Theory of Aces: Fame by chance or merit?

We study empirically how fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement or merit, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; to be precise, there is a strong correlation (~0.7) between achievement and the logarithm of fame. At the same time, the number of individuals achieving a particular level of merit decreases exponentially with the magnitude of the level, leading to a power-law distribution of fame. A stochastic model that can explain the exponential growth of fame with merit is also proposed.