Poisson regression and soccer scores

I have a data set of soccer matches, their respective results and the respective pre-game odds. I would like to study **a simple **strategy based on historical information.

I would like create a simple model that would predict the goals scored by a team from the implied probability of the odds. So I would like to carry out poisson / negative binomial regression to estimate the mean number of goals scored by a team in a match with given bookmaker odds for various outcomes. Then I could plug these lambdas into poisson probability functions to estimate (roughly) probabilities of certain scores.

Now, many authors have done similar modelling but lacking proper knowledge of stats, I do not fully understand how the regressions should be carried out.

E.g. D. Dyte and S. R. Clarke (2000) study whether FIFA rankings explain goals scored by estimating a model

ln(m) = a + bTR + cOR +v

where m is the expected number of goals scored, TR is the team's FIFA ranking, OR is the opponents FIFA ranking and v is a parameter that measures the venue (home, away, neutral) *.

What I am actually wondering then is this:

Isn't it so that the explanatory variables in poisson regression model the the mean of the response variable? Therefore I cannot just regress the goals scored by e.g. the home team to the implied probability of the home team. What should be my dependent variable?

e.g.

ln(m) = a + bPR

where m is the expected number of goals scored and PR is the implied probability of the team. Does anyone have a clue **what is 'the expected number of goals scored' **because it cannot be the actual number goals scored? Or is the equation just an expression and you actually regress the realized scores with the explanatory variables?

Sorry about a confusing question and thanks for everyone who's willing to help!

* D. Dyte and S. R. Clarke (2000). A ratings based Poisson model for World Cup soccer simulation. Journal of the Operational Research Society. Vol. 51., pp. 993-998.