# 2011 Round 4 Results: Just One Kick Away From Profit

/Across the weekend's shortened Round, the Head-to-Head Fund landed 3 from 5 to drag itself almost back to break-even for the season, but the Line Fund bagged just 2 from 4, courtesy of a late surge by the Roos, which proved enough to see our Freo -34.5 line bet go down by a single goal. Reversing that result would have been sufficient for Investors to see black ink for the weekend taken as a whole.

Instead, the Head-to-Head Fund's 5.4% gain coupled with the Line Fund's 10.3% loss meant that Investor Portfolios fell by a further 2.5% this weekend, leaving them now trading at 91.4c. Not great, but not diabolical either.

Here's the detail:

Five favourites won this weekend, and another of them drew, giving BKB a score of 5.5, but with most tipsters also scoring 5.5, BKB still trails the leading tipsters. Combo_NN_2, on 22.5, leads BKB by two tips, and Bookie_9 and Combo_NN_1, on 21.5, lead BKB by one tip. The weekend's worst tipping performance was recorded by HSH, which scored only 3.5.

With nothing much to inspire me on the wagering front this weekend, I spent a little time thinking about additional performance measures for the Margin Predictors. MAPE is a perfectly acceptable measure but it is one dimensional. One Margin Predictor might generate a 30 MAPE by being very close fairly often and very wrong the rest of the time, while another might generate the same MAPE by being moderately close - that is, about 5 goals wrong - almost all of the time. Either behaviour might be preferable depending on the purpose for which you wanted to use a Margin Predictor's outputs.

There's another measure of performance commonly used in statistical modelling called the Root Mean Squared Error (or RMSE for short), which I think might provide additional insight into the Margin Predictors. A Predictor's RMSE can be decomposed into two equally-weighted elements: Bias and Variance. Bias, for our purposes, refers to the difference between the predicted margin for the Home team and the actual margin. A desirable Margin Predictor will, on average, neither predict Home teams to win or lose by too much or by too little. An average bias of 0 would be ideal and small biases are better than large ones.

Variance is a (squared) measure of how far away a Predictor's margins are from actual margins. Small variances are another sign of a desirable Margin Predictor.

The RMSE adds the squared bias to the variance and then takes the square root of the sum. You'll see that I've now included RMSE and its two components in the Margin Predictor section of the MAFL Tipster Dashboard.

Based on the MAPE measure (and, in fact, on RMSE), the Bookie_3 Predictor leads. It has an MAPE of 26.23 points per game, which is 1.31 points per game better than Combo_NN_2 on 27.54. Five tipsters have sub-30 MAPEs, and these five have opened up a 3.44 point gap to the remaining tipsters.

Despite its superior MAPE, Bookie_3 has not been the Predictor most often within 6 points of the actual margin. That claim belongs to the tipsters in positions 2 to 4 - Combo_NN_2, Combo_7 and Bookie_9 - all of which have been within one goal of the actual margin in 7 of 31 games. Nor indeed has Bookie_3 been the Predictor most often within 2 goals, that honour belonging to Combo_NN_2, which has achieved this in 36% of the games so far this season.

You'll notice that all the Margin Predictors have a positive bias. This means that they've all, on average, predicted better margins for Home teams than have actually occurred. Win_3 has been the most biased Predictor, on average predicting results for the Home team that have been 19 points better than what those teams have actually produced. Combo_NN_1 has been least biased, on average being within one goal of the actual Home team result.

The other component of RMSE, Variance (the square root of which I've shown here under the SD column), is where Bookie_3 shines, though Combo_NN_1 does well on this measure too, which is why it is 2nd to Bookie_3 on the overall RMSE measure. What's allowed other Predictors to produce superior MAPEs to Combo_NN_1's is the fact that the MAPE treats large prediction errors far more kindly than does RMSE. Effectively, the MAPE averages these errors whereas RMSE, through the Variance component, averages the square of these errors.

(For the graphs in the Margin Prediction section you'll see that I've graphed SDs relative to 37 and RMSE relative to 37. This is because, historically, a bookie-based margin predictor would have returned about these numbers, perhaps a little higher due to the small Home team bias in bookie margins over recent seasons.)

Most of the Margin Predictors would have fared poorly on line betting this week and so have been dragged back towards and, in some cases, below, the chance 50% level. Only Combo_NN_2, ProPred_7 and ProPred_3 retain a respectable lead over coin-tossing.

The Probability Scores of all head-to-head Probability Predictors remain defiantly positive, reflecting better than chance probability forecasting. There's been no change in the ordering of these tipsters, however.

Lastly, the Line Fund's probability predictions remain poor.