# Whether to use an offset in a Poisson regression when predicting total career goals scored by hockey players

I've got a question concerning wheter or not to use an offset. Assume a very easy model, where you want to describe the (overall)number of goals in hockey. So you have goals, number of games played and a dummy variable "striker" which is equal to 1 if the player is a striker and 0 otherwise. So which of the following models is correctly specified?

1. goals=games+striker , or

2. goals=offset(games)+striker

Again, the goals are overall goals and the number of games are overall games for a single player. For example there could be a player picked up who has 50 goals in 100 games and another player who has 20 goals in 50 games and so on.

What am I supposed to do when I'd like to estimate the number of goals? Is it really necessary to use an offset here?

References:

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What is your dependent variable? Is it total number of goals in a career to date for a specific player? Also, is there a reason why you don't want to predict mean goals per game? –  Jeromy Anglim Jun 5 '11 at 14:37
Yes it is total number of goals! No I don't have the data for every game. I just have the overall data. –  MarkDollar Jun 5 '11 at 14:43
The dependent variable is (number of) goals. (See equations above) –  MarkDollar Jun 5 '11 at 14:45
I've tweaked the title a little bit so that it is not a duplicate of the previous question. Feel free to modify if I've misconstrued. –  Jeromy Anglim Jun 5 '11 at 14:58
Thats fine! Thanks –  MarkDollar Jun 5 '11 at 15:01

An offset model is modeling goals per game, as one can see here:

log(goals/games) = a+bx


is equivalent to

log(goals) -log(games) = a+bx


is equivalent to

log(goals)= a+bx +log(games)   <-this is an offset model, assumes coef on the last term =1


See slide 35 here: http://www.ed.uiuc.edu/courses/EdPsy490AT/lectures/4glm3-ha-online.pdf

If you think a+bx is related to the log ratio of goals to games (the rate), use an offset. If you think there is a more complicated game effect, perhaps from accumulating experience, do not. For more discussion, see this: http://ezinearticles.com/?The-Exposure-and-Offset-Variables-in-Poisson-Regression-Models&id=2155811

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