free–Wilson analysis
Imagine each substituent on a molecule earns or loses a fixed number of activity points, and a compound's total activity is just the sum of the points from all its parts. Free–Wilson analysis is the method, introduced by Spencer Free and James Wilson in 1964, that fits exactly that kind of additive bookkeeping to a series of analogs.
Mechanically, it sets up a regression in which the activity of each compound equals a baseline value plus a contribution term for whichever substituent sits at each varied position. Fitting the model to measured activities across a congeneric series yields a contribution value for every group at every position. Unlike Hansch QSAR, Free–Wilson uses no external physicochemical parameters; the substituents are simply present-or-absent indicators, which makes it a clean way to read off each group's average effect directly from the data.
Free–Wilson analysis is intuitive and needs no measured properties, and it remains a useful descriptive tool — its modern descendants underlie matched-molecular-pair statistics. Its built-in assumption is strict additivity: it presumes substituent contributions are independent and simply sum, so it cannot describe interactions between positions or activity cliffs, and it can only interpolate among substituents already in the dataset, never predict a group it has not seen.
Fitting fifty analogs of one scaffold, the model assigns each substituent a numeric activity contribution, so a chemist can read directly that a meta-CN adds about one log unit while a para-OMe subtracts a little.
Each group gets an additive activity score, read straight from the series with no external parameters.
Free–Wilson assumes additivity; activity cliffs are precisely where additivity breaks, because two positions interact. A poor Free–Wilson fit can itself be a hint that such non-additive effects are present.