The simple but effective system used by 'Mabel' to rate teams and make predictions has, for convenience, been named 'rateform'. However it has its origins in Professor Elo's 'The Rating of Chessplayers', which in turn was adapted for soccer by Tony Drapkin and Richard Forsyth, and described within their excellent book 'The Punter's Revenge'. There are further details in the book 'Football Fortunes', from which the following is an extract.
The basic idea is that as football matches are played over a season individual points totals are updated for each team depending upon match results. Rateform points totals carry forward from one season to the next. These points are used as the basis for match predictions.
Rateform points differ from league division points in a number of ways,
which have severe limitations as a means of rating teams. Not least of these
differences is of course that, at the start of each new football season,
football teams have zero league points!
It is also clear that, in their calculation, league division points
make effective use of only one factor, that is whether a game is won, lost
or drawn. Other important variables, such as the comparative quality of the
opposing teams, or whether results are achieved at home or away, do not figure
in league points allocation. Neither can league points be satisfactorily
used in the prediction of 'cup' games, which frequently involve teams from
different Leagues or divisions.
So the 'rateform' approach has several
advantages.
These are the main features of the 'rateform' method.....
| 1 | Each team in a division has a 'points total' which represents current form. |
| 2 | The 'average' number of points for the teams within a division remains constant at 1000. |
| 3 | For each match played the home and away teams contribute a percentage of their points to a kitty. |
| 4 | The percentage contribution of the home team is greater than that of the away team, and so reflects home advantage. |
| 5 | The winning team takes the complete points kitty. |
| 6 | Teams which draw share the kitty. |
The precise computations are represented by the pseudocode in figure 1 below. Typically the home and away teams might contribute, respectively, 7% and 5% ( variables x and y ) to the kitty. The difference in these percentages represents the advantage to the home team of playing on its own ground, so if the away team overcomes this disadvantage it gains extra points.
Pseudocode to update 'rateform' points
totals - figure 1
CALCULATING 'RATEFORM' POINTS (1)
The HOME team begins with a points total of htot
The AWAY team begins with a points total of atot
For each match played the home team contributes x%
of its points and the away team contributes y%
( x is greater than y ).
The actual points contributions of the home and
away teams are represented by hgives and agives
respectively.
hgives = x% of htot
agives = y% of atot
kitty = hgives + agives
The number of points each team receives from the
kitty is represented by hgets and agets.
If a home win then
hgets = kitty agets = 0
If an away win then
hgets = 0 agets = kitty
If drawn game then
hgets = kitty / 2 ( rounded down )
agets = kitty - hgets
( if kitty is an odd number the away team
gets the extra point )
The nett gain or loss to each team is hnett
and anett.
hnett = hgets minus hgives
anett = agets minus agives
Finally new points totals are calculated for
each team.
htot = htot plus hnett atot = atot plus anett
|
Some specific examples will help demonstrate how the system operates.
Consider three football teams starting out with the points totals shown in figure 2.
Result to points conversion - figure 2
CALCULATING 'RATEFORM' POINTS (2)
Starting points ....
Blackburn 1232 Each to play Oldham (478 points)
Man Utd 1804
West Ham 486
Match 1. Blackburn v Oldham - result HOME win
Blackburn ( home ) Oldham ( away )
1232 pts X 0.07 = 86 478 pts X 0.05 = 24
Kitty has 110 points
From kitty win gives 110 From kitty loss gives 0
Nett gain +24 Nett Loss -24
Match 2. Oldham v West Ham - result AWAY win
Oldham ( home ) West Ham ( away )
478 pts X 0.07 = 33 486 pts X 0.05 = 24
Kitty has 57 points
From kitty, loss gives 0 From kitty win gives 57
Nett Loss -33 Nett Gain +33
Match 3. Man Utd v Oldham - result DRAWN game
Man Utd ( home ) Oldham ( away )
1804 pts X 0.07 = 126 478 pts X 0.05 = 24
Kitty has 150 points
From kitty, draw 75 From kitty draw gives 75
Nett Loss -51 Nett Gain +51
Final points ....
Blackburn 1256 Oldham 472
Man Utd 1753
West Ham 519
|
Each of the teams play Oldham and match results are as indicated. In
match 1 Blackburn are playing at home. Blackburn and Oldham
contribute respectively 7% and 5% of their points totals to the kitty. The
contribution of Blackburn being more because, not only have they the larger
starting points total, they are also the team playing on their home ground.
The kitty now contains 110 points. Blackburn win the match and take all of
the kitty. Oldham receive no points. The nett gain to Blackburn is +24 points.
This is the value of the kitty less the initial contribution. Oldham have
sustained a nett loss of -24 points. You will see that the points average
of 1000 is undisturbed.
In the first match the overall gain to Blackburn has been quite small. They
have won at home against poor opposition. In match 2, Oldham,
now the home team, continue to do badly and are once again defeated. In this
case both teams began with a low points total, but by winning away from home
West Ham have gained extra points.
Finally, match 3 shows one possible consequence of a draw.
Manchester United have drawn at home against Oldham, but have actually lost
points. It was clearly a game they should have won ! Oldham, on the other
hand, have greatly benefited from drawing away from home against top
opposition.
So, using this system, the final points allocation is determined by the
result, the relative quality of the opposing teams, and whether wins or draws
are secured at home or away. The individual team ratings (at least for teams
which remain in the same division) are carried forward from one season to
the next. How quickly points change over the season depends upon the size
of the contributions to the kitty. The lower the percentage contribution
the more 'long term' form is reflected.
There is no doubt that the winning potential of football teams varies
considerably from one season to another, the form of one year being a poor
guide to that of the next. For this reason, as far as relegated and promoted
teams are concerned, there seems little use in retaining the previous season's
points totals when they move to a new division. It is also clear that, as
the years pass, there is insufficient interaction between teams from different
divisions to justify this. This leads to the conclusion that it is probably
best to allocate an average set of points, approximately 1000, to newly promoted or
relegated teams. Such teams are then placed mid-way in their new division.
So, bearing such factors in mind, and the fact that the modern trend is for
considerable changes in team personnel from one season to the next, there is
need for some re-distribution of points at the start of each new season. In
particular certain teams, such as Rangers and Celtic in the Scottish Premier,
invariably amass a vast number of 'rateform' points by the close of the season,
some of which must be re-distributed to ensure the system remains viable.
Up to now consideration has been given to the calculation of individual 'rateform' points. The next step is to use these values to predict results. It will probably come as no surprise that points difference, that is home team points minus away team points, is the basic forecasting unit used in the 'rateform' system. (The use of a points differential, the points 'gap' between teams, is a popular approach in many forecasting systems). Figure 3 shows some 'rateform' predictions.
Examples of 'rateform' predictions - figure 3 'RATEFORM' PREDICTIONS Points totals .... Blackburn 1256 Man United 1753 West Ham 519 Oldham 472 Match 1. Man U v Blackburn 1753 minus 1256 = Points Difference of +497 .... a HOME is forecast Match 2. Oldham v Blackburn 472 minus 1256 = Points Difference of -784 ..... an AWAY is forecast Match 3. West Ham v Oldham 519 minus 472 = Points Difference of +47 ........ a DRAW is forecast ( no adjustment has been made for home advantage or division difference ) |
It can be seen that the size of the points difference determines the
prediction category into which each match falls. For example it might be
decided that any differences of 100 or more should be classified as a potential
home win, and of -100 or less an away win. Any intermediate values to be
draw predictions. As it stands this method does not consider home team advantage,
which is of course the cause of the larger proportion of home wins compared
to aways or draws. The home advantage might be judged to be the equivalent
of a bonus of 100 points to the team playing on its own ground.
In practice another adjustment is necessary. Where cup matches are being
played in which the opposing teams come from different divisions. This can
be done by allocating varying points bonuses to teams depending upon the
league or division in which they play.
In each of the weekend matches analysed by 'Mabel' you will see the rateform points held by opposing teams. The points difference is shown after the adjustments for league division differences and home advantage. The points difference determines the forecast. Of course the rateform prediction is provided for guidance only and no claims are made regarding its profitability!