# 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:

• 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

## 2 Answers

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 few simple points not directly addressing your question about offsets:

• 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.
• Hello Jeromy! What you descirbe is absolutely correct. But there is no way to create a model that measures goals/games. So I'm forced to the model above (goals as the dependent and games as the independant variable). I know that games is correlated with things like skill and that I've to explore this problem (omitted variables problem and Endogenity). But at the moment I'm wondering which of the two models above should be used! – MarkDollar Jun 6 '11 at 8:24