So near yet so far

When Virender Sehwag strode out on the fourth day of the recent Test against South Africa in Chennai, he already had 309 runs to his name. There would have been a great many fans wondering how far he could go: could he top Brian Lara’s 400?

Statistics, however, indicate the fans were very likely to be disappointed [as they were]. The truth is that while 309 and 400 sound like reasonably similar scores, they are not. In fact, it is harder for a batsman to add another 100 runs if he has already made 300, than it is at almost any other score.

There have now been 22 Test triple-centuries, enough for some statistics. Only one of those triples has gone on to produce the magic 400, while 17 others have been dismissed before reaching that mark. Only one out of 18: that is only a 5.6% conversion rate. (The other four innings finished not out between 300 and 399; it is better not to include them in this calculation.) It is interesting to compare this to the conversion rates at other scores:

*0-99 data involves only recognised batsmen (#1-6 in batting order). “Number of successes” refers to the number of innings that have passed through the specified range without dismissal, e.g., for 0-99 it refers to the number of centuries.

While interesting, this data is not very robust for the 300-399 range. If the next batsman to make a triple-century happens to go on to 400, the conversion rate will almost double [to a rate similar to the 300-400 conversion rate in first-class cricket of 11%]. However, the difficulty batsmen encounter above 300 can also be seen when we look more closely, at 20-run increments.

Note the similarity of the pattern at the 200-run mark and the 300-run mark. As batsmen approach 200, their conversion rate rises, only to fall suddenly after reaching the milestone; the same thing happens at 300. A dismissal between 280 and 299 is a rare thing.

It is also striking that a batsman’s ability to add runs once he has reached 300 [67% and 58% for 300-319 and 320-339] is, in effect, no better than for those who have just reached 100 [62% and 65%].

Further perspective can be gained by looking at the one batsman who did make it to 400, Brian Lara at St John’s in 2004. In that innings, Lara played with caution and great focus after reaching 300, taking 178 balls to go from 300 to 400 [56 runs per 100 balls]. This is probably the slowest progression from 300 to 400 in first-class cricket: in doing this under very benign conditions when quick runs were called for, Lara also sacrificed any chance his team had of winning the match.

Few triple-centurions take this approach. The surprisingly high rate of failures after reaching 300, when scoring should be easiest, is probably a combination of mental exhaustion and the need for quick runs in those circumstances. The typical scoring-rate for triple-centurions in their first 300 runs is about 63 runs per 100 balls, but for runs beyond 300 [apart from Lara], the rate is over 80 runs per 100 balls, in time-limited Tests.