### Goal difference vs. Points – A simple statistical analysis

*by MLHS’ Great Dane (written before the weekend games)*

There has been some talk on the site lately as to whether or not the playoffs remain in reach for the Maple Leafs despite a less than mediocre record a quarter of the way through the season, a subject Derek Harmsworth broached in his blog “At the Quarter Pole, Leafs Improved, But Is It Enough?” Statistically speaking, is 20, 21 or 24 points at the quarter pole enough to make the playoffs?

What follows is a small regression analysis of goal difference vs. points based on the records of the 30 teams in the NHL before American Thanksgiving.

The blue dots are the actual observations at the quarter pole, while the Red Line is the estimated relationship between goals for and goals against (goal difference) and points earned.

For this analysis, a valid point of criticism is the fact that points per game would be more relevant to use. However, given the uncertainty in any such analysis, I do not believe that it will change the general conclusions.

The statistical results are shown in the following tables:

For those interested in statistical analysis, it is easy to verify that the regression explain the data very well with a R Square of 0.7354. The t-stats show that all variables are significant as well as the whole regression.

In laymans terms, what does the regression tell us?

First, at the Quarter pole a team with zero goals difference should have approx 23.5 point, which would equal 94 points for the entire season. If a team has a positive goal difference of one, then they should have 6.78 point more.

To illustrate this, Edmonton Oilers has a negative goals difference of 1.5, so they should have 1.5 * 6.78 points less than 23.5. That is 10 points less than 23.5 which is approx. 14 point. That is the actual points total the Oilers had before Thanksgiving.

At the other end of the standings, we have the Capitals with 32 points. Their goal difference is only +0.47, which given the regression should give around 27 points at the quarter pole. That is a difference of 5 points, which shows that when talking about statistical analysis one should never talk about an exact value but an interval.

Turning to our beloved Leafs, I will of course disregard all the comments above.

The Maple Leafs were at the Quarter pole running a goal difference of -0.3 and had 19 points. The model tells us that they should have 21 points, so they are behind the estimate of the model. For the entire season, the model extrapolates to around 84 points, which consensus would say is not enough to make the playoffs.

My conclusion is that the Leafs will end the season with 10 point less than required and therefore need to elevate the goal difference above zero, i.e. an improvement of at least 0.3.

GA/G is this season is down to 2.65 and unless Gustavson suddenly is even better than Price and Thomas combined then the improvement needs to come from goals for.

Given the uncertainty, I would estimate that the Leafs need to improve with 0.5 goals for per game to be on the safe side. Such an improvement would have given almost 3.5 points more that the Quarter pole and 14 points for the entire season. Enough to make the playoffs.

So Burke has one of the following assignments:

- Pray the Leafs with the current roster find 0.5 goals more per game on average

or

- bring one or two players in that will score 40 goals more per season than the players that leave.

Finding players with 40 goals more per season than the players that a leaving seem very difficult. We are talking a center of Eric Staal / Brad Richard caliber combined with a LW a la Semin / Parise.

So will the Leafs make the playoff? Of course they can, but statistically is seems difficult, if they do not start scoring significantly more goals per game than they are now.

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