# Standardizing Performance (sports-related)

#### DantonD

##### New Member
Hi everyone,

I coach a hockey team and we collect a lot of data on our performance. While I'm reasonably numerate, my statistics skills are limited to pretty basic things. So here's my problem.

We collect data each game which feeds into a process measure that provides insight into how our team played in a game (independent of the outcome of that game). I'd like to be able to look at that measure over time (i.e., as the season progresses), but looking at the raw measure would be useless because we're playing against opponents of variable quality from one game to the next. We don't collect this process measure for our opponents, so I'd like to use the opponent's winning percentage (publicly available) as a way to adjust the process measure for each game to better compare apples to apples.

I'm sure this is very basic for a lot of you. I'm just not sure how to do it. Any suggestions?

#### staassis

##### Active Member
The suitable methods depend on how much data you've got. At the very least, you can look into

1) logistic regression for the probability of victory in each game and
2) Poisson regression and negative binomial regression for the points scored in each game.

However, much more is possible in modeling the dynamics over time if the sample size is substantial... Various measures of opponent's strength should act as predictors in the discussed models.

#### DantonD

##### New Member
I guess I'm not so much interested in predicting success as I am in just understanding my own team's process (independent of whether we win or not).

My process measure is shot attempt percentage (the number of shots we attempt expressed as a percentage of the total number of shot attempts in the game). So I'd like to look at how we do on this measure next game (say) and compare that to how we did in our first few games of the season (say). But because we play different teams each night, there would be noise - if we play a bad team, our shot attempt share is going to be higher than if we play a good team, even if our process isn't really as good. So I'd like to control for the quality of the opponent by adjusting the process measure in some way, based on the opponent's winning percentage.

#### staassis

##### Active Member
Yes, and to know how to adjust for the quality of opponent you need a model.

#### GretaGarbo

##### Human
You could search for "Elo rating" that has been used in chess but also in football. You can see how to convert an Elo rating difference to probability to win for teams with rating like 1500 or 2000. You will need to go back a few seasons to give every team an Elo rating. The model is essentially build on a logistic model.

Then when you "know" the skill difference (or at least have an estimate for it) you can use that difference in a model for shot attempts. So if your team is is rated 1800 and the other team rated 1600 you have a difference of 200. I would use that as an explanatory variable in a Poisson regression model for shot attempts. So the number of shots (assumed to be Poisson distributed) is the dependent variable and the rating difference is the explanatory variable ("independent variable"). So if the expected number of shot attempts for the match is 21 then the expected number per periods is seven. If the team has just made 4 shots in the first period, then they have under performed. (But there is a lot of randomness in the Poisson distribution.) (I assumed that you are talking about ice-hockey and not the Indian land-hockey.)

But the beauty with sports like football and hockey is that it is much more dramatic that tossing a dice. Once a team has scored the other team need to to more and more desperate actions. So a goal can change the probability of an event. But I guess that the above can be a start.