Top innings bowler in Tests

Cricket has quirks. Look at it through another lens; learn something new. Today’s angle is wicket-taking. What kinds of bowlers are the leading wicket takers in a particular innings, and what implications does that have?

Since 2010. First five bowlers used only

No surprises here. Let’s go deeper.

Pace bowlers by innings and by position

Since 2010. First five bowlers used only

Opening bowlers are the best pace bowlers. They also get a boost in the first morning on a fresh pitch. In later innings, they are still favourites among pace bowlers (though the spinners start to get a look-in).

First change bowlers are about two-thirds as likely to be leading wicket taker in an innings. Probably two factors – they aren’t quite as good as openers, and (more significantly), they don’t get the new ball, or first crack at the tail. In later innings their chances improve, probably because those innings are shorter, squeezing out the part time bowlers.

The fourth bowler is just as good as the third, until the second half of the match. The fifth bowler gets a reasonable go in the first innings, but not much action in the second. They are surprisingly unlikely to take the most wickets in an innings – it’s kind of a four horse race.

Pace bowlers by Ground

We haven’t the data to do much by ground, but one stadium gets two Tests a year: Lord’s.

Lord’s since 2010. First five bowlers used only

There’s a 75% chance one of the two openers is leading wicket taker in the first innings at Lord’s – batting is hard in that first hour. The change bowlers don’t really get a look in.

Until models are seriously good, they won’t always beat local knowledge. To get that I need domestic stats. Must build that database at some point.

Spin bowlers by Country by innings

Never cut a spinner. Or back one to be leading wicket taker in the first innings in the SENA countries (South africa, England, New Zealand, Australia). The general trend of a gentle increase in top-wicket-taker probability from 19% in the first innings to 26% in the last is not seen worldwide. In India, Sri Lanka and Bangladesh, a front line spinner should rarely be available at longer odds than 3-1 in any innings.

(Also a reminder that spinners go from pointless to prized over the course of five days in England).

Individual players

If ye grind yer [gunpowder] too fine, it’ll blow yer bloody head off, then nobody’ll know who’s best shot; thee or me

Sharpe’s Siege

Do bowlers have preferred grounds? Almost certainly. Does it show up objectively in the data? Maybe, if you know what to look for. I’ve checked just one example: Stuart Broad. Using the data since 2010, Old Trafford was clearly his favourite ground, while The Oval was a graveyard. However, look just outside this horizon, and in Broad’s only previous Old Trafford Test he took 0-79, while in his earlier Oval Tests returned 11 wickets at 19. Regression to the mean? Maybe.

What have we learned?

Nothing earth shattering – hints at how bowling position impacts performance, a reminder that grounds can have peculiar characteristics, another reminder that the usefulness of spin through a match varies by country, and my squeamishness about small sample sizes was reinforced when looking at Broad’s record.

Call this one “knowledge consolidation” – kicking the tyres of what I think I know, and nodding approvingly at the result.

Using judgement when rating cricketers

Yesterday Zak Crawley scored 171*. 

Before the West Indies series I said “he would be a bold and wrong selection, going against the publicly available data… If he succeeds, I will give them credit.” Time for me to issue a credit to the England selectors.

Moving swiftly on, with Crawley and Ben Stokes outperforming their ratings it’s time for a rethink. There’s qualitative data I’ll start using: the judgement of others. We’re in uncharted waters; we’re Going Beyond Stats.

I appraise batsmen based on four years of data (six if they rarely play). It’s a stable method. I don’t have meaningless volatile opinions (like a certain former England captain). There are limitations though. Injuries, new techniques, changing roles can all have an effect. My ratings system is too slow (look at Bairstow – his stellar 2016 is still boosting his rating).

Adding the 171* to my database would boost Crawley’s expected Test average by three runs (going from 26 to 29). Is that enough? Is he better than that?

Rob Key previously said “Crawley is young and his numbers will improve. You just have to watch him bat to know that.” Actually I can’t: I don’t trust my eye. But if people I respect are saying a player is better than their stats, maybe there’s something in that.

With a base average of 29, your chances of 171* (in the first innings, at home, against a strong attack) are around one in 150. In other words, yesterday shouldn’t have happened. Much more likely for a player with a base average of 35 – it’s a one in 60 shot.

After a finite number of innings there is uncertainty about how good a player is. I can tell you roughly how good a player has been, give or take a bit. Luck is a factor, moreso the less data you have. Error bars give a range of possible ratings for a player, with a 95% chance their level of ability lies somewhere in that range.

Let’s jam those two concepts together to add a third step to my ratings framework:

  1. Rate player based on stats
  2. Add error bars to that rating, based on the number of dismissals.
  3. NEW: Adjust the rating within the plausible range based on the views of people you trust.

Oh, and “the views of people you trust” can include selectors. For instance, if someone had rubbish data but is batting at four, then selectors are implicitly telling us the person is better than their stats. We should use that information.

What does that mean for Crawley?

  1. Rating 29
  2. Margin of error +/- 7 (after 83 dismissals in the last three years).
  3. Boost rating by 5.0 to reflect the excitement and that England choose to bat him at three.

Crawley is now expected to average 34 in Tests. This recognises that he is probably at the upper end of the range of plausible averages (22 to 36) because he is trusted to bat at three, and is highly regarded.

I will do the same exercise with all county cricketers to redefine their red ball ratings to incorporate the role they are given. However, there are about to be several meaningless games in the Bob Willis Trophy, so that may have to wait for next year.

I’ll also do that with England’s Test batsmen. For instance, Stokes at 40 +/- 12 might be re-rated at 44 (based on two year record, and pundit judgement).

One innings doesn’t change everything, but I’ve seen enough outliers to want to try something new. Where does this leave us, now data is being tinkered with, and we lose the safety of being moored to pure stats? I draw the parallel with the astronomers maintaining the Earth as the centre of the solar system, as more data made that harder to believe. Models became contorted to fit the data, before being binned. Is that happening here? Time will tell. #OnOn.

Test bowling averages by month in England

Spinners averages are influenced by time of year and innings number. I’ve had a go at quantifying these effects, and looked at the (smaller) impact on pace bowlers. Along the way I’ll make a couple of observations on fourth innings chases.

Starting with spinners, it won’t surprise you to hear that early season English conditions are unfavourable. The first innings average for spinners before August is 59. Spinners are little use in May and June, when pitches are damper and less worn. Twirlymen are generally passengers in the first innings of a match.

Spinners since 2010, first five bowlers used. Later innings have lower averages, likewise for later in the summer.

Spin bowlers average 15% less in August/September than May/June. While spinners are generally more effective in the fourth innings, it’s July when they are matchwinners. Averaging 22, with 49 wickets (so a decent sample size). Next consider the same view but for pace bowlers:

Pace bowlers since 2010, first five bowlers used. Fourth innings has lower averages, likewise for later in the summer.

Much less variation with the seasons for quick bowlers; this graph is much greener, pace bowlers are always a good thing. Averages dropping about 10% from spring to summer. A pronounced dip in the fourth innings (23) against averaging 30 in the first three innings. The sweet spot data point, again, is that fourth innings in July.

Combining spinners and pace bowlers, over the last decade the fourth innings yields 19 runs per wicket in July, compared to 28 in other months. The reason is somewhat counter-intuitive – pitches start out best for batting in July. The higher averages in the first three innings at that time of year mean the fourth innings in July start on average 20 overs later than at other times of year. Cracks, footmarks, the works. Just 3 out of 21 fourth innings chases were successful in July. Conversely, batting last in May/June was successful 5 times out of 13: a 250 chase is achievable.

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Here’s a handy guide for captains of when to bowl spin in England. When do spinners average less than pace? (Or “Should I bowl my spinner if I have a fresh pace bowler?”)

In England, since 2010, performances of first five bowlers used.

I’m being somewhat glib (pace is less effective with an old ball and July 31 is not magically different from August 1), but teams do get this wrong. Just because spin is most effective in the fourth innings doesn’t mean any spinner is the best option. West Indies failed to defend 191 in the fourth innings in May 2012. Marlon Samuels (off spin, part time) bowled ten overs for 51 – Fidel Edwards only got eight overs.

What about the middle overs of the fourth innings? We can have a go at “spin or pace in the fourth innings with an old ball,” by comparing outcomes for spinners to the fourth bowler used (if they are a pace bowler). On this measure spin wins with an average of 25 against 27 for the fourth bowler used. Meanwhile opening bowlers have more fun in the fourth innings in England, averaging 22.

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When slow bowlers look ineffective (early in the summer and early in every match), that’s because they are ineffective. They are still helpful in the fourth innings, but don’t give them the new ball. Spinners are probably overused and overselected in Tests in England.

Keeping things topical: Yasir Shah (Test average 30) should seldom bowl overs that could be Mohammad Abbas’s (Test average 21).

England vs Pakistan Preview – August 2020

An impressive batting unit supported by an exciting bowling attack versus an impressive batting unit supported by an exciting bowling attack.

What will decide the series? Here’s my usual pre-series ramble, with stats on the Pakistan squad at the bottom.

  1. All rounders. England are running out fast. Debateable whether England will even have an all rounder for the first Test. Some names to mull: Ben Stokes (is he fit to bowl?), Joe Denly (dropped), Moeen Ali (dropped), Chris Woakes (struggling with the bat), Sam Curran (is he good enough at either discipline)? As for Pakistan, Shadab Khan averages 34 with the bat from five Tests, but only 27 in First Class – more a number seven than a six. Pakistan will be gambling either way: a five man attack lengthens the tail, an inexperienced four man attack has nowhere to hide.
  2. Pitch preparation. England would be stronger if they could confidently not pick a spinner (Bess didn’t contribute a lot with the ball against West Indies). Pakistan are itching to play two spinners. Why would the Old Trafford groundsman produce a deck that turns? Worth noting in the two Manchester Tests this summer, spin averaged 52 while pace was around half that at 27.
  3. Naseem Shah and Kashif Bhatti. Pakistan’s batting is solid, enough talent that they can cover if any one of them goes full Shai Hope. For all the excitement, I’m uncertain about their bowling. Mohammad Abbas is a banker (Test average 21, and the same average in two devastating seasons at Leicestershire). Shaheen Shah Afridi has 30 Test wickets, so has some track record. Yasir Shah has a proven record – it’s just a bit mediocre (averaging 34 in the last four years). One of Naseem Shah or Bhatti thus has to step up. The signs are good – both average 17 in domestic cricket in the last four years (Bhatti has 125 wickets, the younger N. Shah has only 26).
  4. Rest. West Indies clearly don’t read this blog (or The Daily Telegraph), else they wouldn’t have knackered their bowlers playing three back-to-back Tests. A three Test BTB series is more like a tournament than a traditional Test series: you’ve got to manage bowler workload. The easiest way to do that is to pick the best team for the first game, then half the pace bowlers miss the second Test, and the others miss the third. Sohail Khan is good enough to rotate in – but are the other Pakistan squad bowlers Test standard? With England’s squad depth, their edge will get bigger as the series goes on.
  5. England’s Ashes tunnel vision. Picking Crawley and Bess with an eye on December 2021 is silly. When the West Indies series got real, Crawley was dropped and Bess didn’t get a chance to bowl. Pakistan will be only too happy if England’s team sheet has a number three with a First Class average of 31, and an off spinner for Pakistan’s right handed middle order to milk. Bess isn’t a bad player, it’s just that England would have a better chance of winning playing an extra pacer.

England start as favourites. Burns, Sibley, Root, Stokes are a fine core of a batting order, and there’s healthy bowling options. If Stokes can bowl, a balanced England team playing on increasingly familiar territory should be too strong.

Get to know the Pakistan squad: Stats

Batting:
Note through this lens Babar Azam isn’t the standout batsman.
Bowling:
Note the domestic four year averages of Abbas, N.Shah and Bhatti.

Pace bowlers struggle in back-to-back Tests; Pope Catholic.

No sensational claims today – just quantifying what you already know. Bowling pace across two Tests in quick succession makes a player tired and less effective.

I took all match performances this century, comparing data against the next game that player bowled in. Then cut the data by the number of days between games. For instance, in this England vs West Indies series, the first game started on 8th July, the second on the 16th July – eight days apart. Any gap of nine days or under between start dates, to me, is “back-to-back” (BTB).

What did I find? Pace bowlers in the second of a pair of back to back Tests average 7% more than in the first game.

With more number crunching we can get closer to understanding why this happens:

•            Are there more long hops, driving up averages as bowlers leak runs? No – Economy rates don’t significantly rise.

•            More fielding errors? No – there’s no effect on spinners – so it’s probably not fielding causing it.

•            Pace bowlers must just be less potent when tired. Interestingly, at higher workloads the effect is bigger – pace bowlers bowling over 40 overs in each match of BTB Tests add 8% to their average in the 2nd Test.

Conclusion: this is significant – I’m adding it as an input to my Test match model. Front line pace bowlers add 3.5% to their average if a quick turnaround from the last Test. This rises to 4% if they bowled over 40 overs in the prior Test. Reduce expected average by 3.5% if this match isn’t BTB.

In case you’re wondering why it’s only 3.5%, and not the 7% I quoted earlier, during the first BTB Test, the bowler will be well rested, so 3.5% better than usual. The second Test they’ll expect to be 3.5% worse than usual, giving a 7% gap between performances.

PS. We finally have a mechanism for why home advantage gets bigger as a series goes on – hosts have a huge player pool to draw from, tourists are drained by practice matches.

PPS. This nugget of trivia will make you feel tired just reading it: 38 year old Courtney Walsh delivered a mammoth 128 overs across two BTB Tests in March 2001. It was six months after Ambrose retired, so Walsh was asked the impossible. West Indies lost the series 2-1. To his credit, he took 9-216 across the two games. Understandably, he almost immediately retired from Tests.

Implications for the July 2020 England vs West Indies series

While for most participants the sample size is too small, England’s veterans have kindly left a trail of data over the years: Anderson averages 25 in non BTB, 27 in the second Test of BTB. Broad averages 27 in non BTB, 29 in second Test of BTB (bear this in mind if Broad is picked for the third Test).

Notes:

•            Third Test is back-to-back-to-back – WI will be out on their feet unless some of Raymon Reifer, Rahkeem Cornwall, Chemar Holder get rotated in. Expect Cornwall & one other.

•            What the heck were West Indies thinking fielding first at Old Trafford? The betting markets thought it was a mistake at the time. If they’d planned to field first, why didn’t they bring a fresh bowler into the team?

England vs West Indies (July 2020) – Preview

I recommend you read this back-to-front. Like a newspaper: skip to the tables at the end, digest the stats, make your own mind up – then read my words and see if we’ve reached the same conclusion.

On paper this series is a mismatch – the fourth ranked team hosting the eighth. West Indies averaging 23 runs per wicket over the last three years, facing English bowlers in English conditions. Yet there are reasons to believe in the tourists: eight of their expected top nine are peaking, aged between 27 and 30. They could have the best Test opening bowlers right now in Kemar Roach and Jason Holder. Roach averages 22 over the last four years; Holder 23.

Talk is cheap. It’s easy to argue this either way. What does the data say?

By my ratings, England are 50 runs per innings stronger, a 59% chance of winning (West Indies 29%, Draw 12%). Bookmakers only give West Indies an 11% chance. Intriguing.

Do people underestimate this West Indian side? The difficulty of batting in the West Indies Regional Four Day Competition is roughly comparable with County Championship Division 1 – so the last-six-year domestic records of Brathwaite (avg 45), Hope (57) and Chase (46) indicate their underwhelming Test records are misleading. Note Hope hasn’t played a domestic game in three years. He averages 52 in ODIs, but it looks worryingly like he’ll never fulfill his Test potential. Modern cricket.

Some thoughts on the optimum makeups of the sides:

Holder is best at eight. West Indies’ strength is in bowling; their weakness in batting. With canny selection they can paper over the cracks. Jason Holder, Raymon Reifer and Rahkeem Cornwall could feasibly be 8-9-10 giving West Indies the best of both worlds. However, the lure of picking the best bowlers would lengthen the tail with a batsman being displaced (Holder, West Indies’ highest placed batsman in the ICC rankings, moving up to six as part of a five man attack). That would be a mistake – the West Indies win probability would drop by 4%.

West Indies only have one other decision to make: do West Indies need a front line spinner? This decision should be based on reading the pitch. If not, Roston Chase covers those overs. If they do, then J Holder, Cornwall, Reifer/Gabriel, Roach is logical. Cornwall isn’t the Test prospect he appears: expect a mid-30s average. While he has a fantastic domestic average (23) over the last four years, this is flattered by spinning domestic conditions. Remember that Chase also averages 24 in that period, but 42 in Tests.

The hosts’ shaky top order means England have to pick a number eight that can bat – which limits their choices. If Jack Leach plays, then one of the batting bowlers (likely Chris Woakes) needs to play. Woakes loves bowling at home: in the last four years he averages 21. Alternatively, Moeen Ali could play: this is Stuart Broad’s best chance of joining Archer/Anderson/Stokes as England’s pace quartet. Broad may not make the cut– he’s played every home Test since 2012, but is sliding down the pecking order.

Leach (SLA) is the best slow bowling option. West Indies’ middle order is packed with right handers. Leach & Parkinson turn the ball away, so have an advantage. Leach also has the best county average over the last four years (23). Meanwhile Ali averages 40 against right handers. If Ali plays (for his batting), the West Indies should focus on seeing off the new ball, because favourable conditions await.

It doesn’t really matter which ‘keeper England choose. The gap was marginal when I looked at it before [link]. This just isn’t a debate that excites me- it’s a judgement call, and no criticism should be levied at selectors if it fails. Unlike Zak Crawley, who would be a bold and wrong selection, going against the publicly available data. His best first class season saw an average of 34. If he’s picked and fails, it’s not his fault- blame the selectors. If he succeeds, I will give them credit.

Both teams impress with the ball. The batting will decide the series. England at full strength are better than the West Indies. Most of that advantage comes from Root and Pope. Neither team has much in the way of batting reserves. With Root unavailable for the first Test, England have a lacklustre choice of alternatives. Ballance and Kohler-Cadmore aren’t in the squad. The replacements are c.14 runs per innings weaker than Root.

While the West Indies batsmen are at their peak, England are looking to the future. If England go 2-0 up (which is perfectly plausible), they could have six players aged 24 or under (Sibley, Lawrence, Pope, Bess, Curran, Mahmood) in the dead rubber to ensure the old farts don’t break down with three tests over 21 days. Need to keep something in the tank for Pakistan.

Look out for bowler workloads. Tests on the 8th, 16th, 24th July. James Anderson is 37 years old. Roach and Holder are easily West Indies’ best bowlers. This might have some anti-cricket effects: if the opposition are 200-1 chasing 260 on the fifth day, do you take your best bowler off the field to rest for the next Test? Don’t want to risk them in a lost cause. No problem to fatigue (not injure) Reifer or Archer, but not the star bowlers.

And a left-field hypothesis, which I don’t really believe: Stokes will fail with the bat because he needs a crowd. He feeds off it. Away from thousands of fans he isn’t the same player. In six years of county cricket he averages 25. In the UAE he contributed 88-6.

PS. I’ve cut home advantage in my model to 10% (from 20%) to reflect the lack of crowd. No idea if that’s the right thing to do. The Conversation reckons it’s nil for crowd-free football. Betfair podcast thinks it’s also nil.

Appendix – Data tables

I had these spreadsheets in front of me as printouts when I appeared as a guest on three recent Betfair “Cricket only Bettor” podcasts, which you can listen to here, here and here.

West Indies Batsmen

West Indies Bowlers

England Batsmen

England Bowlers

Test partnerships – does it matter who bats with whom?

Does cricket lose something when we are dispelled of its myths? Some fictions are unhelpful, such as Michael Vaughan’s success without having thrived at county level. However, we like to believe in partnerships: every smile and punch of gloves boosting the batting of our heroes, spurring them on to greater heights.

Thus I write hesitantly – I am loathe to reduce cricket to a spreadsheet, even though I literally do that. Hopefully some unsolved X factors will remain after the stats revolution.

On to today’s topic. Last time we saw that right-left partnerships don’t influence white ball run rate. This post covers the currency of red ball cricket: averages. Does who you’re batting with impact your average?

Considering the period 2010 to today, seven pairs performed much better than expected based on the records of the individuals in that partnership. Two pairs performed worse. They are shown below, ordered by how surprising that out-performance is.

That’s nine outliers – seven good and two bad.

But what are the chances each outlier was just fluke? After all, Clarke & Ponting only had 20 partnerships in the 2010s. After this analysis of error bars on averages we have a way to answer that – by quantifying how likely it is that a specific average (eg. Jermaine Blackwood averaging 37 in England) is arrived at by chance, based on the sample size.

With 120 partnerships (min 20 innings) since 2010, we would expect six pairs to lie two standard deviations from expected average. Actually we have nine. On the face of it, that’s evidence that some duos do get a boost from batting together. However, two of the nine drop off the list with further scrutiny. Kayes and Iqbal happened to bat together more at home than away. Bell/Pietersen somehow had 19 of their 23 partnerships in the first innings. Adjust the calculations to reflect that, and we have seven outliers, whilst by chance we would expect to have six. In layman’s terms, if each duo batted together enough times, their partnership average would eventually reach their combined average.

Here’s the chart of all 120 players, plotting variance to expectation against frequency. Even with small sample sizes, most partnerships average within five runs of expectation.

Where does this leave us? Remembering that “absence of evidence is not evidence of absence“, the jury’s deliberations will continue, but they will now be leaning in favour of specific partnerships not making a significant impact on a player’s average. Cricket is a one on one sport, bowler against the batsman on strike.

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PS. How did I arrive at the expected average for a partnership? Start with the mean of the post-2010 average of the two players in each partnership. Add 1.5 runs for any partnership that isn’t two openers, on the basis that one of the batsmen will start the partnership with their eye-in. Add 4.6% for the extras that would be scored in that innings. It’s a slightly different formula for when a senior batsman is with a tailender.

PPS. Why the cut-off in 2010? “No balls” dropped off then. Here’s the 50 year history of extras in Test cricket. Extras count towards partnership totals, so the maths gets more involved when extras vary significantly by year.

Batting ability in Test cricket is not normally distributed (it just looks like it is).

How is talent distributed in elite cricket? Bell curve (ie. normal distribution), or something else? Here I’ll argue that the distribution of ability is the tail of a normal distribution. The evidence is strong at county level, but rather weaker for Test cricket. As you’ll see, I’ve not let that stop me.

1. Marathon Running & County Cricket

Let’s start with a different sport. Here’s the distribution of running performances for millions of marathon runners:

Fig 1 – Distribution of marathon times. Taken from Allen et al.: Reference-Dependent Preferences: Evidence from Marathon Runners. See here.

The spread of marathon times across the population is broadly a bell curve, but there are some subtleties: firstly, that the unfit are less likely to take up long distance running (myself included), so the distribution is lopsided. Secondly, marathon runners appear to have target times, and performances are bunched around times like four hours.

Focus on the distribution of the elite – the quicker the time, the fewer runners are capable of it. Lots of runners at the bottom of the elite pile, then fewer and fewer as the pace goes up.

County cricket fits that pattern (based on my ratings of how players across 2nd XI and the County Championship would fare in Division 1). Loads of quite talented players who could just about make the grade, whittled down to 22 who would average over 40.

Fig 2 – distribution of redballdata county batting ratings, min 30 innings. Excludes overseas players.

2. Test Cricket

Fans of Occam’s razor might want to look away now. This section sees me building a house on sand.

My previous post demonstrated that averages are a function of luck and talent. We know the impact of luck, we have the actual averages. Thus we can work backwards to estimate the distribution of batting talent. I’ll now suggest a distribution of batting ability in Test cricket.

We start by making a graph of the averages of batsmen in Test Cricket. Looks a teensy bit like a bell curve, and nothing like the County chart. There’s only 300 players so it’s not a smooth distribution.

Fig 3 – Career averages, batsmen minimum 20 matches, since 1970, batting in the top six.

a. Talent Distribution in Test Cricket

However, selection isn’t perfect. Nor is there a continuous supply of Test standard cricketers in each country. This means a sprinkling of selections who are of a lower standard. Also, each country is a different standard. This means the true distribution of Test batting ability is the sum of the curves for each country.

Putting all that together, the distribution takes the form:

Fig 4 – Suggested distribution of talent in Test Cricket. Each curve is the tail of a normal distribution plus a small number of weaker players. To reflect the relative strengths of cricketing nations (and variation over time), the Overall curve is the sum of three curves (for an inferior, average, and superior team).

That yellow curve is probably smoother in the real world. Still, not terrible as a first attempt at answering the question “what does the distribution of Test batting talent over the last 50 years look like”?

b. The Luck Curve

The median player had 75 completed innings, so I’ve used that to derive the spread in averages (versus “true” averages). A reminder: this comes from a simulation of many careers.

Fig 5 – impact of luck on average for a top order batsman that has been dismissed 75 times.

Strictly, I should merge many luck curves – a tight one for Tendulkar (292 dismissals, a wide one for Moin Khan (26 dismissals). Still, every journey starts with a single step.

c. Talent * Luck = Performance

We now combine the Talent and Luck curves (probability densities) and compare them to the observed distribution

Fig 6 – Actual batting averages vs a Theoretical distribution based on proposed luck and talent curves

Not a bad fit. Naturally, the Actual (blue) curve is noisy as there are only 300 players that meet the criteria for inclusion. There are fewer players with very high averages than the talent curve I’ve derived would indicate – implying the real talent curve drops off more steeply than mine.

Discussion

What use is knowing how talented players are (rather than just knowing how well they performed)? In order to judge if a player has been unlucky or is unsuited to Test cricket, one needs to know the level of talent they need to have.

If you feel uneasy about the hand-waving approach I’ve applied here, then don’t worry – because so do I. Tinkering to make one curve look like another (noisy) curve is not the most rigorous analysis I’ve done. Just take away the message that luck plays a big role in averages, and we can’t yet use numbers to know how talented Test batsmen really are.

Further reading

Always worth seeing if someone has asked this question in baseball. Here’s analysis that finds batting ability would be normally distributed if you assume fielding is 30% of the value of a player. I can’t comment on baseball, but for cricket that figure is too high. Thus it’s an interesting technique, but not contradictory to my curves. If one could quantify the value of fielding (and/or other attributes) for top order batsman, then the approach in the linked piece could be replicated.

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*Since 1970, batting in the top six, min 20 matches

Test cricket’s evolution and professionalism

Imagine a sport where only a handful of its best players participated full time. There would be an elite few head and shoulders above the rest, and a lot of weak players. That’s how the era of amateur cricket looks statistically.

Here I’ll demonstrate that the quantum leap in Test Cricket was the 1960s, with professionalism ensuring the brightest talent wasn’t lost to the game.

A 1950’s professional cricketer could earn twice what a manual labourer could.[1] A good wage, but sporting careers are short. There’s no way cricket was attracting all the talent that was out there. In 1963 British county cricket turned fully professional. I don’t know about the evolution in other countries, but it’s striking that in 1962 Richie Benaud was described as “a newspaper reporter by profession” when being recognised as one of Wisden’s Cricketers of the Year.

In the two decades after the Second World War, the depth of talent increased. We can see that in the distribution of batting averages:

Fig 1 – Top order Test averages. Min 10 Tests.

The 1960s distribution reflects a mature sport: lots of players of similar ability, a sprinkling of duffers, and few standing out from the crowd.

Contrast that with the 1930s – over a quarter of the players averaged over 50. Admittedly there were only 42 players that met the criteria, and averages were noisier because there were fewer Tests played then. Bradman’s average should be considered as a function of the era he played in: in the 1930s four others averaged over 65, nobody has achieved that in the last four decades.

There were far fewer batsmen averaging under 25 by the 1960s: this will be a function of a more talented player pool. Interestingly, this wasn’t driven by improving the batting of wicket-keepers: they averaged two runs per wicket less in the 1960s than the 1930s.

Here’s the trend year by year:

Fig 2 – “Mean absolute deviation” is a measure of the extent to which performances differ from the mean. The higher it is, the more outliers there were. While there is a lot of noise, the trend is of a reduction over time.

But what about all the developments since then- improvements in bats, coaching, and technique? These improve all players similarly, so don’t impact the mean absolute deviation. Thus, they aren’t detected by this technique: there will never be one number that says how high the standard of cricket was at a point in time.

For completeness, here’s the decade-by-decade view:

Fig 2 – “Mean absolute deviation” by decade. Top order batsmen, min 10 Tests.

The maturity of Test Cricket was complete by the 1960s. Note that there wasn’t significant impact from the addition of Test teams through the years: indicating sides were generally added when ready (some would say we waited too long).

Professionalism swelled the ranks of the most talented. What we don’t know is the proportion of the high potential players that ever play cricket: could Rooney have been better than Root?

The logical extension to this maturity analysis would be to look at T20 and/or women’s cricket. Let me know if you’d find this interesting.

***

P.S. while researching this piece, a story from the late David Sheppard about the social division between amateurs and professionals (like Tom Graveney) caught my eye…

When I was at Cambridge we played against Gloucestershire at Bristol. I had made some runs, and, as we came off the field, Tom Graveney, with whom I had made friends in 2nd XI matches said, “Well played, David.” A few minutes later the Gloucestershire captain walked into our dressing-room and came over to me. “I’m terribly sorry about Graveney’s impertinence,” he said. “I think you’ll find it won’t happen again”.[2]

[1] Rain Stops Play, Andrew Hignell

[2] Amateurs and professionals in post-war British sport, edited by Dilwyn Porter & Adrian Smith

Leg spin: What we can learn from Statsguru

My statistical goal is a theory of everything: expected averages for any situation. So far I’ve excluded the influence of match ups (specific bowler vs batsman) as being Very Difficult Indeed. That ends now: join me as I dip a toe into that field, starting with some analysis of leg spinners in Tests.

**Update 24/04/2020 – the methodology below was flawed: the Statsguru page I used reflects the score a batsman was on when dismissed, rather than the head-to-head score. Interestingly, after further work it looks like the conclusions were reasonably accurate, even if the workings weren’t.

1. Leg spinners and favour right handers

The logic for it being more expensive to bowl leg spin (LS) against left handed batsmen (LHB) in white ball cricket is that the batsman can play with the spin, and minor errors in line provide opportunities for scoring. Here’s CricViz on that topic.

In longer format cricket, I expected leg spinners to be agnostic to the batsman’s stance. Against right handers (RHB) a straight line threatens every kind of dismissal apart from timed out, while for LHB a line well outside off can still threaten the stumps and both edges, while asking the batsman to play well away from their body.

What does the data show? At the highest level of Test Cricket, nine of the ten leg spin bowlers sampled favour right handers. Expect a leggie to average 22% more against left handers in Tests.

Shane Warne took 708 Test wickets at 25, yet against LHB he was average. Still, that makes him significantly better than his competitors – none of the other recent leg spin bowlers averaged under 35 against LHB. What’s the reason? I think it’s the required line against left handers making bowled and LBW less likely. Against right handers bowled and LBW make up 37% of dismissals. For left handers that drops to 31%.

2. Elite leg spinners come into their own against the tail

There’s a neat split between Warne, MacGill, Kumble, Ahmed and the rest. The top four took 1,742 wickets at 28, while the other six took their wickets at 39. Individually, there’s not enough data on the six lesser players – so I’ve lumped them together to compare their careers to the elite four.

The ratio of Elite vs Second Rate averages reveals the trend: Elite leg spinners bamboozle lower order batsmen (anyone with a career average under 20).

What does this mean for strategy? Captains will intuitively know that a strong leg spinner is an asset against the tail. If you have an inferior leg spinner, how should you deploy them? I would argue they are best used against the top order (once the ball is no longer new), in order to keep the best bowlers fresh. It’s a question of managing resources and getting the best out of the attack over a 90 over day.

3. Elite bowlers are flattered by bowling at weaker batsmen

The weaker leg spinners claimed 58% of their wickets against batsmen who average 30+. For the elite four that figure is just 51%.

The above impact can flatter averages; for instance Stuart MacGill (42% wickets against top order, career average 29) was not so much better than Devendra Bishoo (61% wickets against top order, career average 37).

A full system would include this when rating bowlers: a rough estimate says MacGill’s true rating was 31, whilst Bishoo’s true average was 35. A quick check shows these adjusted averages are more in line with FC averages, indicating there’s a ring of truth to this.

Methodology

I’ll level with you – there are some assumptions here. Cricinfo’s excellent and free data gives a bowler’s averages split by batsmen (here’s MacGill’s). However, this doesn’t cover how many runs were conceded against batsmen who they haven’t dismissed. I’ve attributed the unallocated runs to batsmen in proportion to their average and number of matches played against that bowler.

***

That was fun! We’ve seen a hint of what matchups can do and I’m very late to the party. That said, I’ll stick to my guns: most patterns are just data mining and we need proper evidence (at the level of the above or better) before drawing conclusions. Those conclusions are best done at the “off spinner vs opening batsman” level rather than the “Moeen Ali to Dean Elgar” level.