Raw values or z-scores when adjusting stats

[podonne]

I've been trying to create a general way of calculating an adjusted value for NHL statistics by taking into account the league average and the opponents estimated average.

It would basically work like this, say, for goals scored (G):

G_adjusted = G_Actual - (OppAllowed_G - LeagueAllowed_G)
 
where:
G_Actual = The actual number of goals scored in the game
OppAllowed_G = The average number of goals allowed by (scored against) the opponent that season
LeagueAllowed_G = The average number of goals allowed by (scored against) the entire league that season

This should take a statistic and adjust it so that it represents what the team would have scored if they were playing a league-average team instead of that opponent.

My question, is the equation above correct? Or should I convert the G_Actual and OppAllowed_G to z-scores using the mean and standard deviation of LeagueAllowed_G, then convert back to get an adjusted value?

Does anyone have a term for what I'm doing here? I assume it's been done before.

Thanks,
podonne

[podonne]

Just to be clear, I'm trying to calculate an adjusted team stat, like goals scored by Chicago. In the equation above, G_Actual should be the actual number of goals scored by that team.

Its not clear in my text that in G_Actual, I'm talking about the team's goals scored, not the total number of goals scored by all teams.

[pedro803]

Try them both and compare the results to see which seems to give you results that look like you would expect. But off the top of my head I am thinking what you have would be better than z-scores because z-scores are not meaningful in terms of goals scored. I think z-score is just an overlay to the normal distribution -- so that if results are normally distributed z-score gives you the odds of a given result falling within a given range. So I am thinking your raw stat should have more meaning in this computational stage and the z-score might be of more use later on down the line when you are trying to analyze the stat.

[buby74]

Based on the log5 and pythag formulas I prefer multiplication rather than addition for this type of analysis so to find out the normalised scoring the goals scored per game of a team and divide it by the goals allowed average of the opponents then multiply by the league average so a team scoring 4 per game against opponents allowing 3 per game in a 2 goal per game league would be predicted to score 2.6667 against average opponents

[TomG]

conquering risk actually explains this pretty well and provides examples

[podonne]

Based on the log5 and pythag formulas I prefer multiplication rather than addition for this type of analysis so to find out the normalised scoring the goals scored per game of a team and divide it by the goals allowed average of the opponents then multiply by the league average so a team scoring 4 per game against opponents allowing 3 per game in a 2 goal per game league would be predicted to score 2.6667 against average opponents

I suppose its a matter of what more closley approximates the result. Have you done tests on this vs the arithmatic approach?