One usually writes A.I. programs to be used on a range of examples which, although similar in kind, differ in detail. This paper shows how to predict where, in a space of problem instances, the hardest problems are to be found and where the fluctuations in difficulty are greatest. Our key insight is to shift emphasis from modelling sophisticated algorithms directly to rnodelling a search space which captures their principal effects. This allows us to analyze complex A.I. problems in a simple and intuitive way. We present a sample analysis, compare our model’s quantitative predictions with data obtained independently and describe how to exploit the results to estimate the value of preprocessing. Finally, we circumscribe the kind problems to which the methodology is suited.