Is Dravid more risky batsman than Sehwag?

It is an oft-repeated comment that players like Virender Sehwag or Kevin Pietersen carry much more risk in their batting than those like Rahul Dravid or Jacques Kallis. While on the face, it appears a no-brainer, closer scrutiny reveals that the any such claim may be far from settled. Here is a simple intutive explanation. (I have thought about it, but may be wrong on some strands of the logic constructed!)

The odds faced by a batsman surviving a ball are largely determined by four factors - the quality of the bowling, the nature of the wicket and conditions, the batting style (or intent) of the batsman, and the ability of the batsman. Confining ourselves to batsmen of more or less equal abilities, we are left with the three remaining factors.

It is only too obvious that on easy wickets and against weak bowling attacks, the risks inherent in different batting styles can be discounted away. This brings us to the case of batting on difficult conditions (overcast weather, bouncy or spinning wickets) against good bowling attacks. For simplicity, we will keep aside the permutations between these two factors.

Ceterus Paribus, the probability of a batsman surviving a ball is 50%. In simple terms, this means that the more balls you face, greater are the chances of getting out. So a Sehwag, who scores at a run a ball and therefore scores his century in far lesser number of balls, has a greater chance of scoring a century than a Dravid who takes two or more balls to score a run.

Against good bowling and in difficult conditions, the probability of a batsman getting out to an unplayable ball (or "jaffa") is significantly higher. Even discounting for the ability of the batsman and the fact that a settled batsman stands a greater chance of surviving, the difference between the probabilities of survival of batsmen with different batting styles gets narrowed. In other words, in difficult conditions and against good bowling attacks, the risks inherent in batting styles becomes a less important factor in determining their respective survival probabilities.

It is true that in such conditions, a Sehwag carries more risk, when seen in the context of each ball faced. But when seen in terms of scoring runs, a Sehwag, who faces far lesser number of balls than a Dravid, has a greater probability of scoring a century.

This aforementioned reasons and the fact that nowadays batsmen, in general, score at a faster pace may partially explain why batting averages of modern day batsmen are higher. I am inclined to believe that the average numbers of balls faced (per innings) by the typical modern top-order batsman over a career is much lower than that faced by his predecessors. So it is natural that the probability of his scoring more runs before every dismissal, and hence batting average, increases.

This may also partially explain why we have been having more successful fourth innings run chases in recent years. Statistically atleast, batsmen have a greater chance of survival if they try to score of a fewer balls than attempt to survive larger number of balls.

As an afterthrought, fielding placements are another reason that works in favour of an aggressive batsmen. If the batsman is defensive, the fielding captain crowds him with fielders in catching positions, thereby increasing the possibility of getting out. In contrast, with fewer fielders in catching positions, spread out field and resultant gaps, the batsman has greater freedom to score singles and twos with fewer risks.