This paper is about performance assessment in serious games. We conceive serious gaming as a process of player-lead decision taking. Starting from combinatorics and item-response theory we provide an analytical model that makes explicit to what extent observed player performances (decisions) are blurred by chance processes (guessing behaviors). We found large effects both theoretically and practically. In two existing serious games random guess scores were found to explain up to 41 of total scores. Monte Carlo simulation of random game play confirmed the substantial impact of randomness on performance. For valid performance assessments, be it in-game or post-game, the effects of randomness should be included to produce re-calibrated scores that can reasonably be interpreted as the players' achievements.