What if the 2005 Ashes had been a draft?

What would happen if the 2005 Ashes series started with a draft? I ran this scenario as a way to test my upgraded Test match model. By enlisting outsiders to draft the teams, they were then eagle-eyed in reviewing the results (thanks to Rob and Pud for their contribution).

Brilliantly, the series was decided in the last hour at the Oval, with Michael Vaughan shepherding the tail against the new ball.

Model updates

Since the last iteration I’ve added matchups, refreshed ground data, added realistic spin/seam performance by innings, and had another go at lifelike bowling changes.

With this much improvement comes lots of testing, and this exercise is just one small part of that.

Rating Players

Instead of career averages, I used performances up to July 2005 to rate the players. This is how I would have rated players at the time – serving as an additional check of my ratings process.

It throws up a few oddities: Having averaged 54 over the last four years’ County Championship, Rob Key looked Kevin Pietersen’s equal.

The Draft

Squad analysis

Rob foolishly excluded Martyn and Thorpe, but we’ll let him off because England dropped Thorpe in the real world.

Gilchrist is so much better than Geriant Jones that it was a surprise Gilchrist was eighth pick: there was huge value in securing his services early.

Clever from Rob to grab Flintoff and Warne. Once he had done that, there was a premium on Collingwood as the last all rounder: he should have been earlier than 18th pick.

The Series

Rob negotiated a tricky chase of 190 at Lord’s before comfortable back-to-back wins for Pud at Trent Bridge and Edgbaston. McGrath’s match figures of 6-74 at Edgbaston exposed Rob’s tail.

Hubris set in for Pud at Headingley – winning the toss and batting, nobody made it to 30. Then all four bowlers conceded centuries as Rob amassed 504 (Strauss 235*) to set up a comfortable win.

All square two-all going to the Oval. A characteristically flat pitch, yet the pressure almost got to Rob at the toss. With Warne struggling, Rob considered fielding first before his better judgement kicked in.

Three scores in excess of 400 put the game out of Pud’s reach, leaving him 102 overs to survive to share the Ashes. Wickets fell steadily. Collingwood (23) was fifth man out just after lunch, leaving Vaughan (102*) and Gilchrist much to do.

Bizarrely, Gilchrist (52 from 68) counter-attacked. Pud’s views when Warne bagged the wicket are unbroadcastable. With ten overs to go, Vaughan and Harmison were standing firm, but two wickets in two balls for Hoggard won the match and the series, for Rob.

Batting Averages

Andrew Strauss was “Man of the Series” for his 557 runs at an average of 80.

Bowling Averages

Warne’s performance was unlucky. His average of 46 was unexpected. Subsequent testing confirmed that he should have thrived against Pud’s numerous right handers, but it didn’t happen for him.

Model upgrades required

– Bring back best bowlers when a team is seven or eight down. Collingwood shouldn’t have bowled at the tail as much as he did – this is why Collingwood bagged 19 wickets at 23.

– Build in the ability to play for the draw. Gilchrist’s five-an-over antics were unlikely on the fifth day with 300 required to win.

Conclusion

A decent hour’s entertainment and two improvements for the model. A success.

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.

***

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

Adding error bars to averages

A batting average is a record of what a player has achieved. The fewer matches played, the less meaningful that average. I propose an approach to estimate the range of possible long term averages a player might have, based on their current average plus the number of innings played. I’ll talk about Mark Ramprakash too, just to keep things fun.

Imagine a new batsman on the scene. Assume we magically know they have the technique to average exactly 30. By using a Monte Carlo simulation, we can see the paths their average might take by chance.*

Fig 1 – Expected range of averages after 15/30/100 innings. Even after 30 innings a player’s data may not reflect their talent, with 1% averaging 20, and another 1% averaging 40- just through luck. Curves should be smooth but I only ran the simulation 150,000 times, causing some noise.

By embracing the uncertainty in averages we can better interpret them. Using the simulated data, we can estimate the uncertainty (standard deviation) of a player’s average once they have played a given number of games.**

Fig 2 – Standard deviation in batting average as a function of innings played and average. Note that 68% of results lie within one standard deviation of the mean, and 95% within two standard deviations. Also note the rapid reduction in uncertainty during the first 40 innings.

A standard deviation of 10 means a 95% chance the true average is within 20 runs of the observed average. That’s where we are for a top order batsman after 15 innings: it’s too early to use the data to conclude, though qualitative judgements on technique are possible.

There are four practical uses for this analysis:

1. Identifying players out of their depth

Mark Ramprakash averaged 53 in First Class but only half as much in Tests. We can now quantify how likely it is that he wasn’t going to cut it as a Test batsman: and thus propose an approach for when players should be dropped.

Ramprakash’s career: 671 dismissals in First Class means a negligible level of uncertainty in his FC abilities (albeit we could fit an age curve to this for a better estimate of his peak talent). 86 Test dismissals averaging 27.3 (that takes me back to the 1990s).

Let’s assume Tests were about 20% harder than 1990s First Class cricket. Ramps’ theoretical Test average would be 53 * 0.8 = 42.4. Now for the distribution of averages for a batsman with that skill level playing 86 innings:

Fig 3: Range of averages after 86 dismissals if a player’s true average were 42.4 (ie. the implied average Ramprakash would have had in Tests based on his FC record). Note that over the 2,000 iterations none came out with an average lower than Ramprakash’s 27.42.

Figure 3 tells us it’s almost certain Ramprakash wasn’t the same player in Tests.

But when should he have been dropped? He got a lot of chances. Assume the weakest specialist batsman averages 35. A player should be dropped when they are underperforming the reasonable range of scores that a batsman averaging 35 would produce.

Fig 4 – chance a player was unlucky vs dismissals. Note this is for a player averaging 27 who needs to average 35. The further their performance is from the target average, the faster it becomes clear that it’s not just bad luck.

We can see that after 86 dismissals there was a less than 2% chance Ramprakash was capable of averaging 35 in Tests***. Personally, once a player is down to a 15% chance of just having been unlucky, I’d be looking to drop them. That’s 25 innings averaging 27 or under. There’s some evidence that England are already thinking along these lines. Jennings got 31 Test innings, (averaging 25), Denly 26 (30), Compton 27 (29), Malan 26 (28), Hales 21 (27), Vince 22 (25), Stoneman 19 (28). Note that a stronger county or 50 over record should get a player more caps- as it increases the chance that early Test struggles were bad luck (after 30 Test innings Kallis averaged 29, he ended up averaging 55).

I’m intrigued by the possibilities this method presents – I’ll follow up at a later date by looking at promising 2nd XI players who have struggled in County Cricket, and assessing whether they deserve another shot, or they’ve probably had their chips.

2. Adding error bars to averages

Remember here where I analyzed county players by expected D1 average? I now have the tools to add error bars to those ratings. Back in September I rated Pope above Root. What I wasn’t able to do at that time was reflect the uncertainty in Pope’s ranking because he only had 42 completed innings. Will cover that in a future blog post (with two small children at home, it’s surprisingly difficult to find time for analysis). Spoiler alert – after that many innings, we can say Pope’s expected Division 1 average was 61 (+/-14).

3. Modelling

I can use the uncertainty in Pope’s rating when modelling match performance. Something like for each innings assigning him an expected average based on the distribution of possible averages he might end up with in the long term. That uncertainty will be one of the inputs in my next Test match model (along with Matchups, realistic bowling changes, impact of ball age).

There will be greater uncertainty in a player’s rating when they have just stepped up or down a level.

4. Matchups

We can move from the limited “Jones averages 31 against left handers” to the precise “Jones averages 31 +/- 12 against left handers”, just by taking into account the number of dismissals involved. The cricketing world can banish the cherry pickers and charlatans with this simple change, where stats come with error bars.

***

There’s plenty to chew on here. I’ve not found any similar analysis of cricket before – kindly drop me a line and tell me what you think.

* A bit more detail – my model assumes a geometric distribution of innings-by-innings scoring. With that, one can assign probabilities of all possible outcomes to each ball, then simulate an innings ball-by-ball. To see the spread of outcomes after 100 innings, I ran the simulation 150,000 times, then grouped scores into 1,500 batches of 100 innings. Previous discussion about the limitations of using the first 30 innings as a guide to future performance is here.

** This isn’t perfect. This method estimates the range of observed averages from a given level of ability. In the real world it’s the other way around. That’s a more complicated calculation.

*** Actually slightly better than 2%, because his first class record was so strong (114 hundreds). Ramprakash was an unusual case: there was an argument for him playing far fewer Tests, and an equally good one for him to have been managed better and picked more consistently. I did a twitter poll which was split down the middle on these two choices. Nobody thought stopping slightly earlier would have been the right choice.

First Day Blues – when multiple debutants struggled with the bat

44 Test players picked up a pair on debut. This article covers when a raft of new faces are introduced, and things don’t go to plan.

While looking at some proper analysis (“has professionalism seen an increase in the depth of batting lineups?”), I noticed the torrid time Pakistan Women had at the hands of Denmark in the 1997 Women’s World Cup. That inspired me to trawl through the records and see what we can learn from history.

This could be interpreted as being somewhat cruel – that’s not my intention. Just a bit of trivia, and the pleasure of hearing some new stories from scorecards of the past.

5. Sri Lanka vs Pakistan, 1994 Test. Pakistan won by an innings and 52 runs. Debutants scored 19-6. Average 3.2 runs per wicket.

In their defence, two of the three hapless debutants were batting at 10 and 11 (see here). Also Pakistan had Younis, Akram and Mushtaq Ahmed.

4. New Zealand vs Australia, 1946 Test. Australia won by an innings and 103 runs. Debutants scored 35-12. Average 2.9 runs per wicket.

Hard to be too critical as countries rebuilt after World War Two. New Zealand were outclassed, making just 96 runs in the match. Len Butterfield and Gordon Rowe bagged two of the 44 pairs mentioned above. 32 year old Butterfield went wicketless in his only Test, and final First Class match.

There were two silver linings. It was the only Test for Ces Burke (2-30) thus securing a career average of 15. Also, New Zealand didn’t stay in the doldrums for long: going on an unbeaten run of six draws after this defeat.

3. Turkey vs Luxembourg, 2019 T20I. Luxembourg won by 8 wickets. Debutants scored 21-10. Average 2.1 runs per wicket.

The Romania Cup in 2019 is best known for bringing Pavel Florin into the limelight. It also yielded this blowout – 21 runs off the bat, 28 all out. One boundary in 69 balls of T20, the top scorer made seven.

During the tournament Turkey were rolled for the three lowest T20I scores ever recorded. On two of these occasions they were bowled out in the first ten overs.

Luxembourg’s chase is on Youtube. Turkey look really raw – at 21:10 Serkan Kizilkaya takes a wicket while fine leg was sprinting to third man, having not noticed the single off the previous ball.

Let’s try to “take the positives”: Peshawar Zalmi of the Pakistan Super League hosted two of the Turkish team during the 2019 PSL, as part of a programme to support Turkey Developing Sports Branches Federation. One success was the development of 19-year-old Mehmat Sert, whose 42 runs were 31% of Turkey’s tally in the Romania Cup.

2. Pakistan Women vs Denmark Women, 1997 ODI. Denmark Women won by 8 wickets. Debutants scored 3-6. Average 0.5 runs per wicket.

This is my favourite of the five tales. Denmark Women, in the ’97 World Cup, beating Pakistan. There’s no writeup I can find, so crumbs from the scorecard will do:

Pakistan were inserted. From 58-4 when Asma Farzand was run out, the other five debutants contributed 0-5 from 19 balls as Susanne Neilsen and Janni Jonsson ran amok. Somehow (if Cricinfo is to be believed), Shazia Hassan managed to be LBW without facing a ball.

There were 29 extras in Pakistan’s 65 all out – 45% of the runs were sundries. Let me know if you can find a higher ratio in international adult Cricket.

Despite it being a limited overs game, Pakistan’s quickest scorer went at 28 runs per hundred balls.

1. Mali Women vs Rwanda Women, 2019 T20. Rwanda Women won by 10 wickets. Debutants scored 1-10. Average 0.1 runs per wicket.

The card: 1 0 0 0 0 0 0 0 0 0* 0

Rwanda truly turned the screw. Six wicket maidens and two maidens. They knocked the target off in four balls – just think of the net run rate.

Take pity on Margueritte Vumiliya – Rwanda’s opening bowler had figures of 3-3-0-2 and got pipped to the player of the match award.

I mentioned Turkey being bowled out twice in under 10 overs. The only other international side to manage that was Mali Women. Twice.

***

Just because New Zealand and Sri Lanka went on to become strong teams, doesn’t mean that Turkey or Mali Women will. Denmark Women folded in 1999. What did we learn from this? Nothing. In my excitement to say something about Denmark Women’s win in 1997, I’ve created a listicle.

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

How to win a Super Over

I had a piece published in Vox Cricket’s first issue.

Suggest you read the full article there. In case you don’t fancy clicking, here are the key drivers to Super Over success…

  1. Score at least twelve runs if batting first
  1. Pick a set batsman if batting first
  1. Don’t let the number three play it safe if batting first
  1. Stay calm when chasing
  2. Pick a bowler to trouble their opening batsmen
  3. Put the best batsman on strike for the first ball
  4. Plan for a second super over

That’s seven factors without even considering lines, lengths, field placings or shot selection. Super Overs might look like a six ball thrashabout – but there are subtle forces at play.

Women’s T20 World Cup – Rating the teams

Now that every team (bar Pakistan) have played, I can use the batting and bowling records of each starting XI to paint a picture of what we can expect to happen in the group stages.

This is a quick and dirty piece of analysis – I’ve only used ODI and T20I data between the top nine teams. Scarcity of T20I data meant ODI was used as a proxy – scaling down the averages by 76% and increasing the strike rates by 147%. Time will tell how good this method is.

Somehow watching sport without understanding context and probabilities no longer satisfies me – I want to know what is happening, and to do that data is required. Hence this piece.

The below chart ranks batting strength on the x-axis (expected runs on an average pitch against an average attack). The y-axis is the same but for runs conceded. The ideal team would be in the bottom right of the chart.

The big three stand out: Australia, New Zealand and England. These are consistent with the ICC rankings.

Let’s look at the groups.

Group A is marginally stronger. Despite beating Australia, India aren’t all that hot at batting – remove Shafali Verma early and the rest of the order are unlikely to score at much over a run a ball. Both India’s wins have come after Verma set a platform. Bangladesh have what is on paper an economical bowling attack, though having slipped up against India, they’ll have a tall order containing Australia and New Zealand.

Current expectation is that two of Australia, New Zealand and India should go through. Australia vs New Zealand on 2nd March is the final game of the group, and is likely to decide both who goes through and the position they go through in.

Group B is more clear cut. England lost to South Africa, which was seen as something of an upset, though player data indicates the sides are fairly well matched.

Aside from Chloe Tryon, South Africa aren’t an explosive batting unit. What they have in their favour is that they are dependable. Strong averages down the order mean they will rarely get rolled. That should be good enough to get them three wins out of four and into the semi finals. Note that the women’s version of T20 cricket is subtly different – with lower averages, teams are at much greater risk of being bowled out: so the averages of the lower middle order matter.

England are a similar proposition to South Africa – no stars with the bat, yet a top eight who should all yield more than a run a ball. Hard to see anyone other than England and South Africa progressing.

Being frank, West Indies and Pakistan are holed below the water line once three wickets are down. Look out for them wasting good starts.

Wrapping up, it’s hard to look past the big three teams. Still, South Africa at odds of 14-1 look tempting since I’d expect them to be the fourth semi-finalist. (Odds as at 25th Feb).