right.
This is where most groups either guess, split everything equally, or let whoever yells loudest take the biggest share. But there’s a better way, one that game theory figured out decades ago. It reveals something surprising about value: what you bring to the table is often worth more than you realize.
The Problem With Obvious Solutions
When people work together to create something valuable, figuring out who deserves what becomes messy fast. The simplest approach is dividing everything equally. Three people, thirty dollars, ten each. Done. But equal splits ignore reality. If Sarah had stayed home, there would be no cake at all. If Lisa had stayed home, there would be ingredients sitting on a counter going stale.
Some groups try tracking hours worked or money spent. Michael spent eight dollars on ingredients, so maybe he gets that back first, then everyone splits what’s left. But this approach treats time and money as the only things that matter. What about Lisa’s expertise? What about the fact that Sarah convinced everyone to do this in the first place?
The real question is deeper than addition. What matters is not what each person put in, but what would have been lost without them.
Enter Lloyd Shapley and a Radical Idea
In 1951, a mathematician named Lloyd Shapley asked a deceptively simple question: if a group creates value together, how much of that value can we attribute to each member fairly? Not based on guesses or negotiation skills, but on logic.
His answer became the Shapley Value, and it works like this. Imagine every possible way the group could have formed. Sarah arrives first, then Michael, then Lisa. Or Lisa shows up alone, then Sarah joins, then Michael. Or all three arrive together. Every sequence, every combination.
For each scenario, ask what changed when each person joined. When Sarah walks in alone with flour, she creates zero value because you cannot sell flour to people expecting cake. When Michael joins Sarah, they still have zero value because nobody wants unbaked batter. But when Lisa arrives third, suddenly there’s a thirty dollar cake. Lisa just added thirty dollars of value to this particular sequence.
Now run it again with a different order. Lisa arrives first with her oven and recipe. Value created: zero. Then Sarah shows up with dry ingredients. Still zero. Then Michael brings the eggs and butter, and boom, thirty dollar cake. Michael just added thirty dollars in this version.
The Shapley Value says: calculate every possible order people could join, figure out what each person added in each scenario, then average it all out. The result tells you each person’s true contribution.
Why This Feels Counterintuitive
Here’s where it gets interesting. In the first scenario, Lisa added all thirty dollars. In the second, Michael did. So is Lisa worth thirty or Michael worth thirty? Neither, actually.
The Shapley Value recognizes something subtle about cooperation. Lisa’s oven only creates value because other people brought ingredients. Michael’s eggs only create value because someone can bake them. Nobody is independently valuable. Everyone is interdependently valuable.
When you run through all the possible sequences, the math accounts for every situation where each person was critical and every situation where they were redundant. It counts the times Sarah’s flour made everything possible and the times it sat there useless without someone to bake it. The final numbers reflect not what happened in reality, but what would have happened across all possible realities.
This means the Shapley Value often gives people more credit than they expect. In most groups, people only see the obvious, direct impact of their work. Sarah sees flour and sugar. But the Shapley Value sees something else: the countless scenarios where Sarah’s arrival transformed zero value into potential value, even if that potential needed others to activate it.
Running the Numbers
Let’s calculate this for real. The cake scenario has six possible orderings.
Order one: Sarah, Michael, Lisa. Sarah adds nothing because flour alone creates no value. Michael adds nothing because flour and eggs still create no value. Lisa adds thirty dollars because now there’s a cake.
Order two: Sarah, Lisa, Michael. Sarah adds nothing. Lisa adds nothing because flour and an oven still need more ingredients. Michael adds thirty dollars.
Order three: Michael, Sarah, Lisa. Michael adds nothing. Sarah adds nothing. Lisa adds thirty dollars.
Order four: Michael, Lisa, Sarah. Michael adds nothing. Lisa adds nothing. Sarah adds thirty dollars.
Order five: Lisa, Sarah, Michael. Lisa adds nothing. Sarah adds nothing. Michael adds thirty dollars.
Order six: Lisa, Michael, Sarah. Lisa adds nothing. Michael adds nothing. Sarah adds thirty dollars.
Now average out each person’s contributions across all scenarios. Sarah added thirty dollars in two scenarios out of six, so her Shapley Value is ten dollars. Same calculation for Michael: ten dollars. Lisa also ends up with ten dollars.
Wait. An equal split after all that complexity? In this specific case, yes, because the situation was perfectly symmetric. Each person’s contribution was equally essential. Remove any one of them and the cake becomes impossible. The math confirmed what fairness suggested.
But change the scenario slightly and everything shifts.
When Symmetry Breaks
Suppose Lisa actually owns two ovens and knows five different recipes. Sarah and Michael each bring the same ingredients as before. Now run the calculation again.
If Sarah never showed up, could Michael and Lisa still make something? No, they still need flour. If Michael stayed home, could Sarah and Lisa create value? No, they still need eggs. But Lisa’s extra capabilities matter now. She has redundancy built in. If her first oven breaks, she has another. If one recipe fails, she tries a different one.
The calculation gets more complex, but the principle stays the same. Lisa’s Shapley Value goes up not because she worked harder, but because she reduced risk. Her extra resources made success more robust across different scenarios.
This reveals something counterintuitive about contributions. Sometimes doing more of the same thing adds little value. Michael buying twice as many eggs doesn’t help much when the recipe only needs three. But bringing different kinds of value, things that make success possible in more scenarios, that compounds your worth exponentially.
The Birthday Party Paradox
Consider another example that highlights how the Shapley Value captures something basic human instinct misses.
Eight friends organize a surprise birthday party. Seven people each chip in fifteen dollars for food, decorations, and a gift. The eighth person, Jamie, contributes nothing financially but offers their apartment as the venue.
An equal split would give everyone the same credit. A cost based split would give Jamie zero credit. Both feel wrong. The party literally cannot happen without the venue. Jamie’s contribution might be the most valuable of all.
The Shapley Value calculation confirms this. Without any one of the seven people paying, the party still happens but gets slightly worse. Maybe less food or cheaper decorations. But without Jamie, there’s no party at all. Jamie gets venue credit across every possible scenario, while each payer only gets marginal credit for improving what was already possible.
Jamie’s Shapley Value ends up higher than anyone else’s, even though Jamie spent nothing. The math recognized what everyone felt but struggled to quantify: some contributions are gates that must pass through, while others are enhancements that make things better.
Why Companies Get This Wrong
Most workplaces assign credit based on visibility. The salesperson who closed the deal gets celebrated. The engineer who fixed the critical bug at midnight gets a pat on the back if anyone notices. The person who organized the documentation that made onboarding new team members possible gets nothing because their impact is invisible.
The Shapley Value would tell a different story. It would ask: across all possible versions of this project, how many succeed without the salesperson versus how many succeed without the midnight bug fix versus how many succeed without proper documentation? The answers might be surprising.
That critical bug might have only affected ten percent of users in specific edge cases. The documentation might have enabled three new engineers to contribute effectively for years. The sale might have happened anyway because the product solved a clear need and five competitors were pursuing the same client.
Running these calculations precisely is hard in complex organizations. But the principle remains valuable: contribution is not about who’s loudest or most visible. It’s about what becomes impossible without you.
The Fallacy of the Last Touch
Sports fans know this bias well. The player who scores the winning goal gets the glory. But what about the defender who prevented an early goal that would have changed the momentum? What about the midfielder who made the crucial pass that created the scoring opportunity? What about the coach who substituted a tired player at exactly the right moment?
The last touch gets remembered, but the Shapley Value asks us to consider all the touches across all the possible games that could have been played. In some scenarios, the defender’s early save was the difference between winning and losing. In others, the substitution changed everything. The goal scorer’s Shapley Value is high, but so is everyone else’s who made that goal possible.
This applies everywhere. The person who sends the final email closing a deal gets credit, but maybe the deal was already ninety percent done by someone else’s groundwork. The person who adds the final feature before launch gets visibility, but maybe the product was already valuable because of the foundation others built.
Understanding this doesn’t diminish anyone’s achievement. It expands our view of achievement to include all the critical moments that made the visible moments possible.
What This Means for You
If you’ve ever felt undervalued at work, in group projects, or in collaborative efforts, the Shapley Value offers a framework for understanding why. Most people only see direct, immediate impact. They miss the enabling conditions, the risk reduction, the foundation building, the knowledge transfer, the coordination effort.
Your contribution is probably worth more than anyone gives you credit for, including yourself.
That documentation you wrote might seem like a small task, but it enabled five people to work independently instead of constantly asking questions. That process you improved might save thirty minutes per person per week. Multiply that across months and people, and your Shapley Value is enormous.
That introduction you made might seem trivial, but it connected two people who went on to build something significant. Without you, that specific connection never happens, meaning your Shapley Value captures the full downstream impact.
The framework also explains why some contributions feel thankless. If you’re doing work that others could do almost as well, your Shapley Value is low because removing you doesn’t change outcomes much. But if you’re doing work that creates unique possibilities, work that makes ten other things possible that weren’t before, your value skyrockets even if nobody notices.
The Catch
The Shapley Value is mathematically fair, but it requires information nobody has. You need to know what would have happened in every alternate reality where different people joined in different orders. You need to know the value created in scenarios that never occurred.
In practice, we approximate. We ask counterfactuals. What if this person hadn’t shown up? What if we’d tried this without that resource? These questions help, but they’re still guesses.
The value isn’t in calculating exact numbers. The value is in changing how we think about contribution. Instead of asking who did the most visible work, ask who made things possible. Instead of looking at final results, look at all the moments where things could have fallen apart but didn’t because someone was there.
A Final Scenario
Twenty people show up to clean a park. Nineteen bring trash bags, gloves, and enthusiasm. One person brings a truck to haul away everything collected. At the end, there are forty bags of trash.
An equal split gives everyone the same credit. A task based split gives more credit to people who filled more bags. But without the truck, those bags sit in the park accomplishing nothing. The person with the truck enabled the entire effort.
Their Shapley Value captures this. Across all the scenarios where different people showed up, the truck person was the bottleneck, the critical resource that determined whether the project succeeded or failed. Nineteen people working without a truck create zero value. One person with a truck but no help creates minimal value. Together they create something real.
This is what the Shapley Value teaches us. Value is not additive. It’s multiplicative, interdependent, and often invisible. What you contribute enables others to contribute. What others contribute enables you. Figuring out who deserves credit isn’t about dividing a pie. It’s about recognizing that without each slice, there is no pie at all.
The next time you doubt whether your work matters, remember this. Somewhere in the calculation, there’s a scenario where everything falls apart without you. Your Shapley Value counts that scenario just as much as all the others. You’re not worth what you think you’re worth. You’re worth what you make possible.
