# Betting with Betfair – Better Value and Statistical Arbitrage if you Look in the Right Places

Because Betfair is a marketplace rather than a bookmaker, I’ve become accustomed to the Betfair experience being different to that of a standard betting agency. However Betfair still continues to throw me surprises, which makes me realise there are still a lot of quirks and intricacies to learn and take advantage of. To be more specific, if you use your cunning in sufficiently liquid Betfair markets, you can take advantage of better value and statistical arbitrage.

Yesterday afternoon Australia and England kicked off their second One Day International (ODI) cricket match in Hobart. The series consists of seven games, with Australia having previously won the first game in Melbourne. Off the top of my head, I recall seeing odds of 1.76 for Australia to win the second match, but an email from Betfair caught my eye, which stated you could get 50.00 odds on Australia to win the series 7-0. At this point I wondered what these odds would drop to should Australia win the second game. With 6 fixtures remaining, I calculated that the 50.00 odds implied 1.92 odds on Australia to win each remaining fixture (50^(1/6) = 1.92; alternatively, 1.92^6 = 50). So with each fixture that Australia wins, the odds on winning the series 7-0 would be divided by 1.92. This obviously ignores the fact that the implied odds of winning each game will likely drop should Australia go 2-0 up. Hence I felt the odds on winning the series would drop by more than a factor of 1/1.92 if Australia won game 2. For this reason, I placed a \$5 bet on Australia to win the series 7-0, with the intention to lay a bet against a 7-0 scoreline should Australia win the second game in Hobart.

As you may know, Australia did win the second game, so I logged into Betfair this morning expecting odds of around 25.00 for the 7-0 series score. This would enable me to lay a \$10 bet against the 7-0 scoreline. If Australia does win the series 7-0 I would profit [\$245 – (25-1)*\$10] = \$5. If Australia fails to win the series 7-0 I would profit \$10-\$5 = \$5. Hence I would have effectively received 2.00 odds for Australia winning as opposed to 1.76 had I simply backed Australia in the head-to-head bet.

However, when I did log in the lay odds were 12.50! This enabled me to lay a \$20 bet at 12.50 odds to lock in a \$15 profit on my original \$5 bet. So instead of receiving 1.76 odds for backing Australia, I effectively received 4.00 odds on Australia to win one game against England! For those who are interested, the 12.50 odds with five games remaining imply 12.5^(1/5) = 1.66 odds on Australia to win each subsequent game. It was was this drop in the implied odds from 1.92 to 1.66 that enabled me to scoop such high effective odds.

I acknowledge that with head-to-head betting you know the odds in advance, whereas with my strategy I had no means of knowing what the odds shift would be. However, it just goes to show that if you apply less conventional strategies, you can take advantage of numerous quirks within Betfair. In hindsight, I could have backed England in a head-to-head bet (at odds of over 2.00), backed Australia in the 7-0 score line, and then placed a lay bet against Australia should Australia win the second game. Due to the drop in implied odds for Australia to win each subsequent game, I would have profited regardless of the result. You could call this statistical arbitrage (as opposed to deterministic arbitrage). For those who aren’t familiar with the terms statistical and deterministic arbitrage, Wikipedia describes them as follows. “In deterministic arbitrage, a sure profit can be obtained from being long some securities and short others. In statistical arbitrage, there is a statistical mispricing of one or more assets based on the expected value of these assets. In other words, statistical arbitrage conjectures statistical mispricings of price relationships that are true in expectation, in the long run when repeating a trading strategy.” Investopedia points out that “Statistical arbitrage is not without risk; it depends heavily on the ability of market prices to return to a historical or predicted normal.”

Let’s apply this to the series score betting I was involved in. Suppose the head-to-head odds on the Australia v England ODI are:
Australia: 1.76
England: 2.07
If the odds on Australia to win the series 7-0 are 50.00, then with 6 games to be played, this implies 50^(1/6) = 1.92 odds on Australia to win each game.

Suppose you can reasonably expect the implied odds on Australia to win each subsequent game to drop should they take a 2-0 series lead. By how much would the odds need to drop to lock in a profit regardless of the result? Note that this strategy involves backing England at 2.07 odds, backing Australia to win the series 7-0, and then laying a bet against Australia to win the series if Australia does win the second game.

Suppose you bet \$100 on England and \$100 on Australia to win the series 7-0. If England wins the second game you lock in a deterministic \$7 profit. If Australia wins, you would require the lay odds on Australia to win the series 7-0 to drop to at least 25.00 to avoid a loss. With five games now remaining, you calculate the implied odds as 25^(1/5) = 1.903. Hence, if the odds on Australia to win each subsequent game fall below 1.90, you would make a profit regardless of the outcome. If you can reasonably expect the odds to drop by at least this much, then statistical arbitrage is possible.

In my case the lay odds for a 7-0 score dropped from 50.00 to 12.50, so the implied odds dropped from 1.92 to 1.66. This netted me 4.00 effective odds on Australia to win one game against England!

In general use, simply compare the head-to-head odds to the implied odds calculated from the series score market for the team to win every remaining fixture. If there are x games remaining, and Y odds on the team to win every remaining game, calculate the implied odds as Y^(1/x). If the implied odds are higher than the head-to-head odds, then you may get better value by participating in the series score market. In some occasions, the implied odds may be substantially higher than the head-to-head odds, in which case statistical arbitrage may be possible by also backing the opposing team in the head-to-head market.

### Caveats

There are a few caveats to the content of this article. The first is I haven’t incorporated Betfair fees. These vary depending on the level of account activity, and they don’t have a significant impact on the key results. The second caveat is you require sufficient liquidity in the market to take advantage of statistical arbitrage. By liquidity I mean player participation. If only a few people participate in the market then there will be huge gaps between the back and lay odds. These gaps could kill off any profit opportunities. For this reason, you should always stick to popular markets. In the cricket series score market, \$11,442 had been matched at the time of writing, which provided only just enough liquidity for me. This lack of liquidity was the reason I only bet \$5 in the first place. While I was able to get 12.50 lay odds this morning, the odds have since jumped to 19.00. These odds are still hugely profitable, but it does illustrate the dangers of participating in markets with few participants.

Lastly, I acknowledge that I will have missed out on \$245 in profit should Australia go on win the series 7-0. While \$245 does make \$15 look paltry, at least I won’t have to chew my nails for the rest of the series. I will now be cheering England on to win at least one of the next five games!