What “should” the tennis set price be?

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.

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