Consensus Test Results
Consensus Prediction System
Is it true that you can combine the predictions of several handicappers to get even better wagering success results than the handicappers individually acheive? My test program says so, and I'll tell you how to do it yourself. The technique is very simple: you obtain prediction sets from multiple cappers, all of whom have success rates above 50%, then combine their prediction sets together using either the Consensus or the ANDing method (described later in this article). The result is a pick set with better success rate than the average of the sources' success rates. How is this possible?
I wrote a simple little Perl program that simulates this technique using a programmable number of cappers. The program simulates predictions made during one NFL season and tallies up the overall success rate acheived by a set of handicappers taken in Consensus. It then runs this simulation for 100 seasons and averages the results to minimize statistical variance. Finally, the test program sets the hypothetical capper success rates to 0%, or "idiot cappers", and increases this in 5% steps until it reaches 100%, or "genius cappers". Obviously our idiot cappers lose every bet and our genius cappers win every bet, but what is interesting is that a realistic set of cappers with, say, 55% success rate on average will combine to produce a final result that is higher than 55%. The following table is the program's output when the number of handicappers is set to 3.
capper consensus avg result (%) (%) _________________ 0.0 0.0 5.0 0.8 10.0 2.8 15.0 6.0 20.0 10.5 25.0 15.6 30.0 21.4 35.0 28.2 40.0 35.3 45.0 42.3 50.0 49.7 <-- threshold at 50% 55.0 57.8 <-- typical results here 60.0 64.5 65.0 72.2 70.0 78.3 75.0 84.3 80.0 89.7 85.0 93.9 90.0 97.1 95.0 99.2 100.0 100.0
I chose to study only 3 cappers because that is the number of sources that is readily available to everyone and anyone: my first program, my second program, and fading the public. You may, however, have additional sources such as your own predictions or predictions from the web. The more good sources you have the better your results will be. I can say that for two reasons: 1. it's obvious that better input generally produces better output, and 2. the test program says so. The shape of the curve made when the above table is plotted is a sigmoid, or "S" shape. It starts out hugging the y=0% line, increases exponentially, passes through the 50/50 point, then decays exponentially and ends up hugging the y=100% line. Interestingly, as you vary the number of handicappers you get a variation in the sharpness of the curve. The curve with one capper looks like a straight line while the curve with 20 or more cappers looks more like a step function. What does this mean to us?
It means that the more good handicappers we include in our system, the higher the success rate will be. In the table above we see that 3 55% cappers combine to produce about 58% success rate, but it gets even better for more cappers. If we have 7 55% cappers, the result is 61% and if we have a huge number, say 21 55% cappers, the result is 68%. You can see the full curves of these three examples in the plot at the upper left of this page (click to enlarge). This is because of the fact that more cappers drive the sweep to a step function centered at 50%.
I said that I would describe the Consensus and the ANDing methods, so here goes. Consensus is really just a voting system. You list all of your prediction sets in a text file or on a piece of paper if you prefer, and you make a list of all the games in the format: "Team1 0 at Team2 0", one game per line. Then you go through each prediction set and increment that zero number for each time a team is predicted. In the end you will probably have some games with no votes, some games with an equal number of votes for each team, and some games with a different number of votes for each team. The first two you ignore and for the third, you select the team that has the most number of votes. If that was confusing, just do this: hold a pretend voting session where you tally up the votes of the cappers for each game, then bet on the voted winners. That's the Consensus method.
The ANDing method, as I call it for lack of a better name, is similar except in this case you will bet on those teams that are selected by all of your handicapping sources. For this to work you need to have sources that predict many games each. My admittedly very unscientific results indicate that ANDing predictions produce higher success rates than Consensus predictions. Most of the time though you will have to rely on the Consensus method because the ANDing method will produce zero picks.
Why does this Consensus system work? One possible explanation is that each handicapping source must consider only a small subset of all of the vast amount of information available for predicting the game. Whether it's a computer or a human, each can only consider part of the information. When we combine multiple sources for a particular game, we are in a sense taking the set theory operation of "union" on their information sets. So we are incorporating more information in our selection process, which naturally produces better results. Also, for information that multiple cappers have considered there is more consideration in the totals. This makes sense because if more sources deemed said information to be important then it is probably worthy of enhanced consideraion.
If you would like to verify the consensus system for yourself, just download my consensus test program which is on the download page. You need to have the Perl programming language installed, then just run "perl Consensus_Test.PL" and examine the output, then the code. Please let me know if you find any discrepancies, thanks.
In conclusion, I have stumbled across an interesting wagering system that seems to have the magical property of producing better results than the average of its source information. It does this by harnessing the power of voting as applied to sports handicapping predictions. A simple simulation program suggests that this method works, and you may wish to paper test it yourself. As always, good luck to all and always wager responsibly.
Addendum
It is important to note that the consensus system works if your cappers are all above 50%, however be forewarned that if your cappers are below 50%, the reverse will happepn. In other words the consensus system is a double-edged sword, so be careful with it. Think of it like this: if you have one stooge, he's not too much trouble, maybe hits himself on the head once in a while but otherwise OK. Add another stooge and now you've got eye-poking, cheek slapping, etc. and we all know what happens when there are three stooges involved! So make sure your sources are winners not stooges and you'll do fine with the consensus system!
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