They say that before you have studied Zen, a mountain is just a mountain. Then, as you study and gain greater insight, you slowly come to realise that it is more subtle and complex than that. A mountain is no longer just a mountain. When, after years of study, you finally achieve enlightenment, you discover that a mountain is… just a mountain.

The path to mastery is the same, for the monk, the teacher, the writer, or the bowler. It is the path from simplicity, through complexity, to simplicity.

The beginner uses simple, basic techniques. They are all he knows and all he can cope with. As he learns, he gains greater fluency in these. Then, as he grows more adept, he embraces more technical complexity and masters a greater variety of skills and methods. He studies more deeply the intricacies of his art, and experiments with a wider range of ideas.

Then the process reverses itself. After thousands of hours of immersion in the subtleties, and near endless refinements, he comes to understand what works best and what doesn't. The range and complexity of ideas on which he regularly relies start to shrink.

For the master craftsman, true mastery of his art involves a return to simplicity, a pared-down palette that he now wields to sublime effect. This is a simplicity born of understanding his true form, and different from the place where he started.

Cricket is a simple game, but one with endless subtleties and nuances that matter. We are allowed to take it apart to see how it works - just so long as we can put it back together again. I take the time to describe this because I suspect at some point you're going to think that I'm making a simple game very complicated. Don't worry - we will finish with simplicity.

There was plenty written and said on the subject of England bowling too short in the first Test at Lord's this summer against Pakistan. It is a perennial talking point and it will probably return again in the series against India. Let's pull it apart, explain how it works, and try to progress from there to some basic principles we can agree on.

To start with, what do we mean by length? For our purposes, length is the distance from the point where the ball bounces, to the batsman's stumps. In Test cricket, the average length for seam bowlers is roughly 7m, give or take half a metre (based on representative samples from Tests in all countries), and the vast majority (87.7%) of balls land between 2m and 10m.

The length of a delivery has two main effects. It dictates the height at which the ball will arrive at the batsman, and the amount of time he has to react after it bounces. Each of these has an impact on the danger the ball poses to the batsman and the opportunities it presents to him.

A delivery from an average fast bowler comes off the pitch at about 32 metres per second. The fastest recorded human reaction to a visual stimulus is 120 milliseconds (most people struggle to beat 200ms, even with training). It is safe to assume that most top-order Test batsmen are in the 1% of the population who can get anywhere close to the 120-180ms range. This means that the ball will travel 4-5m in the time that it takes a batsman to react to what he sees.

Determining the path of the ball after it pitches requires at least a metre or so of flight. So anything that pitches within 5-6m of the batsman doesn't leave him enough time to adjust his shot. If the batsman is on the front foot, his interception point is around 2m away from the stumps, so this puts the minimum length at which the batsman can start to react at about 8m.

And we see exactly this in the performance figures. In Test cricket, balls pitching in the 6-8m zone average 22.6 against top-order batsmen (from Nos. 1-6) - that is they take a wicket for every 22.6 runs they concede. Those in the 8-9m zone are nearly twice as expensive, averaging 40.1 runs per wicket.

This is the main reason that a traditional "good" length for a quick bowler is the area roughly 6-8m from the stumps. It is the length for an 80-85mph bowler that gives the ball the most room to deviate and beat the bat, without giving the batsman time to adjust to that deviation.

Outcomes for different lengths in all Tests* Ball type Length % balls bowled Ave Econ SR Half-volley <5m 10 43.7 5.5 48 Full length 5-6m 13 31.4 4.0 48 Good length 6-8m 43 22.6 2.0 67 Back of a length 8-9m 15 40.1 3.0 81 Short >9m 7 47.4 4.3 66

* All Tests for which Hawk-Eye data is available

Aware of the danger these balls pose, batsmen generally avoid attacking deliveries of this length. The harder you swing the bat, the smaller the margin for error, so playing an attacking shot significantly increases the chances of edging or missing the ball. Batsmen will, for the most part, leave or defend good-length balls and wait for a ball that is safer to attack.

Batsmen's intent by length Ball type Length % Attacked % Left Half-volley <5m 29 7 Full length 5-6m 29 11 Good length 6-8m 13 29 Back of a length 8-9m 17 19 Short >9m 26 12

* Rotating the strike and defending are the other two intent options

Clearly we are generalising here, but it is still a useful exercise in understanding the structure of the argument. For example, length is only one factor - a half-volley on the stumps averages 25.2 in Tests, but outside off stump it averages 72.4. But this is not the place to try and unravel the complex interplay of line, length and height. For now let's treat our different lengths as homogenous blocks. (If you do want to hear the full version, then feel free to buy me a pint and brace yourself for a very long evening, or read my book The Test, where these themes are explored at greater length.)

So in general, the evidence is clear. Averaged across a whole match there can be no dispute over the optimum length to bowl: around 6-8m from the stumps, a traditional good length, costs fewer runs per wicket than any other length - some of which take wickets more often. In England, a top-order wicket costs a smidge over 24 runs on a good length. Move a metre fuller and those wickets now cost 30 runs apiece - the opposition's expected total just went up by 20%.

The arithmetic is simple enough, then, for any team with the accuracy and patience to make use of it. Hit this length as often as you can and you will bowl the opposition out as cheaply as possible. In most situations the fielding team will happily trade 20 overs more in the field for bowling the opposition out for 40 runs fewer.

The apotheosis of the type of bowler who hit this length regularly is arguably the greatest fast bowler of all. In his three Tests at Lord's, Glenn McGrath took 26 wickets at an average of 11.5. Of the balls he bowled at Lord's, 61.5% were of that 6-8m length, and virtually nothing was fuller than that. Overall, for the matches in his career that we have data for, he hit a good length with 57.5% of the balls he bowled.

Highest good-length percentages* Player Good-length % Mohammad Asif 59.5 Ryan Sidebottom 59.1 Glenn McGrath 57.5 Bhuvneshwar Kumar 57.4 Vernon Philander 53.8

*Since the time Hawk-Eye data has been available

And we see the same pattern when we look at bowlers who are playing now. Of the bowlers who have delivered over 1000 balls since the start of 2016, the four with the highest 6-8m length percentage have the lowest bowling averages.

Girish TS / © ESPNcricinfo Ltd

One interesting aspect of these bowlers is that, although we think of them as pitch-it-up bowlers, Abbas, Philander and Kumar actually have the three lowest percentages of balls bowled fuller than 5m. They don't bowl half-volleys, they bang out length.

Why then do you hear ex-players and commentators urging the bowlers to pitch it up? Well, what they understand is that not all periods of a match are equal. There are times when conditions are in the bowler's favour, when taking wickets is easier and cheaper. Generally and most predictably, this comes at the start of the innings, when the ball is new. In particular, it is the case on the first morning, when the pitch is often at its most helpful. "Take advantage of these conditions", runs the argument. "Don't worry about conceding runs, bowl to take wickets."

(There is an extreme strand that says fuller is better regardless - all day, in all conditions. There is little or no evidence for this in the data. On average, a good length is a good length.)

As we can see from the first table in this article, going that metre or so fuller accelerates the game. Both wickets and runs come much quicker. So throwing it up there is your joker: rewards and penalties are doubled. Backing yourself to win this round of the game, you are raising the stakes while the odds are in your favour.

So if you had to play your joker at any point during a match, when would it be?

In England, top-order batsmen average 33.5 against pace bowlers in the first 30 overs of an innings, and 39.5 in the next 50. In the first innings the difference is even greater: 32.8 and 40.2 respectively. That is, wickets become 20% more expensive after lunch on the first day. This then seems like a sound argument for being more attacking in that first session. You may pay a little more in runs per wicket, but you will take your wickets much faster, capitalising on favourable conditions.

Bowling averages in Tests* in England, by session and ball type Ball type Length Overs 1-30 Overs 30+ Half-volley <5m 48.1 55.0 Full length 5-6m 28.8 34.4 Good length 6-8m 24.5 27.9 Back of a length 8-9m 38.1 62.9 Short >9m 53.7 67.5

* All Tests for which Hawk-Eye data is available

If you look at the above table carefully though, there is also an argument in favour of patience. We need to make sure that the price we are paying for our wickets on a full length before lunch (on special offer, though they are) is better than the price we will pay after lunch on a good length.

The full ball before lunch averages 28.8, the length ball after lunch averages 27.9. As such a small difference is not enough to distinguish between the two, neither strategy is demonstrably superior across the board. So we need to look more closely at different conditions. To do this we need to understand how different lengths affect the batsman, his options, and his likely success under different circumstances.

Here, the physics of the ball's trajectory starts to have a significant impact. First, it is common sense that a fuller ball will swing further. It is in the air for longer, and therefore has more time to deviate. And you see this in the data: the fuller the length the larger the average deviation in the air. (The causality doesn't all run one way in this relationship, but the gradient of the graph suggests that we can accept the above statement.)

Second, shorter balls deviate more off the wicket. They hit the ground with a greater vertical component to their velocity, and so are more likely to deviate off the pitch and to do so to a greater degree. A ball banged in on a good length (8m) hits the ground 30% harder than a half volley (3m), and deviates on average about 15% more. This is then exaggerated by the fact that any deviation on pitching will have a greater effect the further the ball travels afterwards.

Sideways movement for different lengths in all Tests* Ball type Length Ave swing (degrees) Ave seam movement (degrees) Yorker <2m 1.76 0.52 Half-volley 2-5m 1.67 0.62 Full length 5-6m 1.49 0.63 Good length 6-8m 1.33 0.69 Back of a length 8-9m 1.11 0.73 Short 9-10.5m 0.95 0.77 Bouncer >10.5m 0.67 0.81

* All Tests for which there is ball-tracking data

Third, fuller lengths bring the stumps into play more. On most English pitches, a ball landing in the 6-7m range will either hit the top of the stumps or bounce just over them. Balls fuller than that are unlikely to bounce over the stumps, so full balls are twice as likely to hit the stumps as length balls.

Percentage of balls hitting stumps in Tests* in England Ball type Length % hitting stumps Half-volley <5m 28 Full length 5-6m 22 Good length 6-8m 10 Back of a length 8-9m 2 Short >9m 1

* All Tests for which there is Hawk-Eye data

Finally, the batsman will play these different lengths in different ways. This turns out to be a key difference.

Let's take each of those points in turn. First, what effect does swing have on our lengths equation?

As you can see in the table below, if the ball swings less than 1.5 degrees then good length still trumps full length (so McGrath, not a big swinger of the ball, was pursuing exactly the right approach for his style of bowling). Even in England, with the Dukes ball, 68% of balls swing less than 1.5 degrees (all Tests for which there is Hawk-Eye data), so this is the default situation. Once the ball is moving extravagantly, though, the fuller length has a better record not only in strike rate but also in average.

Bowling average by degree of swing Ball type Length < 0.75 0.75-1.50 1.50-2.25 2.25-3.00 >3.00 Half-volley <5m 56.4 54.9 36.1 54.3 61.1 Full length 5-6m 33.7 47.5 19.6 20.9 29.3 Good length 6-8m 25.7 25.0 26.3 24.0 34.0 Back of a length 8-9m 48.0 61.8 40.3 31.3 35.5 43% 25% 13% 10% 9%

There is one more complication for the swing bowler. Because of the unpredictable nature of their art, they find it harder to hold a consistent line. They are more likely to let the ball slide onto the batsman's pads, or to give him width outside off. Length then becomes their only defence against being hit. So the swing bowler is simultaneously more incentivised to pitch it up, and more prone to losing control if he does so.

Now let's take a look at movment off the pitch. Most wickets in Test cricket (nearly 70%, from Tests for which we have ball-tracking) are generated by edges and misses. As a rule of thumb, one edge in seven will produce a wicket. The biggest predictor of whether a ball will be missed, edged or successfully hit is the degree to which it seams.

I've heard bowlers counter the pitch-it-up advice by saying that they bowl a good length because that's the length batsmen nick. There is some truth in this. Whether the batsman is attacking, defending, or trying to rotate the strike, he is more likely to edge or miss a good-length ball than one on a full length.

False shots by length and intent Ball type Length Defend Rotate Attack Missed Edged Missed Edged Missed Edged Half-volley <5m 3.4% 6.3% 2.8% 5.0% 4.8% 6.9% Full length 5-6m 4.7% 6.2% 3.4% 5.2% 6.1% 8.2% Good length 6-8m 8.2% 8.5% 7.2% 7.5% 10.7% 9.2% Back of a length 8-9m 5.6% 5.8% 6.5% 6.5% 10.2% 9.6% Short >9m 3.3% 4.6% 5.5% 5.5% 9.3% 8.7%

However, as we saw earlier (in the second table), a batsman is more likely to leave and less likely to attack good-length balls. This means that the overall figures are less clear-cut.

Percentages of false shots by length Ball type Length Edges Misses Half-volley <5m 6.9% 5.4% Full length 5-6m 7.8% 5.5% Good length 6-8m 6.7% 7.2% Back of a length 8-9m 5.8% 6.8% Short >9m 5.8% 6.7%

So this is why the fuller length has better strike rates: it induces more edges, and although it generates fewer misses, the balls that are missed are more likely to hit the stumps, and so produce more wickets.

If these distances sound large - after all, a metre sounds like a big target to hit - it is worth remembering that these areas are effectively much smaller due to the angle the ball is landing at. The difference in release angle between a ball that will land 6m away from the stumps, and one that will land 5m away is about 0.8 degrees. This is the same angular difference between hitting the top and bottom of the bullseye for a darts player. And darts players don't have to launch their projectile at 85mph.

Try it. Mark out two lines a metre apart on a full-ish length and see how many balls you can land between the two. Remember that the faster you bowl, the smaller the target becomes: the flatter trajectory of the ball makes the target effectively 25% smaller at 85mph than it is at a club bowler's 65mph. Pace and accuracy are not mutually exclusive, but for a number of reasons each makes the other considerably harder to achieve. Even for the most skilful bowlers, the levers they have at their disposal to adjust things like length are not as finely tuned as they might wish. So we aren't talking about putting every ball into any of these areas, and anyway, variation is a valuable part of the bowler's armoury. We are merely looking at the relative merits of moving some of the balls a bowler bowls from one length to another.

Glenn McGrath: the best argument in favour of bowling a good length Robert Cianflone / © Getty Images

Let's try to move in the direction of simplicity. In summary:

Full (5-6m) - gives the ball more time to swing, induces more attacking shots, brings the stumps into play more, generally has a lower strike rate.

Good (6-8m) - produces more seam movement, gives the ball more time to deviate, generally has the lowest average, and economy rate.

I've given you the basic facts from which you can draw your own conclusions. There seems to be a reasonable amount of truth and good sense on both sides, and more doubt than the more entrenched prognosticators will allow.

Going fuller in favourable conditions is one very valid tactic. But it seems clear that it is not the only one, nor is it demonstrably more effective than other alternatives except under certain conditions. If that statement is too pine-splintered, then I will come off the fence enough to say that I think the evidence justifies the following approach.

If you are not a swing bowler then do as the master did. McGrath's 560 wickets at 21 and all the evidence above suggest he wasn't wrong.

If swing is part of your arsenal, then you have a slightly subtler calculus:

- If the ball is swinging big - pitch it up.

- If it isn't, but it is seaming around, then either strategy is valid, so long as you think that this seam movement is going to fade.

- But if the pitch is likely to offer help throughout the innings, then you are better off being patient and holding that good length.

- Finally, if there is little sideways movement in the air or off the pitch, then hold your length… and good luck.

There is a rule of thumb in analysing sport that where the received wisdom differs from the mathematically most efficient strategy, then generally what the maths suggests is riskier and more aggressive than what pros do in practice. The stats say you should shoot three-pointers, run the ball on a fourth down, bowl first on a flat Test pitch, and attack the new ball in ODIs. All of these feel like gambles, and so they have traditionally been seen as cocky, over-aggressive or foolish.

We are all naturally risk-averse - it is hardwired into us for good evolutionary reasons - but those instincts work against us when evaluating even fairly simple strategies. You will miss more of those three-pointers - you will fail more often than if you take the easier shots. So you run the more conservative strategy. Stats, on the other hand, are bloodless, and fearless, and they don't hear the crowd groan as the ball bounces off the rim… again. They just know that by shooting more three-pointers you will average more points in the long run.

Then again there is also the momentum of the contest that none of these stats can capture. Bowlers don't want batsmen to get away to a good start. They would rather establish control early. This is the control that enables them to keep close catchers in, so that when the edge comes, it's caught, rather than going flying through a vacant third slip, where the captain just moved a man from to plug that hole in the covers through which the ball keeps disappearing for four. And there is the selflessness: creating pressure that helps the bowler at the other end.

There are few crafts more punishing than bowling fast in Test cricket, few sporting roles more cursed with long, bitter, toil-laden days in the heat and dirt. Raw and aching joints, the ruined feet, the fractured vertebrae; it is this that shapes the bodies and minds of those who endure it through lengthy careers.

They don't need the finely parsed statistical analysis above, because they have bowled thousands of overs and lived with the resulting pain and joy. In Greek mythology, Zeus decreed that mortal man could only learn truth through bitter experience; that wisdom must come through suffering.

"Even in our sleep, pain which cannot forget

falls drop by drop upon the heart

until, in our despair, against our will,

comes wisdom through the awful grace of God."



- Oresteia Aeschylus, 458BC

This is what we see when we watch Stuart Broad, James Anderson, or Philander - or McGrath, Curtly Ambrose or Courtney Walsh - in late career. We are looking at the pared-down palette of the master craftsman. There is over 100 Tests'-worth of pain-scoured wisdom behind every small adjustment of pace or line. There is undeniably consummate skill. But each last ounce of unnecessary complication has been burned away. It is not the crude simplicity of the novice but the refined elegance of the master. That is what drives the cost of their wickets steadily down, point by unforgiving decimal point. It is the difference between knowing something and having it burned into every last neuron.

It's worth noting that what these bowlers do on their good days is what they do on their bad days. Compare Broad's lengths at Lord's in the first Test against Pakistan with his lengths when he took 8 for 15 to win the Ashes at Trent Bridge, and you will see they are near identical.

Stuart Broad's lengths in the first ten overs Ball type Length Trent Bridge v Aus, 2015 Lord's v Pak, 2018 Half-volley <5m 9% 10% Full length 5-6m 22% 21% Good length 6-8m 49% 53% Back of a length 8-9m 16% 12% Short >9m 5% 4%

Or compare the lengths Anderson and Broad bowled at Lord's earlier this year with when they bowled out New Zealand for 68 there five years ago, taking all ten wickets between them. You will see that they bowled fuller this year. Or indeed, compare them with Mohammad Amir's lengths in his opening spell in the same match. They are certainly no shorter.

Broad, Anderson, Amir and McGrath at Lord's, first ten overs

Broad and Anderson Amir McGrath Ball type Length v NZ, 2013 v Pak, 2018 2018 2005 Half-volley <5m 7% 9% 8% 3% Full length 5-6m 9% 19% 9% 7% Good length 6-8m 56% 52% 62% 62% Back of a length 8-9m 19% 14% 17% 25% Short >9m 9% 6% 4% 3%

They are just doing what has brought them their greatest successes, and nearly a thousand Test wickets.

Because, when all is said and done, a mountain is just a mountain.

Nathan Leamon is the England Team Performance Analyst and England Cricket's Lead for Research and Innovation. His latest book is The Test

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