How good is James Bracey?

James Bracey (FC avg 37) is now in the England squad. That surprises me, so I’m going to take a closer look.

37 is a very good average. But players with better averages are a long way from Test honours (his captain, Chris Dent, averages 38). Their stats are based on facing second division bowling. Thus I was expecting Bracey to average in the low 30s this year in the more challenging conference system.

Actually, Bracey has started 2021 brightly, with 478 runs in five games. That’s enough to boost his expected* Test average to 29 (+/-7)**. Here’s his record:

James Bracey in County Cricket. Note that prior to 2021, the 2017 performances look like the outliers, including the 156 against Glamorgan which was shoring up his average.

That +/-7 is important. England rate Bracey highly – with Lions tours already under his belt. Thus you might presume he’s doing better in the nets than in the middle – and put him at the upper end of the range, with an expected Test average of 33/34.

Context 1: batting in the top three. When cricket was a summer sport, it would be odd to pick a batsman averaging under 40. But top order batting in England in the spring and autumn is hard. Comparing Bracey to a selection of his peers (five number three batsmen in D2) from 2017-19, they averaged 30 and he outperformed them by 21%. Looking at this season, the top three clearly get the worst of the conditions. We should adjust expectations accordingly.

Context 2: Other bright young things. It looks like England are picking players on potential. If we look at the best batsmen born after 1997, most of them are in or around the squad.

NameAgeExpected 2021 FC AvgTests
OJ Pope235017
JJ Bohannon2440
H Hameed24393
DW Lawrence23385
Z Crawley233512
R Vasconcelos2335
SM Curran223421
JR Bracey2431Squad
TC Lace2230
DM Bess233014
GA Bartlett2330
Best U24 batsmen in County Cricket. Note that if England are looking at players with upside as they move up the age curve, Josh Bohannon (averaging 46 this year) and Ricardo Vasconcelos (70) might be worth watching.

Context 3: First Class vs Test. I thought Zak Crawley (FC avg 32) made his Test debut far too soon. Yet he’s averaging more in Tests after 20 innings (34) than FC. It could be that performances against medium pace and junk spin should be excluded when working out who has international potential. I’ve started a ball by ball county database to get more detail – here’s the limited data so far, and yes – strip our the medium pacers and Bracey looks great. Watch out for his performances against off-spin though.

Bracey vs Bowler matchups, 2021 County Championship to 22nd May.

James Bracey is young, and bats in the top three – so his ability won’t be reflected in his average. He’s not (yet) a star, but it’s not inconceivable that in future he could average 35 in Tests and earn England’s troublesome number three spot.

*Expected Test average is calculated on the basis of runs scored, adjusted for difficulty, divided by number of times dismissed. Normally I’d use the last four years of data. It’s also adjusted for where they play: batting at Bristol is quite easy, I make it the fourth easiest ground for batting, inflating averages by 4%.

** Uncertainty: calculated with the formula Uncertainty = 2 * Average * (Times dismissed)^-0.5. This gives a 90% confidence estimate of someone’s ability, which gets more precise as the number of innings increases.

The case against Zak Crawley

Running England’s first innings (NZ vs Eng, 29th Nov 2019) through my model told me that Zak Crawley had a median first innings score of 12. Absurdly low.

Rather than just spout that opinion in a tweet, I’ll walk you through how the model got there, and we’ll see if there are any gaps in logic. Have England made a terrible selection?

Zak Crawley’s County Cricket Record – Average 31

County Championship Division Two: 2017-18 – Runs 830. Dismissed 30 times. Average 27.7

County Championship Division One: 2019 – Runs 820. Dismissed 24 times. Average 34.2.

Second XI Cricket: 2016-18 – Runs 708. Dismissed 22 times. Average 32.2. Ratings – Expected D1 Average 30 – Rating those performances, and placing more weight towards recent performances, Crawley’s expected Division One average next year is 29.6.

Adjusting for Age – Expected D1 Average 30.4 – Zak Crawley is 21. He gets a c.3% boost to his expected average because his average is based on runs scored when he was 18/19/20.

Adjust for this innings – Expected Average 19.4 – A Test Match, away, against a strong New Zealand attack is much harder than a county game. That has a severe impact on average.

Run all that expected average of 19.4 through the model, and it predicted a median score of 12.0. What you would expect from a number eight batsman, not a specialist.

Gaps and biases

Let’s look at this from England’s point of view – why is Crawley in the team? I can think of three reasons:

  • He was in the squad, they didn’t really expect him to play. (That links to home advantage getting bigger as a series goes on: in this case it’s because injury means that a squad player, there to gain experience, gets drafted into the team.
  • England selectors use a different age curve and/or bias towards recent matches – bumping up Crawley’s expected average (along with every other young player).
  • Something in performance specific data (that doesn’t show up in averages) makes the England selectors think he’ll be especially suited to batting in New Zealand.

What happened?

Crawley made one run before Wagner got him. That additional innings has moved his expected average down a little more.

Anderson vs Woakes

When I was at university there was a rumour that one of the Geology professors was about to predict a massive earthquake in South America. This would have been a career limiting move if nothing happened.

In the end neither the bold prediction or the earthquake materialised.

I thought of that professor’s reputational gamble when I had the idea of asking whether Chris Woakes might be preferred to James Anderson for the Fourth Ashes Test. To misquote Nasser Hussain, “No Ed Bayliss, you cannot do that.”

The scenario

If you are reading this years from now, Sir James Anderson is currently England’s best bowler, though he doesn’t bat very well. Woakes is a decent batsman, and almost good enough to get into the England team as a bowler. Woakes shores up a mediocre top seven and gives the team balance, especially as Jack Leach is a non-batting spinner. Anderson pulled up during the first Test with a calf injury. He missed the next two Tests and has been added to the squad for the fourth. The series is level 1-1 with two to play. Current speculation is that Woakes might make way for Anderson.

Fig 1 – Career Test records

When weighing the merit of the two players, I’ll look at two factors: England and Australia’s expected runs. To do this, I’ll run my model using each player’s career record as the input* and see how the different teams fare.


If Woakes were dropped, England would have Broad, Leach and Anderson as a long tail. That means a higher probability that a good batsmen gets left stranded and not out. The following table shows the impact on expected runs over the course of a match of replacing Woakes with Anderson and rejigging the batting order:

Fig 2: Comparing modelled runs scored per Match by batting position in the two scenarios. Note that Bairstow would expect to score two runs fewer per game as a result of more frequently running out of partners.

England would expect to score 29 runs fewer per match with Anderson rather than Woakes.

Interesting that Broad batting at ten outscores Leach in that position by so much – I think it’s because the likely partnerships with Leach at ten (9th wicket: Broad-Leach, 10th wicket: Leach-Anderson) won’t last long.


From a bowling perspective, Anderson has an average that’s four runs per wicket better than Woakes. Their strike rates are similar (Anderson 56, Woakes 59). It’s likely this gap is narrower in English conditions (both average 23 at home), but let’s use the raw data rather than run the risk of flattering Woakes.

Note that England have a solid fifth bowler in Ben Stokes, (unlike some teams that would need to use a part-timer if they are bowling all day).

Running this through the model, adjusting for home advantage and Austalia’s brittle batting order, the benefit of Anderson’s bowling over Woakes is 13 runs per match. Not enough to offset the weaker batting.

That seems a little low to me, four wickets per match at four extra runs per wicket would be 16 runs – I think it ends up lower because Australia are away from home and aren’t that strong at batting.


Bringing Anderson into the team for Woakes would be a mistake. Maybe there’s a case for such a change in a must-win match (as the odds of a draw are reduced), but the model does not support such a change for the fourth Test.

It’s important to put this analysis into context. I’m not saying that all specialist bowlers should be replaced by all-rounders. Nor am I saying that Anderson shouldn’t be in the team because he can’t bat.

The head-to-head between Woakes and Anderson is considered in this specific scenario where England have a high quality fifth bowler (Test average 32), but two weak batsmen in Broad and Leach.

James Anderson is England’s best bowler. If fit he should play. If Anderson is fit one needs to reframe the question: you can pick two of Woakes, Broad and Archer. Just make sure one of them is Woakes. Whatever you do, don’t bring in Anderson for Woakes.

*This might be slightly contentious. Any debate on this topic (though the participant may not realise it) will boil down to whether they believe that career record is the right input to use. For example, I’m not making an adjustment for Woakes’ unusually strong home record, nor am I adjusting to reflect more recent performances (which would boost Anderson’s bowling). Nor am I adjusting because Woakes hasn’t scored many runs this series.