Towards more useful metrics for test bowling

For a long time, there was only one metric that was used for bowlers in test cricket - bowling average.

It's become the most intuitive statistic - how many runs do they concede for each wicket, but it is only familiarity that makes it so. To the uninitiated, it seems nonsensical to suggest that someone with an average of 40 is worse than someone with an average of 20. 

It is also a metric that has difficulties when someone has not taken a wicket. Dividing by 0 is never something that any mathematician feels comfortable with.

There is an easy solution to both of those problems. Reverse the fraction. Instead of looking at runs per wicket, look at wickets per run (or - in order to have friendlier numbers per hundred runs.)

It would take a while to get used to that, but once we do, it would make much more sense than the other way round. 

It is particularly useful when having a quick look at things like series averages, where there is a high chance of incidents of 0 wickets.

Here's an example - Dale Steyn's series average vs his Wickets per Hundred Runs per series.

The very tall bar in the top graph is the series in Sri Lanka where he got injured early and did not take any wickets in the series. I capped the graph at 125, but as that was effectively infinite, it went off the graph no matter what scale was used.

The peaks in the second graph are the series where he had the best returns. They stand out more, and the difference between the series where he took 2/178 and the one where he took 0/30 is shown by one very low bar, and one at 0.

We are used to good performances being the highest lines, so this makes more sense.

It's also better for getting an estimate of the career average. If the series with no wickets is ignored, the mean of the averages is 26.12, while the mean of the wphr's is the equivalent of a bowling average of 21.79. Given Steyn's career average is 22.95, that's a much better estimate.

The same thing works for every other bowler that I tested. For example - Mitchell Johnson's equivalient numbers are 33.32 with bowling average and 28.22 with wphr - compared to his actual average of 28.40, and Muttaih Muralitheran's numbers are 33.54 with averages, 21.42 with wphr compared with a career average of 22.72. In both cases the series averages would lead someone to overestimate the player's average (and hence under-estimate their ability), while the Wickets per hundred Runs method would get a better representation.

Bowling average is not the only statistic that is collected, and this technique would aply to others too. The equivalent statistics would be Wickets per 100 balls (to replace Strike Rate) Runs per Hundred balls (to replace Economy rate - useful to keep everything per hundred and Balls per Hundred Runs (this is useful for some other analysis later on)

These extra measures can also be combined to create two separate measures. I've called these the Strike Bowling Rating (SBR) and the Holding Rating (HR). 

The SBR is found by multiplying wphb and wphr (effectively wickets squared divided by balls times runs) while the HR is found by multiplying the wphr and the bphr (then dividing by 100 to make the numbers look similar).

This allows some better visualisation of bowlers performances:

Here's one way that bowler's ways of operating could have been displayed with the traditional statistics - this is every bowler who debuted after the Second World War to have taken 95+ wickets, coloured by average.

The bowlers averages fall along hyperbolic lines, and these could be drawn in to show them too.

Here's the same data, but displayed using the new metrics.

There is still hyperbolic bands for the bowler's averages, but this time the better ones are at the top instead of the bottom. The positive outliers are highlighted, rather than the negative ones - and that's a good thing. The positioning of Waqar Younis, Kagiso Rabada and Curtley Ambrose are more interesting than Carl Hooper, Nicky Boje or Fidel Edwards.

This visualisation also allows us to see some role-players who did an excellent job, despite perhaps not having the average to show it. Hugh Tayfield, Lasith Malinga, Ray Illingworth and Waqar Younis all are on the edges of the group, showing that they were exceptional at the job that they were asked to do. Umesh Yadav is starting to look like he's becoming a bowler in that mold too. 

Looking at the two metrics - brings these two top 10 lists:

I intend on looking into this a bit more over the coming weeks. But for now I think they are an interesting way to look at bowling data, and a way that may help people understand the different roles that bowlers sometimes fulfill when operating in partnership.