"Inconsistent" draw no bet odds

Colonel Sanders

During the world cup I noticed a small anomaly during the Uruguay v Ghana game. The draw no bet odds were "inconsistent" with the 90 minute odds. Around 2pm on the afternoon of the game Betfair 90 minute odds were as follows:

Uruguay 2.06
Ghana 4.4
Draw 3.4

for an over round of 100.7%

The prices moved closer to kick off as Uruguay shortened but thats not relevant to the logic presented here.

Scaling the associated probabilities to an even 100% book yo get the following:

P(Uruguay win) = 48.2%
P(Ghana win) = 22.6%
P(Draw) = 29.2%

Therefore the draw no bet odds implied from the 90 minute market were

Uruguay 1.47
Ghana 3.14

again in a 100% book

However Betfair odds were 1.54 & 2.84 respectively

Here's where it gets interesting. Assuming the 90 minute odds are correct backing Uruguay (to a stake of 100 "units") draw no bet (ignoring commission for one minute) gives the following outcomes with associated probabilities:

Uruguay win => win 54 (and probability of occurrence is 48.2%)
Ghana win => lose 100 (and probability of occurrence is 22.6%)
Draw => "win" 0 (and probability of occurrence is 29.2%)

therefore your the expected profit is:

54x.482 - 100x.226 + 0x.292 = 3.46

Factoring in 5% commission the expected profit is 2.16. The game finished as a draw so stakes were returned in any case

I kept checking all games for inconsistencies after this. Uruguay v Holland was again inconsistent but factoring in Betfair commission erased any expected profit. Betfair draw not bet odds on Spain v Germany were consistent but using Betfair 90 minute odds as the "correct" odds Bwin's even money Spain DNB gave an expected profit from backing Spain

I have created a spreadsheet which takes 90 minute odds and gives implied DNB odds assuming the 90 minute odds are correct. Insert prices into cells B2:B4. Insert your Betfair commission rate into cell B6. Implied DNB odds appear in cells G3:G4. Enter actual available DNB odds into cells I3:I4. The expectations can then be seen

Just a few points:

• Is my logic correct? Got a few work colleagues to give it the once over and the said the logic was sound however....
• The "logic" depends on the 90 minute odds being assumed to be correct. I assumed the 90 minute odds were correct as the market is enormously more liquid than the DNB market on Betfair
• This is not an arbitrage. It is merely an indicator of whether a team represent better value in the draw no bet market rather than the 90 minute market

Any comments or criticisms welcome

Colonel Sanders

forgot to upload spreadsheet

L'prof

Colonel Sanders wrote: »

It is merely an indicator of whether a team represent better value in the draw no bet market rather than the 90 minute market

In other words, based on this you'd be selecting which market you were going to bet on? I'm a bit tired at the moment, so I can't follow exactly what you're doing.

UrbanSea

My brain hurts,but I can see what you mean. Quick of you to spot it Colonel.

Colonel Sanders

L'prof wrote: »

In other words, based on this you'd be selecting which market you were going to bet on? I'm a bit tired at the moment, so I can't follow exactly what you're doing.

Pretty much

I think Team X will beat Team Y. A method like this gives an indication of whether it's better value to get with them in the 90 minute market or the DNB market

Healio

The process you have above is almost exactly how bookmakers work out the DNB price, but they multiply the probabilities by their margain.

1/1.47 = 0.6802 * 1.08 = 0.7346
1/3.14 = 0.3184 * 1.08 = 0.3439

Bookmakers general price would be:

1/.7346 = 1.36 (4/11)
1/.3439 = 2.90 (rounded down to 15/8 usually)

So the 1.54 was massive value by the looks.