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### Expected Value

Every bettor who has used an odds comparison will know that bookmakers have different odds for the same event. Bookmakers compete for customers, and one way to signal to them that they are better than their rivals is to offer longer odds. Sometimes those odds are so good that, mathematically at least, they will be offering what is called expected value. Odds of 2.10 on a coin toss would be an obvious example. You won’t win every coin toss, but after 10,000 of them, there’s a very high chance, or expectation, that you will be in profit.

Arbitrage bettors exploit this phenomenon by searching for the best odds for all possible outcomes in a contest which will guarantee them a small profit no matter what the result. However, because of the bookmakers’ margins, the odds for all possible outcomes need to be very generous for the arbitrage to become available in the first place. Hence, they are not that common. More usually, the odds for one of the outcomes might be particularly generous, but the others less so, so the arbitrage opportunity doesn’t exist.

One solution to that would be to bet only the generous odds. Sure, you’re then making a more traditional bet with the risk of losing, but at least you have bet the value option, right? Yes, in principle, that is so, but to be more confident we have a winning methodology here, we need some independent way of knowing that the odds we are betting do hold value. Of course, that is the age-old problem facing all bettors.

I spent many years trying to crack that nut, trying all sorts of forecasting systems, with only limited success. Then it occurred to me: if I can’t beat the bookmakers, why not join them? To be more specific, rather than trying to devise my outcome probabilities, why not use the bookmakers’ probabilities instead? After all, if they are hard to beat, their forecasts must be pretty good. But we already know that their odds vary, so not all bookmakers can be right. Perhaps some odds are better than others.

### Pinnacle has the Best Odds

After a lot of data analysis looking at odds from different bookmakers that I’d been collecting over many years for my website Football-Data.co.uk, I discovered that the best, or most predictive, odds belonged to Pinnacle. Pinnacle has a reputation for the smallest margins in the industry. On the face of it, you might think that this would mean they have the best odds and offer the bettor the greatest chance of profitability. Yes, indeed, their odds are often the longest, but they are also typically the most accurate. Accurate odds will be the hardest to beat, even if the margin is small.

Pinnacle’s football odds are so accurate that on average they represent a very good measure of the true outcome probabilities. Hence, to find the true odds of a football team winning, I didn’t need to spend large amounts of time developing my forecasting systems, all I had to do was check Pinnacle’s odds and strip out their betting margin. The way this is removed is somewhat complex and took some work attempting to understand how they may have applied their margin in the first place, but to keep a long story short, it just required some understanding of the favorite-longshot bias, a phenomenon I’ve talked about in all four of my books and numerous Pinnacle betting articles. You can read more about my margin removal methodology on my website.

If Pinnacle odds, with their margin removed, are a good measure of the true price, I can form a hypothesis: 2nd bookmaker odds divided by Pinnacle odds (margin removed) = expected value. For example, if Pinnacle odds are 1.95, and 2.00 once their margin is removed, another bookmaker offering 2.10 will hold an expected value of 2.10/2.00 = 1.05 or 105%. I’ll win some and I’ll lose some because of chance, but if my hypothesis is right, after many, many bets I should have returned 105% of the money I staked, for a 5% profit.

### Backtesting the Bets

In 2015, when I first developed my hypothesis, I tested it retrospectively on a large set of football betting odds. By this method, there were nearly 67,000 odds from other bookmakers that offered expected value in my data sample. I predicted an expected profit of 2.2%. Given the football results that happened, I would have made a profit of 3.3%. This was better than expected, but the difference was not statistically significant. It was simply down to good luck that it had performed better than predicted.

Going forward, from August 2015 I started to post these value odds on my website. I opted to add a little extra safety margin: only bet if the expected value is more than 102% (rather than 100%). Since then, there have been nearly 18,000 value odds. The predicted profit from these has been 4.0%. The actual profit has been 3.7%. A slight under-performance but not statistically significant, just bad luck.

Knowing the true odds by using Pinnacle’s means I can bet another bookmaker’s odds when they are longer than the true odds. I no longer need to make an arbitrage bet and I can be confident that what I am betting on has real value, and that I can calculate that value with a fair degree of accuracy. Knowing your true advantage in betting is important since that will allow you to undertake all sorts of risk management assessments concerning losing runs, drawdowns, and the impact of different staking methodologies.

I called my betting methodology the Wisdom of the Crowd. Why? Because Pinnacle uses its customers’ betting activity to continuously sharpen the accuracy of its markets. Other bookmakers, by contrast, may restrict customers who appear to be better at assessing outcome probabilities than their traders. In truth, it is Pinnacles’ odds setters and a small handful of their sharpest customers who will be defining these ‘true’ odds. Perhaps a better name would have been the Wisdom of the Pinnacle Crowd.

Of course, since other bookmakers restrict their winning customers, there will always be the danger that using this methodology to eke out a profit will see your betting account restricted too. It is then up to the bettor to find ways to disguise their betting, so the bookmaker’s algorithms don’t suspect you to be an advantage player. Small stakes and putting value bets into multiples are a couple of ways you can increase your disguise. There are others but beyond the scope of this article.

### Pinnacle Odds Dropper

The Pinnacle Odds Dropper service is really like a sibling to my Wisdom of the (Pinnacle) Crowd methodology. It also assumes that Pinnacle offers the most accurate odds. However, it offers a further dimension, making it even more robust: target odds when Pinnacle’s price has already shortened. Often, a shortening (or steaming) price is indicative that the market feels the original odds were overvalued and the outcome more probable than they originally implied. Nowhere will this be truer than at Pinnacle, whose pricing model implicitly takes into account the weight of customer money. Other bookmakers are often slower to respond, and it is these delays that the Pinnacle Odds Dropper service seeks to exploit. An additional advantage is that it sends customers automated alerts. For my Wisdom of the (Pinnacle) Crowd, I largely leave it to the readers to search for their value bets.

Whether you use the Pinnacle Odds Dropper or Wisdom of the (Pinnacle) Crowd, you can be confident that the methodology underpinning them is robust and fully tested. There is no such thing as free money in betting, but I think this is about as close to it as you can get.

About the author: For 20 years, Joseph Buchdahl has worked as a betting analyst, providing historical sports data and betting odds through his websites Football-Data.co.uk and Tennis-Data.co.uk. He is the author of Fixed Odds Sports Betting, How to Find a Black Cat in a Coal Cellar, Squares & Sharps, Suckers and Sharks and Monte Carlo or Bust published by High Stakes Publishing, and has been a regular contributor to the online sportsbook Pinnacle, with over 60 betting-related articles. He continues to tweet regularly via @12Xpert.