Abstract. We present the only model to date that predicts the discrete probability distribution of a golfer's score for each hole of a tournament on a shot-by-shot basis. We first generalized Broadie's technique of score-based skill estimation to allow a golfer's skill (e.g. scoring average, driving spray, iron play, putting) to vary continuously by time-weighting data with exponential decay. Training a single-layer 50-node neural network to predict probabilities of scoring by hole resulted in an out-of-sample cross-entropy error of 0.974. We then added features of each hole (e.g. par, green size, sand area) onto the model, representing golfers and holes in an N-by-M dimensional space and achieved an error of 0.953. Adding in course features provided by ShotLink (e.g. fairway height, firmness, wind speed) dropped error to 0.9374. Finally, generalizing the model to update probabilities per shot further reduced error to 0.891. This work helps players understand which skill sets they should improve on, manage courses better (better to miss fairway right or left on hole 13 of Bethpage Black?) and select the best tournament to enter. It also revolutionizes the viewing experience of the PGA by live updating odds to win per shot (similar to WSOP) and helps sports books offer more accurate betting lines.