A few weeks ago Vic Ferrari and I had a lively debate on face-offs, due to school I have been unable to respond to the post correctly and felt I should complete the discussion. Before starting I would like to thank Vic Ferrari for pointing me to some excellent resources and much of this article is based on the great face-off article found at that site.
The above graph shows the effects of the different face-offs on goals against (O = offense zone, D = defensive zone), you should notice a lag for offensive zone face-offs in terms of goals against as one has to skate the length of the ice before scoring. One should notice that the primary effects occur in the first 15 seconds, the results after that aren’t clearly dominant like the first 15 seconds with a net effect (difference between offensive and defensive face-offs) of around 400 goals (incorrectly estimated it to be 200 in the above comments as my scripts were poor). There is a slight increase in scoring after the initial 15 seconds as well, which could be the result of better teams having get more offensive draws or it could also be a slight effect of possible zone control 15 seconds after a face-off. 400 goals over the course of 26,000 face-offs works out to 0.016 goals per defensive face-off so the cost associated with the defensive face-off is: 0.016 goals against (this should be a good metric to quantify the cost of icing). The majority of the effect is caused by losing the draw in the defensive zone, so if you don’t win the draw the effect isn’t really there (at least not as much).
In terms of individual players, this effect will be minimal due to the simple fact that some players see a very small difference in offensive zone vs. defensive zone resulting in a mean of 0 and standard deviation of around 50, so 95% of the players are within around ±100. This results in a standard deviation for the cost to a center man of around 0.016*50 = 0.8, in fact only 8% of players saw their pluses improve by more than 1 as result of taking more offensive face-offs and 10% saw their minus hurt by less than -1. Lecavalier has the largest difference of 207 resulting in an estimated benefit to Lecavalier of around +3.3 and left Andreychuk to pick up some extra defensive zone face-offs (160 defensive vs. 46 offensive). So in terms of individuals this is not a huge issue. One team saw an extra 360 defensive zone face-offs (