So I got a question on twitter regarding an old blogpost from last year about calculating what the odds should be after first set and how to calculate it. http://betfairtennistrader.blogspot.co.uk/2013/12/question-from-reader.html

The question I got was instead of having the pre-match odds @ 2.00 for both players. "Lasse" wanted to know how the math is done for a

**1.60-2.67**match. So I had a look at the card for the day to have an example. Tonight David Goffin plays versus Jerzy Janowicz. The odds on betfair when I write this is now @ 1.65-2.54 which is close to what we want to calculate here. To make it easy we use "Lasse's" prices.

So this is basic probability calculations and in theory what the price "should" be after first set. You have always consider if the match was rightfully priced from the beginning and what is happening during the first set.

Anyways, here goes...

Lets start to look at what the market is giving us for probability for each player winning the match.

David Goffin (favorite): 1.60 -> 1/1.60=

**63% (0.63)**- So the favorite is priced to have a 63% chance of winning the match. Now its easy to calculate the chances for the underdog.

Jerzy Janowicz (underdog): 100%-63% =

**37% (0.37)**

So we assume that each player have the same chance of winning a set, and now that we have probabilities for winning the match its pretty easy to get the theoretical set prices for both players. This is probably where the "mindf*ck" part comes into it but its easy when you know how to do it. Ill skip the probability mumbojumbo and just go straight into how to calculate it.

Lets assume that Goffin wins first set. To calculate his set price, we calculate Janowicz chances of winning the match first from being behind a set. This means what are Janowicz chances of winning two straight sets.

37%*37% (0.37*0.37) = 0.1367 = 13.7%

If we subtract 13.7% from 100% -> 86.3% (0.863) (This is Goffins chance of winning the match after he won first set)

And to get this into odds form -> 1/0.863 =

**1.16**

**Lets see if you can get Jerzy Janowicz theoretical set prices if he wins first set! I think you can do it! =)**

Stay Sharp!

/Sammy

Hi,

ReplyDeleteVery interesting post! There is something I don't get. how come you are assuming that both players have the same probability to win the set when they clearly have different probabilities? If you do the proper calculation you will get odds around 1.23 not 1.16, and that's based on their SP. Cheers

Thats great! I love being wrong then i can learn to be right. Ive always done like this but this must be very flawed i reckon. Do you feel like sharing your calculations?

DeleteHi,

ReplyDeleteI agree with Rafael that you have made something wrong in your calculations. Just because the chances of winning the match is 37% for Janowicz does not mean that the chances of him winning a set is 37% as you have assumed in your calculations. I don´t know how to calculate the probability of winning a set if you know the probability for a player winning a best of three sets, but certainly the chances for Janowicz winning a specific set must be larger than 37%.

Why?

DeleteHi guys, interesting stuff. Rafa could you show calculations of how you come up with your numbers... Its probably basic math but I always thought like Sammy did that probability of winning each set is the same. Kris

ReplyDeleteHi guys, i did it the same way than Sammy. But after seeing a lot matchs I see than is more exactly "discount" the 70% of the odd. For example: In the match of Goffin - Janowicz odds where at 1.60 - 2.67. (0.60 * 70%) / 100 = 0.42 1.60 - 1.42 = 1.18 If Goffin won first set that odd he should have for me. In Janowicz case should be: (1.67 * 70%) / 100 = 1.169 2.67 - 1.169 = 1.501 Janowicz before winning first set in this match he paid 1.53 very close. At last said that this is not a "exactly science" it´s different to win a set 7-6 than 6-0 but like I said it´s a very close way to see where the odds will go. Congrats Sammy for the web, it´s wonderfull.

ReplyDeletePD: Sorry for my english i am from Chile.

I think we can't say that the odds for Goffin to win each set are the same as his odds to win the match. If his chances to win a set are 63%, his chances to win the match are 63%*63% + 63%*37%*63% + 37%*63%*63% = 69% . This is the sum of the chances of him winning 2-0, 2-1 after winning the first set and 2-1 after losing the first set. This means that in this case his odds to win the match should be 1.45, not 1.6.

ReplyDeleteWe can also reverse this of course. We know that his odds for the match are 1.6, and this means that his odds to win a set are 58.75%. With this we can calculate that his odds to lose the match after winning set 1 are 41.25%*41.25% = 17% , so his chances to win are 83% and his odds should be close to 1.2 .

Problem with this is of course that the chances of one of the players winning a set are will probably different depending on how the first set actually played out...

Hey Rico! Thanks for your input, looks super good.... i feel dumb, but you lost me at the 2nd part ... how do you get 58.75% to win a set? Cheers!

DeleteOhh ok got you know. Pretty complexed equation don't know how to solve it but excel does the trick if you reverse it.. Cheers!

DeleteI indeed used excel as well to get to the number. Don't have a lot of appetite to try solving cubic functions without it :)

Deletewhat's the formula for excel?

ReplyDeleteIf it's not a problem could someone share the formula for excel mentioned by Sammy and Rico... BTW very interesting blog. Keep up good work Sammy. Kris

ReplyDeleteLet's say we know match odds for player A are 1.6 and we want to find set odds (assuming these stay constant during the match). There are three ways for player A to win, he can win by 2-0 or by 2-1 after winning set 1 and losing set 1. Let's say his odds to win a set are x, then his chance to win by 2-0 is x^2. His chance to win 2-1 after winning set 1 are x*x*(1-x)=x^2-x^3 and this is the same for winning 2-1 after losing set 1. We can sum these three chances and get to the total chance of 3*x^2-2*x^3 . We now have to find the value of x where this sum is equal to 1.6 and by using the solver in Excel you can fnd that x=58.75% .

ReplyDeleteThis is the last comment I'll make on this, because it's not my intention to hijack your blog, sammy :)

No no Rico your not hijacking the blog at all. Its been great fun with all the comments and educational with the discussion! Many thanks for all of the input.

DeleteIll make a blogpost when I find time, about how I was wrong and correct my statements with your explanations =)

Cheers!

/Sammy

In order to calculate match or set winning probabilities you should first model a tennis game using markov chains. Then you assign point winning probabilities to each player from where you can derive the probability to win a game, a set or the match. It's not just a quick and simple formula that will give you a number. It's rather a hierarchical combination of the probability to win a point, a game, a set etc... If you are interested there is plenty of work on the internet! Cheers and keep up the good work!

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