Sunday, August 10, 2014

Averaging Numbers May Lead to False Results

When people try to predict football games, they often fall into a trap of their own making. That trap is called averaging. When two numbers are averaged together, they sometimes cause false results. When two teams are playing, many handicappers try to predict the final score so they can make an informed decision on which team to bet on. To arrive at a score, they average the 2 teams together, comparing offense to the defense.  

Averaging two numbers when the numbers are on different sides of average works okay. The trouble happens when both numbers are on the same side of average. That may be a hard concept to visualize, but after a couple examples it should become clear.

The average number of points scored by a team in the NFL during the 2013 NFL season was 23.4, which can be rounded down to 23. If team A comes into the game scoring on average 34 points a game and team B comes in allowing 10 points a game, averaging the totals together gives a result of 22 points scored for team A. (34 + 10 = 44, divided by 2 = 22.) One team scores above the league average of 23 and the other team allows below the league average of 23, so that works well and gives a good result.  

If team C comes in scoring 34 points a game and team D comes in allowing 28 points a game, averaging the totals together would give a result of team C scoring 31 points, which is less than what they normally score. That just doesn’t make sense. Team C comes into the game with a really good offense that scores well above average, and when faced with a poor defense that allows more than average, why would they be predicted to score less than they normally do?

The problem is, both teams are on the same side of the league average, which gives false results. It makes good teams seem worse and bad teams seem better. The fix is simple enough. Add the two scores together and subtract the NFL average to get a good prediction.

Using teams C and D, the better number is calculated like this:
34 + 28 = 62
 62 - 23 (the league average) = 39

Where averaging gave a score of 31 for team C, subtracting the league average gives a score of 39, a huge difference of 8 points. To obtain consistently better results, don’t average numbers together to make predictions in the NFL.

Here’s a full game mock up to illustrate the difference. These numbers are just an example, and we’ll use the Seahawks and Lions for the teams.

The Seahawks come in with a season average game score of 31-24. The Lions come in with a season average of 20-27. When using averaging, the result is a predicted score of the Seahawks winning 29-22. When using the recommended method, the predicted score becomes Seahawks winning by 35-21. Using the average, the Seahawks are predicted to win the game by 7 points. Using the correct method I’ve laid out, the Seahawks are predicated to win by 14 points.  If the Seahawks were a 10-point favorite, a handicapper could be fooled into thinking the Lions +10 was a good bet if he averaged the numbers. Using the correct method, the Seahawks -10 is the clear choice.

Averaging when comparing teams is a very common mistake and also one of the costliest.

Be aware and beware!

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