Why do we think Test chases of over 300 aren't all that tough?

Something doesn't feel right. The ball thumps into Roshen Silva's pads and England go up, but it feels like a theatre appeal. No one truly believes it. Sri Lanka started their chase needing over 300 runs and they still need over 150. Their top four are gone, but luck, fate, momentum, or whatever made-up thing you hold dear, is on their side.

The partnership has gone past 50, which is over 16% of the chase, and these two now appear permanent at the crease. Despite the early wickets, the tough pitch and England having a plethora of bowlers, you can see how Sri Lanka will win the second Test.

There's a noise that cricket fans make in chases like this, as if cricket's global consciousness tightens at once, and it squeaks. In a Test chase, partnerships bring this extra sense of assurance. Fans of the chasing side dare to dream, bowling fans panic, and cricket seems to be on the verge of making something magical happen. A lucky swipe that lands in a gap is no longer seen as a sign a wicket is coming; it's proof the game has changed. Oh, look, now crows are on the outfield; clearly they signify the death of this bowling attack.

All rational thinking suggests that the chasing side almost never wins when they chase big totals. We've seen them fail to do so our entire cricketing lives. Depending on your age, you've seen this in our incredible current batting era, the great Test years from the '70s to the '90s, or before that, in the days of uncovered pitches. And yet here you are, with all that cricket-watching knowledge and plenty of stories from your grandparents. You've read the books, swiped the notifications, listened to the wireless and sat in front of countless illegal streams, and yet you still believe.

We don't behave rationally in chases. In the history of Tests, a target of 300-plus has been set 666 times; only 30 times has the chase been successful. No matter how much this partnership feels like an indestructible force because of whatever cricket god you pray to, or what your cricket senses are telling you, the bowling team almost always wins with runs on the board. Despite your raised heart rate, in 300-plus chases, only 4.5% of the times do the batsmen win. It's less than a one-in-20 shot.

England win by 57 runs.

***

This decade, teams have won 3.2% of chases over 300. It's the lowest - by a distance - since the 1960s, when pitches were still uncovered. This decade also has the highest percentage of 300-plus chases set - 53% of all chases. So batsmen have never had to chase this many big totals before, and they've rarely been worse at it.

Fourth-innings batting has been a struggle this decade, as you can see from the runs-per-wicket average, which has dropped 15.4% from the last decade. It's the lowest average decades-wise since the 1910s. It's a batsman's game for three innings, then the bowlers take charge. (The 1940s looks like nothing else in fourth-innings history because it only had 27 fourth innings, which included a couple of big drawn scores, and a world-record chase.)

It's only a decade ago that fourth-innings batting was solid. Techniques have changed a lot in that time, but maybe pitches are also being allowed to slightly decay more, after the CEO pitches of the 2000s that were built to last five days. You could argue that there have been more fourth innings in Asia than ever before this decade, and Asia is a tough place to bat in the fourth innings. (In the '90s it was the second worst place to bat in the fourth innings, but in the '70s, '80s and 2000s it was the worst.)

So more Tests there would explain this dip, except, the fourth-innings average in Asia hasn't dipped like in other places. Despite the fact that limited-overs cricket has probably had more effect in Asia than anywhere else - perhaps bar the West Indies - the fall in Asia is only 3.5 runs per innings from the 2000s. And I say that only as a comparison to the drop elsewhere. In the West Indies it has dropped over six runs, in Zimbabwe and South Africa it has dropped over eight runs, and in England, the drop has been nine runs. This means for this decade Asia has been among the better places to bat last.

It is clear that batsmen haven't scored so few runs in the fourth innings in the last 100 years. All this while batsmen have dominated Tests. Batting in the fourth innings is tough, but it varies depending on what you chase.

Even through their period of supremacy Australia still carried the stigma of struggling in smaller chases. Pakistan have carried it seemingly forever. Australia have succeeded in 73% of fourth-innings chases of between 100 and 200 runs, whereas the overall success rate for that kind of chase is 69%. West Indies have the best record here, with 75% success.

Pakistan's reputation is not misplaced: their record in those chases is 63%, which even for Asia (68% of all such chases in Asia end in defeat for the chasing team) is really low. South Africa, for all their reputation as chokers in ODI cricket, are successful in 74% of these chases. It does mean, however, that even the best teams only win three out of four in what is thought of as a relatively simple chase. Bowling teams who set targets between 100 and 200 have won 46 of 297 matches, making it about a one in six chance.

Teams that chase under 100 have won 264 times, and lost only twice, so you have a 97% chance of getting those targets.

The interesting thing with chases of 200 to 250 is that it's a 50-50 win-loss situation. That target has been set 166 times, and if you set aside the 60 draws and one tie, there have been 53 wins and 52 losses.

But it seems like 250 - and not the more symbolic 300 - is where chases get tough. History says that one in almost three times, a target of between 201 and 250 will be chased down, but you're nearer one in five (18%) if the target is between 251 and 300.

That drops to one in ten once you look at 300 to 350. Which is obviously where most of the successful chases over 300 have been made. But every run over 300 just makes it so much harder. So if you are chasing over 350 you are worse than a four-in-100 shot.

It's not that the psychology of short chases doesn't exist either. Chasing a smaller total should be quite easy, yet it brings back thoughts of what batsmen fear: failure. You can't fail in a big chase; you are - despite moments of grand delusion - expected to lose. In small chases you're supposed to win, so you can only do what everyone thinks you will, or fail tragically.

Imagine being a batsman in one of these small chases where there has been a slight wobble before you. The ball is short of a length, 130kph, and bounces right into the zone from which you have played 10,000 back-foot punches through covers. But your arms are tighter, you're not feeling okay, the bloke at the other end is having trouble with the footmarks, and you think the next batsman in is soft, so you half-play your safest shot. The ball hits an indentation on the pitch, holds up the slightest amount, and balloons to cover-point. Then the next player strides in, gets two streaky boundaries, benefits from some panicked overthrows and the bowling's team back is broken.

Somehow in fourth-innings chases, we as cricket watchers convince ourselves - because of one ball sometimes - the least likely result will occur. Whatever that is. But if that's true in small chasing totals, it's never more obvious than in large totals.

The first successful 300-plus chase was completed in 1902. England set Australia 315, Clem Hill made 97 before Hugh Trumble's unbeaten 62 won the game. We've had 29 since then. Some are legendary, like Don Bradman and Arthur Morris for the Invincibles in Leeds in 1948. India's chase of 403 against West Indies changed the way West Indies played their cricket, and therefore how everyone played their cricket. And there was West Indies' own world-record chase against a near unbeatable Australian team in 2003. Until 1980, it had happened just nine times. The frequency of successful chases per Test hasn't changed much; we've just seen a lot more because we see more Tests.

This is why teams will continue to bat first when winning the toss. Despite what has been said about T20 and batting second, for international cricket, the best chance of winning in T20 or Tests is batting first. Even accounting for the difference in sample sizes (because the formats have not been around for the same amount of time), the fact is, batting first still seems to work.

Chasing has always been tough. Think of all the things that can go wrong in a chase. And it's important to factor them in because they happen often. The pitches break up through wear and tear, or they are designed to. Either way, batting in the last innings has always been grim.

Limited-overs cricket might have made chases feel more comfortable, but there has been no significant transfer of all these skills to Tests. Michael Bevan might have given us a template for chasing, but his plans were ODI-based. Batsmen now prepare more than ever for limited-overs cricket and those skills often work well in Tests when the pitch is still relatively flat, or consistent with bounce. But as it breaks up, swinging at balls in your wheelhouse, premeditating shots, and backing your instincts is hard. Power doesn't help as much when something fizzes out of the footholes. You don't have to overcome cracks too often in limited-overs cricket. It's not that batsmen are less skilful, it's that they are a different kind of skilled: less soft hands, more fast hands.

Even a team of expert chasers like Bevan, Virat Kohli, MS Dhoni and Kieron Pollard wouldn't be sure things chasing on a fourth or fifth day. Those guys do it on pitches that haven't deteriorated, in a format of the game that is set up to make it about as easy to set a total as chase it. They don't even have to factor in draws.

In Tests, there are significant differences to chasing in limited-overs. The first is the ball. The white ball isn't as good as the red one, and it doesn't last well; it ends up as little more than something for batsmen to hit. The red ball lasts longer, swings for longer, seams for longer, and can be replaced in big enough chases by a brand spanking new one.

Then there are the physical differences. You are more tired on day four or five. You react slower to the ball deviating, and you will not have the same power to hit boundaries, or speed for runs. But the biggest problem is the mental side. Tired people make poorer decisions. For the bowling team, they can afford a few poor choices, a few technical errors, and some overall blunders. The batting team have a much smaller allowance.

And Tests are five days of decisions, not just for captains but for fielders, batsmen and bowlers. Decision fatigue comes in, and your judgement gets worse. If you are chasing 300, unless the pitch is incredible, you will not be going at much quicker than 3.5 runs an over, which means it will take you 514 balls to get there. That is a lot of assessments to make after days of deciding, pushing your body, thinking about the game, and trying to survive a few short balls.

That's before we get to an age-old cricket truth: runs on the board matter. Cricketers are conditioned - through cricket groupthink and the game itself - to bat first and put a total on the board. The shared DNA of cricket has told us that runs on the board matter, and that affects our psychology as cricketers.

And if you want to really how much runs on the board matter, look at chases over 400. There have been 302 set, and only four won. When chasing between 201 and 400, teams have drawn 41% of the time. When chasing over 400, that drops to 19%. For teams chasing 400, historically there has been a one-in-five chance of drawing, and a one-in-75 chance of winning.

Think of all the changes in cricket: fitness, pitches, the death of leg-theory, fielding restrictions, and equipment to name but the obvious ones, and yet, after all this time, runs on the board - probably the first boring cricket truth uttered - still holds sway. Batting to chase, batting to survive, is hard.

***

So I have told you all this. But I do the research anew every time there is a chase. That's because I don't entirely trust it. I think perhaps I've misremembered; perhaps it has changed, surely batting is getting easier these days. They hit more boundaries now. Young batsmen are born without the crippling fear of the previous generations. Pitches have never been this flat.

Part of this is because of all the great things in cricket - the six over cover, the bouncer that swings towards the batsman's grill, or all of legspin - fourth-innings chases are the most primal.

You are watching someone go into the heart of darkness, enter the Coliseum, and throw stones at Goliath. Everything is stacked against them. It always has been, it can't possibly end well, yet you can't help hope, or worry. The hero gets the girl; the mother finds her son; even in tragedy, there is a moral redemption. It doesn't matter if they can, it's the "maybe they can" that hooks you. The once-in-a-lifetime narrative, the "this time" feel you get. You're going to see something special and be a small part of it.

When England were all out for 230 in Colombo in November, Sri Lanka needed 327 to win the third Test. Sri Lanka had only made that many runs once in the entire series. They looked down, and overnight they were 53 for 4. But Kusal Mendis couldn't stop middling the ball, and he wasn't batting like a player who averages in the mid-30s. This was going to be the moment he lived up to the surrounding hype of his potential.

And then, he's run out by a direct hit from the outfield, possibly because they forgot that Jack Leach bowls left-arm but throws right. I'm snapped back to reality; they can't win this. Obviously.

Roshen Silva was at the other end, and if there is anything Silva does at the crease, it's act like he's not going anywhere. He edges, nudges and misses, but all seems right, like he knows what he's doing. Silva keeps going, often wearing his cap, like some throwback to the '70s cricketer who doesn't care that much. He's all late hands, small shots and casual elegance. He seems so unflustered by all this that you can see him trot to victory. But Moeen Ali traps him, England review, and Silva is gone. Again, why would I believe?

Silva is the ninth wicket, Sri Lanka still need 101 to win. The highest ever partnership for the last wicket in a fourth innings is 118, between Nathan Astle and Chris Cairns. No other tenth-wicket partnership in a fourth innings has ever passed 87. Malinda Pushpakumara has a top score of 80 in first-class cricket, from ten years ago. Suranga Lakmal has never passed 42 in Tests. The highest fourth-innings partnership to win a match is 57, between Inzamam-ul-Haq and Mushtaq Ahmed. I know all of this, I have it all in front of me, but...

Pushpakumara is slogging the ball, Lakmal's forward defence is made of granite, and England suddenly look tired. They limp their way through the extra half-hour before tea, and I think, this is something, it's gonna happen, they will do this. Forget all the history, the numbers, the reality, Pushpakumara even survives a vicious hit from Stuart Broad. And if you need a better sign, straight afterwards he's right in line, middle of the bat. David just blocked Goliath.

Sure, statistically it was a one-in-twenty shot of happening when they started, and now it's probably one in 100, but maybe, just maybe, this time it will be the one.

England win by 42 runs.