predictor_selection.txt

We want to predict the total number of goals scored during the match.
We thought it depends on the performances or playing styles of the teams involved,
so decided that some variables that may be relevant are the average number of goals home/away has scored as home/away. 
We extracted this data together with their variances and 
values for other team involved as well (e.g. average goals when away for home team), 
in order not to lose any data, in case they may be useful as well.
Of course, we calculated these metrics for the teams for only a fraction of the played matches(first 3000),
as these will be our training data. Actually, we may want to incorporate the variances in the model as well;
as their expectation is visibly the same as the average, some teams have lower or higher values. Our linear
model may subtract the variance multiplied by a factor from the average ant therefore decrease the impact of
the indicators with a higher variance, but we will analyze how significant this effect may be. 


Later, we thought the odds for the given matches may be direct indicators for probability distribution
of the total number of goals, so we analyzed that data as well. We found, however, that
there are many handicap types most of which are only seldom used. So we counted their frequencies and
determined which handicaps are the most essential and unsurprisingly found them to be (0:5)+0.5.


Then we Put these 20 numbers together for every match in a data table. But it needed further processing,
as we didn't have any odd data for first 190 matches and an over/under odd cannot be a linear indicator of
the expected number of matches. We would better transform the bet into another variable that may give a linear
relationship. Transforming it into the implied probability is a good starting point, but we still can't expect
the implication on outcome to be a linear relationship. What it tells about the expectation is that if we assume
a gaussian curve centered at the expectation the area of the curve on the left and right of the given value will be
the probabilites calculated from the odds. So if we calculate the z-value for these probabilites, we would find
what the odds actually imly about the expected number of goals: number of std-devs the expectation is above/below
this handicap. The fact that it does not give hints about the value of std-dev complicates things, but assuming it
is about the same for different handicaps suggests its expectation is also a linear function of the z-values we found.
Even if it is not precisely included in the model, it seems better than other -linear- alternatives.
Therefore we may expect a linear model of these z-values to be able to give a reasonable estimate.

While doing this processing we realized something amazing. The standard deviation for goal number estimate from the odds
was almost constant for all matches! So our linear model with z values without standard deviation may be very successful.
We demonstrated this in the same file we calculated z-values (z-analysis.r).