Odds, probability and winning records

As a task for my statistics students I often use tennis results to create probabilities for players to beat each other, and then get my students to construct a probability tree to find out the probability of each player winning a tournament. I normally tell them the semi finalists, or one game before the semi-finalits are found, to avoid the tree taking too long to construct. (It's better to spend that time thinking rather than writing in meaningless numbers).

The system is flawed in a number of ways, but mostly because the true probability of a player winning is much more complicated than just the sum of their previous results. Things like fitness, form, and surface make a big difference. And yet in some ways the data is the most accurate and most quantifiable that we have. Also often the person that we find the greatest probability for ends up winning the tournament.

I was having a conversation with someone about how I wanted England to beat Sri Lanka, because New Zealand had a much better record against England than Sri Lanka. It got me thinking that perhaps I could do what I have had my students do.

So I got the data for the last 10 years (the results from before that not really very relevant) and used them to generate some probabilities. The results were actually quite interesting. Here are the 5 most one sided match ups in terms of recent history:

Fot those of you for whom probability is a long way in the past, I've included odds on the favourite, which may be a more familiar way of measuring it. (I've assumed an even chance is at odds of $1.85, this differs between bookmakers)

Matchup	Prob.	Odds
NZ vs Eng	0.714	$1.30
Ind vs Eng	0.667	$1.39
SL vs NZ	0.615	$1.50
Ind vs SL	0.589	$1.57
Pak vs NZ	0.581	$1.59

The closest matchup is India vs Pakistan, with both teams having an even record over the last 10 years.

I then put that data into a probability tree, and came out with some interesting data.

Winner	Prob.	Odds
Ind	0.296	$3.13
Pak	0.278	$3.32
NZ	0.239	$3.87
SL	0.123	$7.49
Eng	0.063	$14.66

I also found out the probability of making the final:

Finalist	Prob.	Odds
NZ	0.564	$1.64
Ind	0.5	$1.85
Pak	0.5	$1.85
SL	0.28	$3.31
Eng	0.156	$5.94

The last step was to check these against the odds that actual bookies are offering. I used Bet365 and TAB New Zealand. Here were what they were offering:

Team	Bet365 Win	Bet365 Final	TAB NZ Win	TAB NZ Final
Ind	2.5	1.5	2.4	1.5
Pak	5	2.5	5	2.5
NZ	7.5	2.44	6.5	2.6
SL	4.55	2.25	4	2.15
Eng	9	4.5	9	4.5

There are obvious differences between these numbers and my ones. Part of that is due to the bookies having much more sophisticated methods to make their predictions than just historical wins/losses. Part of it also is that they are having to cover existing bets. A brief look at the numbers suggests that Bet365 are running lower margins on the winner than the NZ TAB, but that is reversed for the finalists.

I'm not sure that I want to make any predictions based on this data, except to suggest that if England beat Sri Lanka, back New Zealand to make the final.