To be better than bookmakers! What does it mean?

I want to predict game results better than bookmakers do. Good goal but how good my model of the game should be? Lets use a statistical information from THE SUNSHINE FORECAST and try to determine the precision of bookies. In files, which one can download from Sunshine forecast web-site he can find two predictions: for odds and for total. Lets start with first.

Here I define line as a number which needs to be subtract from home team score to give a fifty-fifty chances for its win. Only regular season games of NFL seasons 2002-11 are included.

On this figure we can see two important things:

• (trivial) Bookmakers like teams, which plays at home. The mean value of distribution around 2.5. If there would be no field dependence this value should be 0. So we can likely consider it as an average increment for teams which play at home.
• The distribution is not normal, as I expected. This is probably connected with procedure of line preparation.

Lets produce a two-dimensional plot in order to see how precise bookie's predictions are. On Y-axis you can see results of game corrected by line.

There are no visible correlation between Line and Result. This as well as a fact that mean value for corrected result is close to zero tells us that model used by bookmakers works good and allows them to make a profit from any of your bet. The root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity, which is difference in score corrected by line in our case. This variation is quite large 13.5 a bit less than two touchdowns. Now lets check is there any dependency for RMS from Line. To see it I sliced this 2D-figure on X-axis and make a projection to Y-axis.

One can see that RMS has almost no dependence from line! On last panel full statistics is shown. It is perfectly described by normal distribution.

Summary:
It is not easy to win against bookmakers. To do it one should find such types of games where mean value of results corrected by line significantly differs from zero. It is also challenge to produce a better game model which have RMS smaller than 13.5.

In next post I will try to explain how bookies produce their lines.

Yes, I understand that my English is very bad :-) I will try to improve it in future.