Minimax Under Pressure: The Case of Tennis

A series of articles has tested von Neumann’s minimax theory against behavioral evidence based on field data from professional sports. The evidence has been viewed and collectively cited as positive evidence that elite athletes in their familiar sports contexts mix well and behave in line with minimax. In this paper, based on open state-of-the-art tennis data and analytics, we shall uncover new and significant evidence against minimax at the very top of the game, where previously, such results had not been obtained. The kinds of behavioral deviations from minimax that we find become apparent, because we enrich the test strategy to take into account whether or not players face ‘pressure’ situations like break points and other decisive points. Our paper highlights that the prior literature’s failure to reject minimax does not constitute positive behavioral evidence, as some of that literature argued, because it is not robust to data aggregations and separations that are psychologically natural given the relevant real-world context. In this case, this means separating serves into the serve types that players actually consider and separating situations by pressure levels, which leads to clear and sound rejection of minimax.