The Beginning

The cricket bug has caught on and I could not resist doing some basic stuff today. The topic was based off the article on cricinfo (rather the reasoning behind the selection of some players). For instance the choice of Robin Uthappa over Gautam Gambhir was interesting. The claim is that Robin was going great guns in the domestic circuit. Therefore I did a little experiment today.

The idea is to see what is the propensity of scoring a half century or century based on ones performance in all first class matches. The basic model is as follows.

Data: N = Number of innings and Y(i) = Number of 50's or Number of 100's (i compute for both cases). I just set 'theta' as the parameter that I'm interested in estimating which is the propensity to score a 50 or a hundred.

Distribution: I let the y(i) 's follow a binomial distribution and choose an uninformative prior distribution (one that does not influence the probabilities and therefore is useful in just making the model tractable) in the form of a Beta distribution with parameters (1,1). I intend to change this view of zero prior information soon. The idea is since I have only considered first class games, the level of performance might actually be different when they move to the international scene. Apriori we expect the performance to be weaker but that need not be universally true. Therefore the new prior for the next analysis will actually factor in the international performances till date of the players in question. But as i said i reserve that for another blog.

The probabilities are as follows

	50's	100's
	P(theta)	P(theta)
Sachin Tendulkar	0.17	0.25
Rahul Dravid	0.13	0.25
Virendar Sehwag	0.15	0.18
Sourav Ganguly	0.08	0.22
Robin Uthappa	0.12	0.22
Mahendra Dhoni	0.06	0.23
K. D. Karthik	0.06	0.16
Yuvraj Singh	0.14	0.18
Gautam Gambhir	0.15	0.18
Mike Hussey	0.23	0.39
Ricky Ponting	0.19	0.21
Brian Lara	0.15	0.20
Inzamam Ul Haq	0.12	0.22
Kevin Pietersen	0.16	0.20

I find this table intriguing. Among the Indian players the choice of Yuvraj Singh over Gautam Gambhir can be questioned if we go purely by domestic performance. In fact the choice of Dinesh Karthik is even more intriguing. While Robin Uthappa can be justified, the wider variation in his probabilities as compared to Gambhir kind of indicates that risks are higher. Considering the type of player Robin is, this is not surprising. Therefore the question begs as to why was Gambhir not given enough opportunities, considering that his domestic performance is fairly good.

Dont I love the numbers for Mike Hussey! A phenomenal player with an amazing average. We can also see why we consider the other internationals top players. It is interesting to note that the propensity of scoring a century for the other four international players align very closely to that of Sachin and Rahul. This kind of tells us that domestic performance is probably an excellent indicator for success at the international level!

Well, this is kind of a quick overview and the idea is just barebones probability. Please feel free to drop in your thoughts. Alternative interpretations/views/modeling strategy...anything and everything....