In this paper, we develop a logistic regression model to estimate the probability that a particular shot in an NHL game will result in a goal, and use the results to evaluate the performance of NHL skaters, goalies, and teams. We weight each shot based on the estimated probabilities obtained from our model, call this statistic "weighted shots", and use advanced statistics based on weighted shots as the basis of our evaluation. We also analyze whether advanced statistics based on weighted shots outperform traditional statistics as an indicator of future performance of skaters, goalies, and teams. In general, statistics based on weighted shots perform well, but not better than traditional statistics. We conclude that weighted shots should not be viewed as a replacement for those statistics, but can be used in conjunction with those statistics. Finally, we use weighted shots as the dependent variable in an adjusted plus-minus model. The results are estimates of each player's offensive and defensive contribution to his team's weighted shots during even strength, power play, and short handed situations, independent of the strength of his teammates, the strength of his opponents, and the zone in which his shifts begin.