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.

Have number 11's gotten better?

I recently read an article about the impact of DRS and technology on umpiring by Jarrod Kimber. like most of Kimber's articles, it's both informative and readable.

He asked the question in there if number 11's were getting out more or less now to lbws. Umpires seem to be more generous to the bowlers now than they used to be, but they also seem less likely to give horrendous decisions against tail enders now, where it used to seem that if a number 11 got hit on the pad, then it only had to be close for the umpire to give it.

There's also a thought that number 11s are more likely to stay in line now than they used to be.

I decided to have a quick look into it, and found that they were really getting about the same number of lbws now as they were in the pre-DRS days.

I used dismissals per hour, because it tells us more about how likely they were to be given out, as opposed to just looking at proportion of dismissals.

Flat track bullies?

One of the reactions that I got a couple of times to my last article was incredulity about how high up David Warner was. I was assured by a number of people that he was just a flat track bully, and shouldn't be rated as an opener.

I found that suggestion quite strange, because the innings I best remember of Warner's were ones where everyone else had failed, but he had stood up. So I decided to look into it.

I broke his innings into five separate groups, based on the average of every other top 7 batsman in those matches. To set my boundaries, I looked at all test matches since 1970, and found that in roughly 20% of them the top 7 batsmen had averaged below 27, the next quintile borders were roughly 33, 40 and 45.

Looking at the matches where everyone else averaged under 27 gives a good indication of how he went in difficult pitches. In those matches on the most difficult pitches, he averaged 39.45. That seemed to be really good, but it was hard to know without adding in context. What was normal?

I decided to graph the top 50 run scorers, based on those rough quintiles and see how Warner's numbers stacked up. The result is quite messy, but I highlighted a few players to provide some context.

Warner starts just below average for the top players in Quintile 1, and ends just above average for top players in Quintile 5 but generally shows a similar pattern to lots of other top players.

The line that's very high for quintile 4 was one that was of interest to me, and it turned out to be Steven Smith. He's someone who really does cash in once he gets an opportunity, so I thought it would be good to see the big 4 together here.

To get the data for Williamson, I needed to look at batsmen who had scored less than 7000 runs, and once you do that, one player generally shades all others: Don Bradman. Len Hutton also enters the fray, so I decided to extend the axis to show the Don.

The next thing that I though would be interesting was to look at the batsmen who had the biggest  difference between innings on the easier pitches and the harder ones.

Finally, it's possible to get a list of players who were in the top 30% at one end of the graph, and in the bottom 30% at the other.

Four players end up as flat-track bullies in terms of this analysis. Younis Khan, Michael Clarke, Virender Sehwag and David Warner. So it appears that there was certainly merit to those accusations.

At the other end of the spectrum were players who performed better when everyone else didn't: Inzamam-ul-Haq, Ross Taylor, Mathew Hayden and AB de Villiers.

The appearance of two team mates here was interesting. Inzamam and Younis scored 1652 runs batting together, but both had others that they scored more with, and for both of them, their partnerships together were at a worse average than with anyone else that they combined for over 1000 runs with.

The criticism of Warner as being a flat-track bully might have some basis in reality, but the difference between him and most others is really quite small. Anyone who can average just under 40 even when everyone else in the match averages under 27 is someone who is a quality player.