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# The serial toppers: batsmen analysed by series dominance

Cricket statistics are based around individual measures, from a batsman's average to a bowler's strike rate. For a game so heavily dependent on conditions, conventional cricketing numbers hardly include any context. A series played on bowler-friendly pitches might deflate the career averages of the batsmen involved, but that dip fails to account for their performances relative to the conditions. Maybe everyone failed to score, like on South Africa's tour to India in 2015, or India's return tour in 2018?

A series is a fair unit to use to break down careers. Played as a continuous bout over closely spaced matches, with similar teams and under similar conditions, the numbers of a bowler or batsman over a series are self-contained indicators of performance that are also somewhat normalised for conditions.

Here, instead of looking at raw runs, wickets and averages over a series, I will try to look at the relative standing of a player in the run charts in a particular series, and average that over his whole career. The cut-off for this analysis is 4000 Test runs.

The method is simple. A batsman is allotted a percentile value based on his ranking: a top rank gets you 100 points, and the points decrease according to your rank. I then average this value over all series the batsman has played, weighed by the number of matches in each series. Let's look at an example. AB de Villiers scored 211 runs in the recently concluded Test series against India, standing second on a list of 28 batsmen who played in the series. Being second out of 28 gives de Villiers (100*(1 - (2-1)/28) = 96.42 points for this series. For de Villiers, the weighted average of this value of all series comes out to be 81.76. This means he has been above 81.76% of the batsmen in the run-scoring charts of the series he has played, on average.

This "Series Percentile Value" sums up his run-scoring relative to all other batsmen who have played with or against him in a series. It is the average of values all ranging from 0 to 100, and takes into account the length of each series, so dominance over a longer series counts for more.

Here are the top 15 batsmen by this metric (percentile value by runs):

So Don Bradman, on average, was higher than 97.23% of the batsmen who played in a given series he featured in!

Here is the same for some reputed modern batsmen:

We can also look at the proportion of series in which a batsman topped the run-scoring charts, or the proportion of series in which a batsman was in the lower half of the run-scoring table for a series, and so on. Some interesting nuggets:

Being above the 80th percentile in a series is a basic signal of a good batting performance, and the proportion of series where a batsman is above it is a good indicator of the ability to out-bat peers and competitors by playing big innings. Here is the table sorted by the percentage of series in which a batsman was above the 80th percentile:

In conclusion, let's look at another important percentage, the proportion of series in which a batsman has topped the batting tables: who shows absolute dominance the most often? We know Bradman leads this with 54.55%. Who follows him?