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What are Rating Systems?

Defining a probability of one particular outcome of a sporting event is exceptionally complex because there are so many key influencing factors that determine the end result, none of which can be determined exactly. For sports prediction a central approach to determining such probabilities involves analysing past records. Some punters prefer to study such information qualitatively, highlighting key results that he thinks will have a bearing on a future one. Others prefer to employ a more quantitative or numerical approach to such historical analysis, by means of what have commonly become known as ratings systems.

A rating system merely provides a quantitative measure of the superiority of one player or team over their opposition in a sporting contest. Such superiority is determined by analysing and comparing one or more aspects of past performance for each of the sides. Paul Steele, in his book Profitable Football Betting, describes 15 different forecasting models, or rating systems, for football match prediction. The rating systems differ in the way side superiority is calculated, but basically each method calculates a points difference for a forthcoming football match, by subtracting a points rating for the away side from a points rating for the home side. The home and away team points ratings are determined through a quantitative analysis of past performance involving different aspects of a team's strength. The simplest of these uses either league points, league positions or goals conceded and scored, whilst more complex ratings might be based on elaborate match statistics including shots on goal, corners, and perhaps even possession if such data are available.

For many simple rating systems, no account is made of the quality of the opposition. A recent form goal-difference football rating system, for example, simply looks at the number of goals scored and conceded by the two teams for a specified number of matches preceding the contest under examination. One goal is always worth one goal, irrespective of whether it is scored away against Manchester United or at home against Carlisle. Power Ratings overcome this problem by proportioning the worth of each goal scored to the strength of the opposition against whom it was scored. Similarly, goals conceded against stronger opposition count for less in the ratings computation than those conceded against weaker sides. Bolton Wanderers, for example, may have a recent record of 1 win, 3 losses and a draw, scoring 5 goals and conceding 8. A rather unimpressive recent form, one imagines, yet if those games had been against Liverpool, Manchester United, Arsenal, Chelsea and Newcastle, one might naturally expect them to perform better against West Ham in their next match than they otherwise would, had those games been against Charlton, Blackburn, Manchester City, Birmingham and West Bromwich Albion.

A useful and popular rating system, at least with some punters, is the Rateform. Like Power Ratings, it takes into account the quality of the opposition each side has played in games preceding the latest one. This system has its origins in Professor Elo's book The Rating of Chessplayers, which in turn was adapted for UK football by Tony Drapkin and Richard Forsyth in their book The Punter's Revenge. As football matches are played over a season, ratings are updated for each team. Following Bill Hunter in his book Football Fortunes, the essential features of Rateform are that:

  1. each team has a points total or rating which represents its current playing form;
  2. the average number of points for individual teams remains constant at 1,000;
  3. for each match the home and away teams contribute points to a kitty;
  4. the winning team takes the complete points kitty; and that
  5. teams that draw share the kitty.

Typically the home and away teams contribute, respectively, 7% and 5% of their points total 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. For each match played, the points allocation is determined by the result. As for other ratings systems, the home team rating minus the away team rating provides a "points difference" which may be used to predict the outcome of matches.

Manchester United, with 2,165 Rateform points, might play Birmingham City, with 723 points, at Old Trafford. The points difference for this match is +1,442 points, the size of which can provide a probabilistic estimate of the likelihood of a home win, draw or away win. How this association is made is described later in the chapter, although for now the reader will intuitively appreciate that, with such superiority, Manchester United should be expected to win the game. If they do so, they will collect the kitty of 188 points, 7% multiplied by 2,165 (152 points) plus 5% multiplied by 723 (36 points). If, on the other hand, Birmingham win the game, they will collect the 188 points. If the game is drawn, they will each receive back 94 points.

There is an important point to recognise from this redistribution of points. Where a weaker side overcomes stronger opposition, their new rating will receive a proportionally greater increase, particularly if achieved away from home. Conversely, where strong opposition defeats a weak side, more especially at home, their rating will receive relatively little benefit. Manchester United's rating increases by only 36 points with a victory (188 points minus 152 points). Birmingham's rating, by contrast, increases by 152 points after a win (188 points minus 36 points). This is because Manchester United have so much more to lose than Birmingham City, since United at Old Trafford are expected to win this game. If drawn, Birmingham will still collect 58 points overall (94 points minus 36 points), whilst United will lose 58 points (94 points minus 152 points). An away draw is proportionally better than a home draw, particularly if the home side is rated more strongly. In this way, a team's rating at any point in the season provides a reflection not just of the number of games it has won, drawn or lost, but also of the strength of the opposition it has beaten, drawn with or lost to. Ratings may also be carried forward from one season to the next, allowing forecasts to be made at the beginning of each season, a feature not available in many recent form rating systems.