Last wicket partnerships – continued

The last blog post looked at the expected average for a tenth wicket partnership, and here I’m going to examine some strategies to yield better results in the final leg of the innings.

Long-term number eleven batsmen (James Anderson, Makhaya Ntini and Trent Boult) have played enough innings that we can use their successes and failures to determine: what should the last pair do to maximise runs?

There are three main factors to be considered: proportion of balls faced by the number eleven, strike Rate for the number eleven, and strike rate for the senior batsman.

As flagged by Chrisps in the comments last week, we’d ideally also consider bowling and fielding strategies for each batsman, but sadly these aren’t publicly available.

STRATEGY 1: Manage the balls faced by the number eleven (take the single on the fourth ball of the over)

A number eleven gets out around every 20.8 balls. If they face a full over, there is a 26% chance they’ll be dismissed. That means the batting team should do whatever they can to keep the number eleven off strike, right?

Yes and no. During Anderson, Ntini and Boult’s most fruitful partnerships, they faced an average 45% of the strike.

Figure 1 – Anderson, Ntini & Boult’s successful partnerships vs proportion of balls faced

When Root and Anderson put on 198 against India in 2014, Root was carefully managing the strike: Anderson only faced the first ball of the over seven times in 53 overs. He faced the last ball of the over 42 times out of 53. So there’s a contradiction – the number eleven is being protected, and yet facing nearly half the deliveries. What’s going on?

The answer lies in the way Root protected Anderson: taking a single 20 times on the fourth ball of the over. By looking for a single on the fourth ball of the over, there were two further chances to rotate strike that over if Root didn’t find a gap. This gave Anderson just 41% of the strike, and crucially only three risky overs where Anderson had to face all six balls.

If the fielding side counter this strategy by defending the single for the last three balls of every over, there should be plenty of boundary opportunities for the senior batsman.

Figure 2: How batsmen approach sharing the strike when a top seven batsman is joined by a number eleven (partnerships 50 runs or more, since 2000).

The data shows three viable options: take the single from the fourth ball onwards (eg. Root), gamble and go ballistic (Watling) or trust a naturally defensive number eleven to block out an over (Collymore and Sharma).

STRATEGY 2: Keep usual strike rate for the number eleven (three runs per over or more)

Figure 3 – Anderson, Ntini & Boult’s successful partnerships vs their Strike Rate

Well there’s a surprise – the hypothesis was that the number eleven should defend, protecting his wicket while the senior batsman scored the runs. The converse is true: batting normally or counter attacking is the key to success. This may be because batting normally allows the number eleven to get off strike, and means a balanced field rather than an attacking one (think square leg, mid-on, cover rather than three more catchers).

STRATEGY 3: The aggressive senior batsman.

Figure 4 – Anderson, Ntini & Boult’s successful partnerships vs Senior batsman’s Strike Rate

Not too much to say here, just that attacking batting is good. It’s hard to accrue a big last wicket partnership at three an over unless the number eleven can be trusted to soak up a lot of deliveries.

Conclusion – for best tenth wicket results, the number eleven should bat positively but normally. Meanwhile the senior batsman should play aggressively on the first three balls of each over, before looking to take a single from the fourth ball onwards. Only expose a number eleven to a full over if you want a nice not-out to boost your average!

A quick word on methodology – the sampled innings for Figures 1, 3 and 4 only include those where runs were scored, and where the senior batsman played more than 30 innings in their career. The Strike Rates exclude the delivery where the wicket fell – otherwise shorter innings would be disproportionately affected by the wicket ball in which no runs are scored. The “% outperform” metric is how often the runs scored exceeded the mean expected runs for that duo for a given innings, taking into account whether they are at home or away.

Tenth wicket partnerships: Monsters and Modelling

Sri Lanka won a thriller last week (link), chasing down a target of 304 with one wicket in hand. The unbroken last wicket stand of 78 came out of nowhere. If they had been opening the batting for England, this would have been the ninth highest of the last 100 partnerships.

How common are these monster scores?

Considering tenth wicket partnerships since 2000, the Mean score is 14.5 runs, the Median eight, and the mean duration is 25 balls. The chance of scoring 78 or more is roughly 100-1. [1] 

Figure 1

That tells us that very high scores are rare, but what about the big scores – are there any patterns here?

  • Bias towards the first innings of the match
  • Most involve a top order batsman with the number eleven
  • Three blisteringly fast run-a-ball partnerships; most are significantly faster than the average 3.0 runs per over for Test Cricket in this era.
Figure 2

Modelling tenth wicket partnerships

If you have two openers that average 40, you can model the partnership as if it is one batsman that averages 40 – the distribution of scores will be the same. This holds true until you have batsmen with wildly different averages. What would you expect a partnership to yield when a top order batsman is left with a number eleven for company?

A model of expected average for a tenth wicket partnership was created, using the following inputs: each Batsman’s Career Average, Home/Away and the innings number within the match. Various combinations of the two batsmen’s averages were tested against the data since 2000. [2]

Results were tested in two ways. I) Measuring the mean square difference between expected and actual partnership, and II) Seeking a distribution where half the scores are above and half below the expected distribution

The best fit was that the partnership average is: Weaker batsman’s average + 20% of the difference between both batsmen’s averages.

Returning to Sri Lanka’s match winning partnership, Perera (Avg 35) and Fernando (Avg 7) would be expected to average (7) + (35-7)*0.2 = 12.6 for the tenth wicket. Adjust for it being the fourth innings, and being away from home, and the expected average drops below 10. Something else is missing – or that 78 partnership is still a miracle!

Figure 3 – Least likely tenth wicket partnerships

Strategy and Strike Rate

If the number eleven bats defensively, that gives more time for the senior batsman to score runs: the partnership for the tenth wicket is likely to be more lucrative.

Think Chris Martin – he averaged 2.5, but at a Strike Rate of 20 runs per 100 balls. Martin could expect to stick around for 12.5 balls. If he scored at a Strike Rate of 50, he would only last an average of 5.0 balls, and there would quickly be a marooned batsman at the other end.

Ignore Strike Rate and the 84 Chris Martin put on with Tim Southee in 2008 (link) was a one-in-27 million event. Adjust for bludgeoning Southee and circumspect Martin and that drops to 1,500-1.

There is an unquantified boost to the expected partnership through farming the strike to ensure the senior batsman faces more balls. Another increase comes through aggressive batting by the senior batsman. I will consider adding those factors to my Test Match Cricket Model, so it better reflects the reality of occasional monster last stands.

Conclusion

  • Expected value of the tenth wicket: Weaker batsman average + 20% of the difference between both batsmen’s averages.
  • A last wicket partnership is more successful if the number eleven defends, leaving the attacking batting to the senior batsman. If numbers ten and eleven are batting together, they should bat naturally.
  • More very high partnerships than my model expects, driven by attacking batting.

Further reading on batting partnerships

A powerful story, NSFW (because it is something of a tearjerker) https://www.cricketcountry.com/articles/bert-sutcliffe-and-bob-blair-at-ellis-park-a-fairytale-bigger-than-cricket-287471

A paper on batting strategy and partnerships in Tests. Limited in that it covers the general case, rather than a player-specific model. https://pdfs.semanticscholar.org/786b/fa723eb721b66fd6023b4a6f56394968087c.pdf


[1] 100-1 odds for an average last wicket pair. The 600-1 for Sri Lanka reflected the fourth innings, against a fantastic South African bowling attack.

[2] Note that only batsmen with more than 30 career innings were included and matches involving Bangladesh are excluded.

England Lions – red ball doom and gloom.

I’ve always been critical of selectors. Even as a little boy who couldn’t pronounce Sri Lanka (Scarry Lanka), I couldn’t get my head round Graham Gooch not being picked for England ‘A’ when he was dropped by England. My father said that the ‘A’ team was only for young players. That didn’t make sense to me.

I was reminded of that as England Lions got trousered by India ‘A’ this week. Having said nice things about England picking their best batsmen in the Test team, that praise won’t be repeated for Lions batting choices.

This piece showed expected Test averages based on the last three years of First Class and Second XI cricket. Using the same data, we can see where the Lions top seven rank among England’s batting options, and what they would expect to score at Test level.

The data shows Duckett and Pope are solid choices, who could easily find themselves playing in the 2019 Ashes. Billings and Mullaney are slightly left field based on 2016-18, but with stronger career records. Fair enough.

Holden and Gregory? Max Holden was England U19 captain, and is only 21 years old. Gregory has solid white ball numbers, and it could be that the one dayers were the main focus of this tour. I’d suggest that Holden and Gregory wouldn’t be in this squad based on domestic red ball performances.

Sam Hain is 248th on the redballdata.com ranking of England’s batting options, eight places below Toby Roland-Jones. Since 2016 his First Division runs have been at an average of 20 and Second Division runs at 33. Yes, he has a List A average of a stonking 58. Is he Joe Denly’s understudy for the number three role? No. Let’s just say he won’t be in my Fantasy Cricket team next year.

How did this top order perform? Between them they contributed 229-7 and 187-5 in the first “Test” and 99-7 & 145-7 in the second. A collective average of 19, which is just slightly worse than their expected average of 24 – this wasn’t an aberration, the England Lions are light on batting.

Why don’t teams pick their strongest ‘A’ team? Especially in the off season when it’s not like counties are being deprived of their best players. Are these two red ball games just an afterthought? The current selection should be so much better.

Revisiting predictions for West Indies vs England, 2019.

Putting predictions on this blog allows testing of prediction against results. In this post I’ll look back at what I said before England’s tour of the West Indies in 2019.

I was surprised how few concrete predictions were included in previous posts. Next series I may include player by player predictions, so there are more data points.

1.No reason to model Jennings’ expected Test average as anything other than 33. 

❌ Jennings averaged 16. Though it was only four innings, it’s hard to see that prediction as a success! The extra data takes his expected average down to 32.

2. One spinner is the right choice

✅ Rashid’s match figures of 26-1-117-0 with the ball and 12 & 1 with the bat showed England the error of their ways.

3. History says expected average by bowing type Spin 32 Pace 26

✅ Actual averages: spin 35 pace 21, which reflects the quality of bowing on display – both teams have better quicks than spinners.

4. West Indies’ best chance will come if their fast bowlers can keep England under 225 in one innings

✅ Both West Indies victories included innings where England scored under 225. England won the third Test scoring 277 & 361-5. I don’t really like this kind of prediction though: Cricket is won by taking 20 wickets and scoring more runs than your opponent. How you do that is unimportant.

5. England 2019 are at about the level of the 2005 Ashes side, by having no weak links rather than being packed with world-beating batsmen.

❓Most would say that England’s batting was stronger in the past, but the current team has huge potential. My view is that England’s current batting is fragile because it is not that good, while some pundits would have you believe that England are afflicted by “amazing-but-collapse-too-often syndrome”.

6. England have a one in three chance of Whitewashing the West Indies.

⚠️ I stand by this prediction- though hard to appraise the success of this. Just because it didn’t happen doesn’t mean there wasn’t a 33% chance of it. Equally if it did happen that wouldn’t tell us much from one prediction.

I’ll make more testable predictions next series.

Should Jennings’ expected average be reduced after the Bridgetown Test?

There has recently been interest in Keaton Jennings’ average against pace. Two failures in Barbados have stoked this discussion. His average (26) in 16 Tests is below his expected average (33) based on County performances over the last three years. Generally, I would choose the big sample size (County Cricket) over the smaller sample size (Tests), and so rate his expected average at 33, not 26.

But – can we learn anything about technical flaws from Jennings’ Test performances to change that view? Specifically his average against pace:

Keaton Jenningsaverage against pace (16.90) is the lowest of any opener to have played more than 15 Tests, for games in which ball-by-ball data is available.

Wisden (Jan 26th 2019, via Twitter)

I’ve had a look at his performances over the last 3 years on the county circuit. The hypothesis is that there are some very good pace bowlers in County Cricket, and as an opener Jennings will face them (a middle order batsman might be able to make hay without facing much of the best bowlers).

The data supports this hypothesis – 68% of the time he faces at least one opening bowler with Test experience.

Keaton Jennings has played two of the last three seasons in Division 1, scoring 11 hundreds, and making runs in a variety of conditions (including April and September- when the deck is stacked in the bowler’s favour). His three year average isn’t amazing, but the key point is that one can’t look at the above data and conclude that Jennings has a problem against pace bowling.

As an aside, this piece is a reminder that I need to build a way to combine the Test performances to the First Class performances to ensure I’m using every available data point in appraising batsmen.

Conclusion: There is no reason to model Jennings’ expected Test average as anything other than 33. Plenty of people will disagree with that!

Automatically declaring the third innings when the lead is 300 – Analysis

One of the benefits of twitter is hearing new ideas. Jonas (@cric_analytics) has suggested the third innings should pause when the lead reaches 300, then the fourth innings takes place.

That way, a team that’s winning doesn’t have to pointlessly bat until the lead is over 500, before crushing an inferior opponent. Here’s how Jonas puts it:

I’ve modelled how this would work in practice, with the aim of answering two questions:

  • Does this make the strong team more likely to win? (Probably)
  • Is the game over sooner? (Generally)

Here’s the summary from the single scenario I looked at:

Scenario: West Indies vs England, Bridgetown.

England have batted first and scored 360. West Indies slipped up and were bowled out for 210. We join the action at the lunch on day three. England lead by 150. Two versions of this were modelled: under the existing laws, and temporarily declaring the third innings if they score 150 more.

Let’s see what happens:

  • In 92% of cases England made it to 150 without being bowled out – and so, with a lead of 300, temporarily declared
  • West Indies scored under 300 83% of the time – so the third innings did not need to re-commence
  • When the West Indies scored more than 300, sometimes the game meandered to a bore draw because the West Indies couldn’t confidently declare

Here’s the distribution of match end times depending on which rules apply:

We can see that there’s a big shift towards Day 4 finishes under compulsory declaration at 300 – mainly from the team batting fourth being bowled out for less than 300.

Worth noting the result wasn’t significantly affected by the rules being used. This would be different in other scenarios – such as if there was less time in the game.

Conclusion – This could be very useful in county cricket (where matches are only 4 days long). Suggest more modelling is required (especially scenarios where the odds are shifted from the draw being favourite to a result being favourite). A trial in County Championship Division 2 would be fascinating.

West Indies vs England: Preview

West Indies can beat England against the odds, but they’ll need their pace bowlers to perform.

****

The blueprint – Bridgetown 2015. 1-0 down in the series, with a first innings deficit of 68, the West Indies were about to be batted out of the Test. Hearing a wicket fall, a reveller in the Party Stand asked “Was that Trott or Cook?” and was baffled to learn that it was in fact Root, and England were 28-4. The new ball had done the damage, and by the time 20 overs had been bowled it was 39-5 and the game was back in the balance.

West Indies were eventually set 192. Darren Bravo marshalled the batsmen to the target with five wickets in hand. The hosts had accrued only three scores over 30 in the Test, but somehow pulled off an unlikely victory, and drawn the series 1-1.

****

With that surprise firmly in mind, let’s make some informed predictions for the upcoming series.

1) One spinner is the right choice. This decade the average is 32 for spinners, 26 for pace bowlers. It may be that pitches are turning more than they used to, and it’s true that spinners get 37% of wickets in the Caribbean, but this turn hasn’t delivered cheaper wickets. That said, if a team can reliably judge a pitch as more spin friendly than the average West Indian pitch, then they should go with two spinners – selectors just need to be sure there will be more in the pitch for spinners than quicks before making that decision.

2) West Indies’ best chance will come if their fast bowlers can keep England under 225 in one innings. Turning pitches or not, the West Indies have no elite spinners. If they are going to win this series it will be through devastating fast bowling.

They are unlikely to amass buckets of runs – so Holder’s bowling unit needs to neutralise England’s batting. Specifically, if England score fewer than 225 in one innings, that sets up a target within the range of the West Indian batting.

****

Taking all factors into account, modelling suggests the probabilities for the first test are: 24% WI. 7% Draw. 69% Eng.

That translates to a one-in-three chance of England managing back to back whitewashes away from home. The last time England achieved that? 1889.

West Indies will probably lose: their batting and spin bowling is inferior to England’s. But if we’ve learned anything from the 2015 series, it’s that home advantage is real, and the new ball could do some serious damage, leaving mystified England supporters to ask “was that Burns or Jennings?” as Stokes returns to the pavilion.

Kohli’s ODI run ranges are as expected for a phenomenal batsman

Clive (@vanillawallah) was looking at Kohli’s scores in ODIs since the last World Cup, suggesting that:

  1. Kohli is consistent
  2. He succeeds more than he failures

To check this, I compared Kohli’s performances against what my model would expect him to do – Kohli’s run ranges are broadly in line with what you would expect given his average. His consistency is a consequence of his ability, rather than a specific trait of his batting.

I modelled 1,000 innings for Kohli batting at 3 for India, with an assumed average of 95 (his average over the last 54 games / 3 ½ years).

The results show slightly more single figure scores in the real world vs model, offsetting slightly fewer scores in the teens. This is likely due to small sample sizes.

Two interesting observations:

  1. In a quarter of innings he would (and did) score a hundred. Phenomenal.
  2. The run distribution is skewed towards the 30-50 range by Kohli running out of time – caused by India successfully chasing down targets and the match ending while he is mid-innings.

Rest of the Top 3

Clive also pulled in data on all other top 3 ODI batsmen since the last World Cup. This is a much larger sample size- and worth checking the distribution as a way of verifying my modelling.

Simulating 1,000 innings with two openers: one of whom averages 35, one of whom averages 45 reasonably reflects the real world distribution of scores that Clive showed.

Two exceptions:

– The real world having more low scores (probably from the times when weaker openers have been selected)

– More hundreds modelled than seen.

P.S. Appreciate this is White Ball ODI Cricket rather than Red Ball Data. Don’t tell the Branding Police.

England’s current Test batting, in the context of the last 20 years

In this post I consider the evolution of England’s batting – how it steadily improved through the 2000s, peaked in 2010-11 (as England became World Number 1), tailed off from 2013, and is only recently recovering as we enter 2019.

The Data

I took the career averages of the top 7 batsmen for each England Test since 2000, and adjusted them for the age of the batsmen (I’ll cover how I do that in a later post). To eliminate artificially low results, Nightwatchmen are excluded. Where someone only played a few Tests, I made a judgement about what their long term average would have been had they played more Tests.

To bring out the trend, the chart above is smoothed with a moving average of the last five Tests.

Evolution: 2000 to 2019

Weakest Team: 29th June 2000, vs West Indies (Home) – Age adjusted Average 218

Atherton, Ramprakash, Vaughan, Hick, Stewart, Knight, White

If you don’t want to remember how bad England used to be, I suggest you skip to the next paragraph. Don’t worry, we’ll be talking about 2005 soon enough.

Let’s reel off why this team was the weakest this century: England had no batsmen in the top 10. Over five tests the highest total England could manage was 303. Only Trescothick and Atherton averaged over 29. Ramprakash and Hick never settled at Test level. By 2000 Hick was 34 and Stewart was 35. The weakest link was White – averaging 25 in 30 Tests is not enough for a number 7. The need for “the next Botham” was real.

That England won that series 3-1 was down to Cork, Gough, Caddick and White dominating with the ball rather than England imposing themselves with the bat.

England vs West Indies in 2000 marked a watershed for West Indies cricket: this was their first series defeat in England since 1969. Their record in Tests in England since is W1 D2 L13. England were on the up.

2005 Ashes Winners – Age adjusted Average 268

Trescothick, Strauss, Vaughan, Bell, Pietersen, Flintoff, Jones.

That’s more like it. Five of the fifteen England batsmen in the modern era to average over 40. This was a good batting side (rather than a great one), with room for improvement at 6 and 7. Flintoff was a proper all-rounder – a luxury England had not had for a long time. He was an all-rounder with a career batting average of 32 however. Geriant Jones was carried that summer, averaging 25 (in line with his career average of 24).

Strongest Team: 26th December 2010, vs Australia (Away) – Total Average 305

Strauss, Cook, Trott, Pietersen, Collingwood, Bell, Prior

It’s too soon for many to realise just how good this team was: World no.1 from August 2011 to August 2012, with a strong enough four man bowling attack to confidently play six specialist batsmen.

In the 2010-11 Ashes series six of the top 7 averaged over 40; they accrued nine hundreds in only five tests.

But the side was aging: Collingwood 34, Strauss 33, Pietersen 30. The eldest (Strauss & the retiring Collingwood) needed to be replaced in 2011. As it was, Strauss stayed on for 18 tests, but would pass 100 only twice more, averaging 31 after the 2010/11 Ashes.

After a decade of continuous improvement the team had peaked. They remarkably managed to have a top 7 who all had career averages over 40. These are hard to replace: a Test team are doing well if they can unearth someone every other year who can average 40.

What happened next?

As players retired they were, predictably, hard to replace. England were also unlucky in that Pietersen and Trott didn’t go on to play full careers with England.

By March 2014 England’s ICC Test Rating had slumped to 100: they went from best in the world to average in 38 months. In May 2014 they lost a home series against Sri Lanka. Some stars (Cook and Root), some young players being played too early to succeed (Ali and Buttler) and Bell had gone on a bit too long.

Current Team: 23rd Jan 2019, vs West Indies (Away) – Expected Average 268

Jennings, Burns, Bairstow, Root, Stokes, Buttler, Foakes

Not bad, probably the best selections that could have made, and should be too strong for the West Indies.

It’s important to see this side for what it is: lacking in stars, yet well balanced with three all-rounders. With Ali bolstering the batting at 8, this team are likely to continue the trend of winning at home but losing away against the top 6.

Verifying the Data

To check this model (age adjusted batting average) against reality, I compared this to the ICC rankings. The correlation is clear. Worth noting that since the Age adjusted Batting Average is smoothed using a 5 point moving average, there is a time lag in the orange curve. This correlation is surprising as the ability of the top 7 batsmen makes up less than half of the strength of a team (the remainder being bowling ability and tail batting strength).

Conclusion: England 2019 are at about the level of the 2005 Ashes side, by having no weak links rather than being packed with world-beating batsmen.

35 is the new (and old) 40

Managers tend to pick a strategy that is the least likely to fail, rather then to pick a strategy that is most efficient. The pain of looking bad is worse than the gain of making the best move.

Moneyball (2003)

In the last 35 years England have had just 15 batsmen who averaged more than 40 over their career. Expectations should shift: aspire to players averaging 40; accept batsmen averaging 35.

The chart below may surprise you – it surprised me. How could barely any recent English batsman reach the benchmark set for them? Averaging 40 (at least in my head) was a minimum, not an elite average.

The data speaks for itself- 45 isn’t the new 40. 35 is the benchmark, and has been for a long time.

We, the red ball loving hordes (and our journalist generals) need to help the selectors by having realistic expectations.

The selectors should return the favour: stick with players that are good enough, even if they aren’t stars, and even if pundits are piling on the pressure.

Next time someone is 10 tests into their career, averaging 34 and with the data saying they would average 35 long term, let’s not call for a change because they aren’t scoring enough. Only remove them if a better prospect comes along – not someone with similar numbers who we might want to gamble on.

There’s a great case study: Andrew Strauss retired in 2012, and received wisdom is that he is yet to be replaced as an opener. We wanted the next Strauss. We should have been looking for the next Rob Key (15 tests averaging 31 between 2003-2005 while we waited for the next star batsman to come along).

Instead Cook was partnered by Compton (average 31) – Root (42) – Carberry (28) – Robson (31) – Trott (12) – Lyth (20) – Ali (14) – Hales (27) – Duckett (23) – Hameed (32) – Jennings (27) – Stoneman (28) – Jennings

Remember who Carberry got his runs against? An away Ashes series in 2013: Harris, Johnson, Siddle, Lyon, Watson. Those 281 runs were well earned.

With hindsight, pretty much every pick between Robson and Jennings was an error. England had viable alternatives for Strauss 3 times: Compton, Carberry and Robson. Having rejected them, playing people out of position (Trott / Ali) and gambling on youth (Duckett / Hameed) as the next cabs off the rank as England moved ever further down the list of possibles.

England chose weaker options because they weren’t willing to settle for a batsman averaging in the low-30s. That cost England runs- and since the selectors’ are employed to pick the best team possible, this is a failure. One they don’t get criticised enough for. Fear not, dear reader, we know England’s best batting options– and will collectively tut if the selectors deviate from them!

Conclusion: England should hold their nerve, even if Burns and Jennings are only averaging 33 coming into the Ashes.