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?


*

*goals=games+striker , or

*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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*See this previous question discussing when to use offsets in Poisson regression in general.
 A: 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
A: A few simple points not directly addressing your question about offsets:


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*I'd have a look at whether number of games is correlated with mean goals scored. In many elite goal scoring sports that I can think of (e.g., soccer, Australian rules football, etc.) I would predict that longevity of a career is related to the success of a career. And at least for players in goal scoring roles, success is related to number of goals scored.
If this is true, then number of games would capture two effects. One would relate to the mere fact that more games played means more opportunities to score goals; and the other would capture skill-related effects.
You could examine the relationship between number of games and mean goals scored (e.g., goals / number of games) to explore this. I think this has substantive implications for any modelling that you do.

*My instincts are to convert the dependent variable into mean goals per game. I realise that you would have more precise measurement of a player's skill for those who played more games, so maybe that would be an issue. Depending on the precision in your model that you desire, and the resulting distribution of player means, you might be able to rely on standard linear modelling techniques. But perhaps this is a bit too applied for your purposes, and perhaps you have reasons for wanting to model total goals scored.

