The 1890 Self-Esteem Formula That Explains Why Silver Hurts More Than Bronze

In 1890, a Harvard professor wrote self-esteem down as if it were a grade-school division problem. A century later, television cameras at the Olympics caught something that looked absurd: the athletes in third place were smiling more than the ones in second.

The professor was William James, and the formula appears in chapter X of The Principles of Psychology, “The Consciousness of Self.”

It is one of the most quoted ideas about self-esteem in the history of psychology, and also one of the most misread.

What is self-esteem, according to William James? A fraction

Here is the formula, exactly as James printed it:

• Self-esteem = Success / Pretensions

The numerator is what you achieve. The denominator is what you set out to achieve.

The math has an immediate consequence, and James spells it out: the fraction can rise by increasing the numerator or by shrinking the denominator.

Hence his line:

To give up pretensions is as blessed a relief as to get them gratified.

His examples are almost comically honest:

• “How pleasant is the day when we give up striving to be young, or slender! Thank God! we say, those illusions are gone.”
• A man who lost every penny in the Civil War and rolled in the dust, saying he had not felt so free and happy since he was born.
• Carlyle: “Make thy claim of wages a zero, then hast thou the world under thy feet.”

The psychologist who didn’t know Greek (and didn’t care)

The key is not the division. It is what counts as a pretension.

James uses himself as the example:

I, who for the time have staked my all on being a psychologist, am mortified if others know much more psychology than I. But I am contented to wallow in the grossest ignorance of Greek.

He never set out to be a linguist, so the gap costs him nothing. Failure doesn’t hurt in the abstract: it hurts only where you have staked yourself.

And since nobody can stake themselves on everything, James lists the selves he would like to be at once:

• handsome
• a great athlete
• a man who makes “a million a year”
• a wit
• a bon vivant
• a lady-killer
• a philosopher
• a philanthropist
• statesman
• warrior
• “African explorer”
• a “tone-poet”
• a saint

It is impossible: the millionaire’s work would run counter to the saint’s. Choosing a self also means choosing where you are allowed to fail.

Why the second-best in the world feels ashamed

Then comes the passage that reads, a century later, like a prediction. James describes “the paradox of a man shamed to death because he is only the second pugilist or the second oarsman in the world.”

Beating the entire population of the globe minus one means nothing to him. He had pitted himself against that one, and until he beats him, “nothing else counts.” Meanwhile, the puny fellow whom everyone beats feels no chagrin at all, because he abandoned that pretension long ago.

Silver vs. bronze: what the Olympic cameras saw

In 1995, Victoria Medvec, Scott Madey and Thomas Gilovich asked students to rate, from television footage, the faces of medalists at the 1992 Barcelona Games, right after their events and on the podium.

The result: bronze medalists looked happier than silver medalists. Their explanation was counterfactual thinking, the comparison with what might have been:

• The silver medalist compares themselves with the gold they nearly won.
• The bronze medalist compares themselves with fourth place, the one who goes home with nothing.

The finding did not stay isolated:

• Matsumoto and Willingham (2006) coded the facial expressions of judo medalists at Athens 2004. Right after the final match, 13 of 14 gold medalists and 18 of 26 bronze medalists (with usable photos) smiled. None of the 14 silver medalists did.
• On the podium almost everyone smiled, but the silver medalists’ smiles were more often controlled or blended with sadness.
• Hedgcock, Luangrath and Webster (2021) used facial-coding software on 413 athletes from 67 countries across five Games (2000 to 2016): bronze medalists were more likely to smile than silver medalists.

The key refinement came from McGraw, Mellers and Tetlock (2005): prior expectations weigh heavily. An athlete who expected gold experiences silver as a defeat.

That is, word for word, James’s denominator.

What does modern psychology say about self-esteem?

In 2001, Jennifer Crocker and Connie Wolfe published their theory of contingencies of self-worth in Psychological Review, explicitly building on James:

• Each person’s self-esteem fluctuates around its typical level.
• Those fluctuations depend mostly on successes and failures in the domains where the person has staked their worth: appearance, other people’s approval, academics, virtue.
• In domains they don’t care about, a failure barely registers, like James’s Greek.

It is the same territory as self-oriented perfectionism, where the bar is set, very high, by the person themselves.

What the formula got right, and what it didn’t

James got the core right: self-esteem does not mirror raw achievement.

It mirrors achievement relative to what you expected of yourself.

But the fraction doesn’t hold up literally:

• It is not a measure. James offered it as an illustration. Researchers use questionnaires, such as the 10-item Rosenberg scale (1965).
• The denominator isn’t chosen alone. James himself wrote that a person has “as many different social selves as there are distinct groups of persons about whose opinion he cares,” and that being ignored by everyone would be worse than “the cruellest bodily tortures.”
• Giving up doesn’t always bring relief. Lowering a goal can be a rest or a retreat; the formula can’t tell them apart.

What it does explain is why the same medal can feel like a triumph or a loss. The self-esteem test lets you see where your own overall self-evaluation sits, and the reason a personal mistake can land almost like a blow is covered in why your brain reacts to self-criticism like a physical threat.

Sources

• James, W. (1890). The Principles of Psychology. Henry Holt and Company.
• Medvec, V. H., Madey, S. F., & Gilovich, T. (1995). When less is more: Counterfactual thinking and satisfaction among Olympic medalists. Journal of Personality and Social Psychology, 69(4), 603-610. https://doi.org/10.1037/0022-3514.69.4.603
• Matsumoto, D., & Willingham, B. (2006). The thrill of victory and the agony of defeat: Spontaneous expressions of medal winners of the 2004 Athens Olympic Games. Journal of Personality and Social Psychology, 91(3), 568-581. https://doi.org/10.1037/0022-3514.91.3.568
• McGraw, A. P., Mellers, B. A., & Tetlock, P. E. (2005). Expectations and emotions of Olympic athletes. Journal of Experimental Social Psychology, 41(4), 438-446. https://doi.org/10.1016/j.jesp.2004.09.001
• Hedgcock, W. M., Luangrath, A. W., & Webster, R. (2021). Counterfactual thinking and facial expressions among Olympic medalists: A conceptual replication of Medvec, Madey, and Gilovich’s (1995) findings. Journal of Experimental Psychology: General, 150(6), e13-e21. https://doi.org/10.1037/xge0000992
• Crocker, J., & Wolfe, C. T. (2001). Contingencies of self-worth. Psychological Review, 108(3), 593-623. https://doi.org/10.1037/0033-295X.108.3.593
• Rosenberg, M. (1965). Society and the adolescent self-image. Princeton University Press.