How important are goals and points in the 2010 MLS season?

In my last post I introduced the following three relationships via linear regression from MLS league data taken from the 2005-2009 seasons.

• Finish position vs. points
• Finish position vs. goal differential
• Points vs. goal differential

Given those relationships, it might be logical to ask,

• How much does an incremental point improve a team's finish position?
• How much does an incremental goal improve a team's finish position or points?

The answer, it turns out, depends on where that team is starting from when adding that incremental point or goal differential.

Finish position vs. goal differential and points

In my last post I mentioned that finish position was normalized using the following equation

-ln[p/(17 -p)]

This means that the resulting linear regression produces a non linear result between p and the regressors - either goal differential or points. This relationship produces a bell shaped curve when looking at incremental benefits, suggesting that their are huge payoffs in the middle and diminishing returns at either end of the data. See Figure 1, which shows a plot of the incremental finishing position dependent upon the starting goal differential or points.

Figure 1: Improvement in table position vs. incremental goal or point dependent upon starting goal or point total

Figure 1 shows the distribution of data across the historical goal differential and point ranges, bounded by the minimum and maximum totals for the 2005 through 2009 seasons. This phenomena makes sense - a team only needs to score so many goals or points to secure their spot towards the top of the table. It's the middle where individual goals or points separate teams table position.

If you're interested in averages in this non-linear behavior, they are:

• 0.25 table position improvement for each incremental goal
• 0.35 table position improvement for each incremental point

Points vs. goal differential

The relationship between incremental goals and incremental points is straightforward as no transformations were required on the data. In this case, each incremental goal leads to a 0.7 point increase for the team.

Conclusions

Going back to the original inspiration for all this work - the Sounders three ties due to extra time goals - leads us to some general conclusions:

• Each tie match costs a team a potential average table improvement of 0.7 positions due to the loss of the 2 points associated with a win.
• Each tie match costs a team a minimum potential average table improvement of 0.25 positions due to the loss of at least one goal in the goal differential attribute.
• Each tie match costs a team an minimum potential average loss of 0.7 points from their season point total.

Keep in mind that these relationships are NOT additive. They are simply different ways of measuring the impact of different metrics on the same variable data set with varying accuracy. They do, however, give us an idea of how costly ties can be in MLS.