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Chi Squares, robustness and the long term.


AJ

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This is a thread about Chi-Square and Goodness fits, but it’s not just about that. This thread is about my education as a sports investor, I no longer consider what I do as gambling. I did not originally create the vast majority of what you’ll see on this thread, it’s merely my interpretation of what I’ve learned. <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Its 4 years ago this week since I stumbled across the punterslounge during a boring afternoon when I really ought to have been creating software to help drive the new economy. I found a group of people that had great knowledge and more importantly were working together to make a long-term profit from the bookie. I was intrigued surely that was impossible I thought, but no it could be done.

I’ve attached an Excel file to this post; it contains my record for the season to date. I didn’t create this file Datapunter did. It’s the best record-keeping file I’ve found so far, so I’ve used it. The calculations have mostly come from Joe, who rarely posts on the Pl these days. His excellent book, “Fixed Odds Sports Betting, by Joseph Buchdahl” is published by High Stakes, and should be required reading for anyone with a interest in long term steady profits, I was also influenced in the early days by OddsAgainst, who left the PL around 2 years ago. My appreciation goes out to all three of you guys, you’ve all helped in my education as a sports investor. :clap :clap

For the record, so far this season I’ve placed 390 bets. I’ve had 280 winners, average odds of 1.508. This strike rate gives me a yield of 3.795%. I have a current profit of 19.22 units.

I started the season with 10pts, with 10% even stake bets. This is aggressive, but as I operate in low stakes I felt it was an acceptable risk, most others would go for 5%. I aimed to double my stake when I double my bank; I did this around bet 270. I’ll do so again when I hit 40 units.

For the purposes if chi square, and ease of calculation, I’ve added 2 extra tabs to this file, one with all bets changed to level stakes, and one that shows my calculations. In order to demonstrate “robustness”, I think we need even stakes.

I have also presumed I’m facing a bookie over round of 112%, all of the following bets were placed with Bet365. This is just due to laziness on my part, as my bank roll increases I will need extra accounts, both to ensure I get the best price, and to avoid me hitting stake limits.

The following was posted by Joe, on the PuntersLounge on the 29th of April 2002, and what follows is the basis of my calculations

  • In cell A1 enter the number of winners, in cell B1 enter the number of losers. 2. Invert each bookies odds for each bet to get the bookies percentage estimation and divide this by 1.12 (roughly the typical overround). This gives you the fair estimation of the team you picked winning assuming the bookies have not made a pricing error. Then calculate the average fair estimation for all your bets. 3. Multiply the average fair estimation (which should be a fraction of 1) by the total number of bets. This gives you your expected number of winners assuming that the bookies have it right and you were no good at tipping. i.e. it's what you'd expect to achieve betting randomly. Subtract this number from the number of bets to get expected losers. 4. Put expected winners number in cell A2 and expected losers number in cell B2. 5. In another cell, type =CHITEST(A1:B1,A2:B2). This will give you a figure as a fraction of 1. 1 means 100% probability that the record is down to luck (which you get if your record was EXACTLY the same as the expected). 0 means 0% chance the record is down to chance. Now, you'll never get to 0, but the lower the number, the more likely your record is down to some other factor other than chance, hopefully you believe your skill. A good statistical measure is to break below at least 0.05 (5% chance record is due to luck) and even better, 0.01 (1% chance). If you what to make the output user friendly like I've done on F-D, subtract the result from 1 and convert to a % figure. This gives you the probability that the record is NOT due to random luck. Now this method assumes a few things: a) all your bets are singles with overrounds of 1.12. If you place doubles or higher this is obviously not the case. b) You're taking average odds available, not the best. c) Fixed sized stakes, so each bet is equally weighted. Now, it's highly unlikely that you'll be following these three assumptions so you can assume that the robustness figure you calculate will most likely be an overestimation of your skill level. However, the test does provide a working method to get a feel for how you're doing and when you can start to convince yourself that you're doing something right. To ensure that I consider the effects of overestimation, my rule of thumb would be to get below 0.01 (>99%).

As Joe stated above, the results should be between 0 & 1, with 1 suggesting that you’re figures are down to luck, and 0 being zero percent chance that the results are random. He thinks you can get a 99% certainty with a result below 0.01. My result of 0.000164355, implies there is a 99.99% certainty that my results are down to skill, and that I should be able to maintain these results in the medium to longer term. It tells me that I’m on the correct track and am quite good at this. Hope this is helpful to some of you
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