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There is one thing Test cricket has over one-dayers and T20: the fourth innings. The drama tends to be most intense in its final act, throwing up tougher tests than the other forms. So turn your eye with me, for a moment, to two contrasting fourth-innings performances from the last couple of seasons.First, Australia v India, Adelaide, December 13, 2014, the first Test of the series. Australia declared their second innings at the start of the fifth day, leaving India a target of 364 in 98 overs. Ordinarily India would have tried to bat the day through: safety first, always, from Merchant to Gavaskar to Dhoni. But Virat Kohli, young and brash, without the baggage and dogmas of the past, and captaining in a Test for the first time, decided to go for a win. India played aggressively, and Kohli led from the front with a sparkling 141. India lost by 48 runs.Second, India v South Africa, New Delhi, December 6, 2015. The fourth innings began on the fourth day, South Africa needing 481 runs in around a day and a half. They did not even consider chasing. Not only that, they didnt even seem to want to score. The batsmen played compact, risk-free cricket, not bothered about running well or putting loose balls away. They let go whatever was obviously missing the stumps, and played defensively to everything else. Hashim Amla, the captain, made 25 off 244 balls, his strike rate of 10.24 the slowest for any Test innings lasting over 200 balls. AB de Villiers, who arguably has a greater range of strokes than any batsman in the history of the game, made 43 off 297 balls. The Indian spinners broke through anyway. South Africa lost by 337 runs.One captain was aggressive and went for the win. The other was ultra-defensive. Both lost. So here are two related questions. One, was the approach of the two captains wrong? Two, should we judge the quality of their decisions according to the result?Im going to argue that not only did Kohli and Amla make the right decision, they essentially made the same decision.Once upon a time, I used to be a cricket writer, and Ive lost count of the series I covered for cricinfo.com (as it was then). Then I moved to other things, which included playing poker professionally for a few years. The most important lesson I learned from poker changed the way I looked at the world - and at cricket. I learnt to think probabilistically.Let me give you an example of probabilistic thinking with the simplest illustration: a coin toss. An evenly weighted coin will fall heads 50% of the time and tails the other 50%. Lets say I come to you with a fair coin, and tell you that we will flip the coin once. I will give you 51 paise if its heads and you will give me 49 paise if its tails.Heres how a poker player thinks in your position. First, he calculates the Expected Value (EV) of the spin. If you were to flip the coin 100 times, youd expect to win 51 paise 50 times and lose 49 paise 50 times, for a total profit of 100 paise. Divide that by 100 and you get the EV of one throw: one paisa. So the proposition is what a poker player would call Plus-EV (or +EV, as Ill write from now).The value of your decision is one paisa. But the individual outcome is entirely different - and entirely misleading if you view it in a vacuum. If the coin lands tails - as it will half the time - that will not mean that your decision to call heads was a bad one.We can extend this thought experiment. I could ask you to pay me 98 paise in return for tossing the coin under these terms 100 times. As the EV of 100 throws is 100 paise, the proposition itself is worth 2 paise to you. Similarly, I could ask you for 150 paise for 100 throws, and if youre not thinking clearly in terms of EV, you might imagine the EV of each throw to be 2 paise instead of 1 (thats our first instinct, since 51 minus 49 = 2), and accept, thinking youre +EV by 50 paise when youre actually -EV by that much. Note, though, that the outcome will seldom match the profitability of the decision. You might get 80 heads or 80 tails, as can happen. But in the long run, after millions of coin tosses, you will break the bank.Poker is basically just this. Every decision carries an EV, and good players learn to calculate it to the best of their ability, and to make the most +EV decision at any given point. If they keep doing this over a period of time, they end up profitable. But the thing to remember is that you are making short-term decisions with only long-term outcomes in mind. What happens in any one hand says nothing about the quality of your decision.This focus on the long run is best expressed in a cliché every poker player is familiar with: dont be results-oriented (this refers to short-term results, of course). You may flip a coin ten times and see it land tails eight times. That doesnt mean your decision to bet on heads was wrong. Now this might make it seem that poker is all about luck, and luck does indeed play a huge role, especially in the short term over a single hand or session. The skill in poker lies in understanding and manipulating the luck, and this skill manifests only in the long run. That is why poker players look to play as many hands as possible, to compress the long run as much as they can, put in volume. If you flip that coin millions of times, the results will converge towards the expected value, and your accumulated 51 paises will make you filthy rich.One way to think about probability is to imagine parallel universes. You flip an evenly weighted coin, and instantly the world splits into 1000 parallel worlds, and the coin falls heads in 500 of them and tails in the other 500. You flip again and these universes are split into units of 250, each showing sequences of HH, HT, TH and TT. You keep flipping.This is true for everything that happens. Every single thing that happens in this world (or may happen) has a probability attached to it. These probabilities change at every instant, affected by all other events to some degree or the other. So imagine, in every single moment, for every single event, the parallel universes multiplying. You can increase or decrease the number of hypothetical parallel universes depending on how granular you wish to make the thought experiment, but there are basically infinite parallel universes, each of them containing unique outcomes. And the world that you are in right now is just one of trillions of trillions of freakin gazillions. Imagine the level of randomness, then, of this world being what it is.Luck plays a far greater role in our lives than we realise. The very fact that we exist is insanely improbable. To be prosperous and educated enough to be reading this on whatever device you have in front of you also makes you perhaps among the top 0.00000001% of all creatures ever born in terms of privilege. We are the luckiest generation of the luckiest species on the luckiest planet that we know of among billions. (Im applying human parameters of luck here, obviously, constrained by our limitations of knowledge and perspective. We cannot see like bats.) Oddly, even repulsively, we take our good fortune for granted.We overrate human agency, and ignore the role of luck and randomness in our lives. Rationally it seems indisputable and even banal that nothing is certain and that all events have probabilities attached to them, and that much of what happens is outside our control. And yet we give undue importance to outcomes. Hindsight bias is partly responsible for this, and a sense of inevitability can often attach itself to past events. We also assign disproportionate credit or blame to ourselves. Success can make us arrogant. Failure can make us diffident and defeatist. And the anxieties that drive all humans often tend to be about outcomes, which is precisely what we should not sweat over.You can get self-help advice here: do not stress over what is not in your control. You can impart management wisdom: focus on processes, not outcomes. You can invoke Lord Krishnas timeless advice to his friend Arjuna in the Bhagavad Gita: just do the right thing, and dont worry about the fruits of your action. (Disclosure: I am an atheist, but I do think Krishna would have been an outstanding poker player, and not just because he would have known what cards everybody held.)That advice, however you contextualise it, is key not just to a virtuous life but to a happy one. The biggest impediments to our happiness are not the things that happen to us, but a) our anxiety about them and b) our acceptance of them. Thinking probabilistically takes care of those. We take the cards were dealt and then do our best.There is a philosophical implication to this as well, in the old determinism v free will debate, which doesnt give due importance to randomness. I think the world is deterministic, but in a probablistic way, and not in a God/biology wills exactly this way. From any given starting point there are sets of probabilities for everything, which are constantly and dynamically being adjusted in all the parallel universes generated in our little thought experiment. It is determined that there will be these infinite number of parallel worlds, all exactly what they are, but it is not determined which one of those will turn out to be the flesh-and-blood world in which you read these words. That is random.What does this have to do with how we think about cricket? Let me turn to a pivotal moment in modern cricket. Pundits agree that India winning the first World T20 in 2007 was a landmark moment: it helped in popularising T20 cricket in India, which subsequently transformed the game; and it built the legend of MS Dhoni, who became the biggest sporting brand in India for most of the decade that followed. But consider how the final ended.India made 157 in their 20 overs, and after 19 overs Pakistan were nine down and needed 13. Dhoni had planned the innings in such a way that this over was bowled not by one of the sides stalwarts but by Joginder Sharma, a rookie. On the face of it, leaving such a crucial over to a newcomer, who had achieved nothing of note before, and hasnt since, was a blunder. And indeed, the first ball was a wide, and the second legal ball was smashed for six by Misbah-ul-Haq. But then Misbah botched a premeditated scoop, the ball ballooned up to Sreesanth at short fine leg, and India won. Naturally, Dhoni was hailed for the master stroke.The course of action that led to Joginder bowling that over had its own probability of success, its own EV - as did other possible courses. We dont know those numbers, but my guess is that Dhoni messed up somewhere, and the mistake turned out to be fortuitous. Whatever the chances of India winning when Joginder lumbered in to bowl that over, they werent 100% and they werent 0%; reasonable people can disagree over where it fell on the line between those numbers. But the media and the fans were always going to rate the decision based on the result. It happened to work, so it was an inspired move by a visionary captain. Had India lost, it would have been a blunder by a callow captain.All decision-making in cricket (as in anything else) has probabilities attached to it, with multiple possibilities, but is judged on binary outcomes. When a batsman in a tense situation skies a ball towards midwicket, it could, among other things, a) go for six, or b) be caught on the boundary, or c) kill a bird and fall on a fielders head, killing him as well. Only the last of these would be ascribed to luck. If the ball is a six, the batsman will be praised for his bold aggression, for taking the attack to the bowler and so on. If he is caught, he will be cursed for playing an irresponsible shot and letting his team down. But in both these cases, the exact same decision would have led to two very different outcomes.To be honest, such thinking is mainly prevalent among fans and media, including some expert commentators who should know better. Cricketers themselves dont fall into these traps, partly because one of the reasons they have got to the top in the first place is by focusing on processes. These days coaches and captains think probabilistically, and calculate the EV of different options, even if they may not use these specific terms.The decision Kohli faced on that fifth morning in Adelaide was an interesting one. Option one: take the default Indian approach of trying to last the day. The team would have no chance of winning, and would either draw or lose. Option two: go for the win. They would win some of the time but would also be more likely to lose than in option one. The thing to note is that the pay offs for winning and losing would not be equally weighted.India had lost eight (and won none) of the 11 Test series they had played in Australia. Out of 40 Tests, they had lost 26 and won just five. They were overwhelmingly likely to lose this series as well, and a loss in Adelaide would cause no reputational damage to Kohli. A win, on the other hand, would make him an instant legend. It would also set the series up brilliantly, and have all kinds of useful meta-game effects. To name one, which would kick in even if India chased valiantly and lost: in future, teams would leave India more runs to win in less time, thus lowering Indias chances of losing. To name another, Indian players would have increased self-confidence, and any sportsman can tell you that self-confidence can set off virtuous cycles and help you perform better.So even if in that particular case India won 5% of the time, lost 80% of the time and drew the rest, it could still be a +EV decision to chase, given the disproportionate pay off for winning. (Also, India would lose a fair amount of the time when they set out to draw anyway.) India ended up losing, but Kohlis decision, in my view, was brave and correct. (It is true that the probabilities kept changing during the course of the day, and Kohli could have modified his approach at various points, such as when all the recognised batsmen were out. Thats a separate debate, though, and Im referring here to Kohlis initial decision.)And what of Amla? South Africa decided at the start of their fourth innings that given the target, and the Indian spinners, and the way the pitch was playing, there was no way they were going to win. With this being the case, runs diminished in value (to zero, in fact), while wickets became more valuable. If you calculate EV with this in mind, the correct approach is obvious.The optimal approach in this case was to play the safest shots possible, block everything that came their way, and not bother too much with running between the wickets. (Indeed, Im actually surprised they ran at all, given that there is always a non-zero chance of a run-out if youre actually running.) Amla and de Villiers stonewalled exceedingly well, though India broke through in the end. The outcome went against Amla - but the decision-making was spot on.I referred to the similarity between these decisions because both could be justified from a cold-blooded EV point of view. These could have been the right decisions taken for the wrong reasons. Indeed, the probabilities of these decisions being taken could change if you change the players involved: if Kohli had grown up in Mumbai instead of Delhi, imbibing the safety-first approach of Mumbai stalwarts like Gavaskar and Tendulkar, would he have been the same captain? Who knows. It is easier to comment on the decisions themselves - human beings tend to be more complicated.Probabilistic thinking is the cornerstone of sports analytics, which is quite advanced when it comes to sports like baseball, basketball and football. For example, Luis Enrique, the Barcelona manager, knows exactly how likely his star player Lionel Messi is to score from outside the penalty area (12.1% of the time) and from a direct free kick (8%), and has similar detailed stats for all his players, alone and when they combine, in different kinds of situations. All of these inform his coaching, and it becomes second nature for his players to take the routes most likely to win them games. When Messi, from outside the box with two defenders in between him and the goal, chooses to pass to Luis Suarez who is making a run into the box, it is because the EV of the pass (the probability of the ball actually getting to Suarez, and Suarez putting it in) is greater than the EV of Messi shooting himself. He doesnt conduct statistical analysis before making this split-second decision, but it is a combination of years of experience and coaching. (Even if he were to never think of these numbers himself, those probabilities exist, and his manager probably knows them.)Data analytics in cricket was quite primitive until recently. Part of the reason, I believe, was a problem of sample size. Test cricket may have been played for close to a century and a half, but there are so many variables that if you were to take a particular situation - an Australian side chasing 300 on the fifth day on a Motera dustbowl in September against a leggie, an offie and a left-arm spinner - the handful of similar situations you find would not make for a meaningful sample. But as T20 becomes the dominant form, and there are more matches over shorter spans of time in more homogenous conditions, this will change. Cricketers have thought probabilistically, in a common-sense kind of way, long before this age of data came upon us. You dont need data to tell you, for example, that smoking is -EV and exercising regularly and getting enough sleep are +EV - even if there appear to be examples to the contrary. Equally, you learn from experience and osmosis what to do in specific situations within matches. And yet, I expect data to affect the way players and coaches think about the game, with more clarity in their decision-making. Like every other sport, cricket will become a numbers game.One example of a strategic shift hastened by probabilistic thinking is aggression within the game. As I wrote in an earlier essay, I believe that the EV of aggressive batting is being vastly underestimated in T20 cricket. Given that teams have the same number of batsmen and bowlers available to them as in an ODI, but 40% of the overs, it stands to reason that they should be far more aggressive while batting. Indeed, they can dispense with the ODI structure of building an innings and just attack from ball one, instead of waiting for artificially designated slog overs. Some teams - West Indies internationally and Gujarat Lions - have figured this out, and front-load their innings. Many others, though, continue to underestimate par scores. Expect strike rates to go up massively in the next few years. The movement upwards that took decades in ODIs will take years in T20s.The Cricket Monthly published an excellent story by Kartikeya Date on the ongoing data revolution in cricket. But it is not data analytics per se that concerns me. Supply and demand will take care of that. It is, rather, the way we, ordinary fans, watch cricket.We are too focused on outcomes, as is evident when people stone cricketers houses or burn effigies of them after a bad loss, or when TV channels look for a Match Ka Mujrim, (culprit of the match) as if causation is so easy, or necessary, to establish. My worry stems not from this being an injustice to the players but from it being such a waste. Cricket is a deep, complex, layered and beautiful game, and most of us watch it in a terribly shallow way, focused on the binaries of outcome. Watching a cricket match like this is like going to Wikipedia and reading a plot summary of a great novel. That misses the drama entirely: all 100% of it.Kyle Alexander Jersey . Kiriasis and brakeman Franziska Fritz finished two runs in one minute 55.41 seconds -- a mere 0.01 seconds ahead of Meyers and Lolo Jones, who likely bolstered her Olympic hopes by helping give USA-1 a huge push in the second heat. Edrice Adebayo Heat Jersey . -- Peyton Manning will have all of his wide receivers available for the first time in a month when the Denver Broncos begin their playoff run Jan. https://www.heatlockerroom.com/Justise-Winslow-City-Edition-Jersey/ . Los Angeles star goalie survived those perilous gymnastics with no problem, and he eventually backstopped the Kings to a skid-snapping win. Quick stopped 27 shots in his return from a 24-game injury absence, Jeff Carter scored the tiebreaking goal with 7:55 to play, and the Kings snapped their five-game losing streak with a 3-1 victory over the Vancouver Canucks on Saturday night. Jeremiah Martin Heat Jersey . LOUIS -- Alexander Steen scored a power-play goal with 59. Tyler Herro Jersey . 1 position. The Mustangs (6-0), who beat Queens 50-31 last weekend, earned 17 first-place votes and 287 points in voting by the Football Reporters of Canada. Western was last ranked first in the country in October 2011.DURHAM, N.C. -- Daniel Jones looked like hes played quarterback at Duke for years.The redshirt freshman threw for two touchdowns and ran for another in his first college start, and Duke routed North Carolina Central 49-6 on Saturday night.Jela Duncan set the tone with a 50-yard touchdown run on the second play from scrimmage, added a 3-yard TD run and matched a career high with 115 yards.Daniel Jones was out there dropping dimes, like I knew he could, Duncan said.The Blue Devils (1-0) once again had an easy time against their lower-level crosstown opponent, building a three-touchdown lead before the Eagles (0-1) ran a play inside Duke territory and leading 49-0 at halftime after scoring TDs on seven of their 10 first-half possessions.It was a lot of fun out there tonight, and I think everyone enjoyed it, Jones said.A year after rolling up 655 total yards against Central, Duke gained 535 yards, gave up just 112 and improved to 5-0 in the series.Jones certainly didnt look like he was playing his first college game. He finished 10 of 15 for 189 yards with touchdown passes of 55 yards to Johnathan Lloyd and 20 yards to Erich Schneider, and added a 17-yard scoring run.Hes smart, and hes talented, and I told you all he could run -- hes really fast, coach David Cutcliffe said. There are a lot of things he can do well. He will learn a lot from that first taste. Its going to get a lot tougher before it gets easier.Brandon McLaren kicked field goals of 48 and 34 yards for Central.The first half was not what we wanted it to be, by any stretch of the imagination, Central coach Jerry Mack said.THE TAKEAWAYN.C. Central: Since making the jump from Division II to the Championship Subdivision roughly a decade ago, the Eagles have now played seven FBS opponents and lost them all by an average of 44 points with three shutouts. Those results sure havent hurt them once they start playing schools at their level: Theyve won shares of tthe past two Mid-Eastern Athletic Conference titles, and figure to contend for another.ddddddddddddDuke: All eyes were on Jones in his starting debut two weeks after returning starter Thomas Sirk was lost for the season when he re-injured the Achilles tendon he tore in February. The QB nicknamed The Future said earlier in the week that he thought he could both run and pass effectively.He spent the first half proving it, starting with his first carry -- a 21-yard gain on a read option before he threw his first pass.I guess that got me comfortable, to get his the first time, Jones said. It got me rolling, I guess.His touchdown run came one play after his prettiest pass of the night -- a 35-yard throw that he dropped over receiver T.J. Rahmings right shoulder near the sideline. Rahming played a big role in Jones first TD pass, throwing the key downfield block that sprung Lloyds catch-and-run.KEY NUMBERSN.C. Central had just four first downs and Duke held a 308-38 advantage in yards rushing. ... This surely would have been even more lopsided had Duke not turned the ball over five times -- three of those coming in the second half when most of the playing time went to the third- and fourth-stringers. ... Duke DT A.J. Wolf had three sacks -- the first time a Duke player accomplished that since 2003.UP NEXTN.C. Central: The Eagles get another crack at an FBS school next week when they visit Western Michigan -- which knocked off Northwestern in Week 1.Duke: The Blue Devils dive into Atlantic Coast Conference play with a visit from Wake Forest. Duke has won four straight in the series with its instate league rival.---Follow Joedy McCreary at http://twitter.com/joedyap. His work can be found at http://bigstory.ap.org/content/joedy-mccreary---AP college football site: http://collegefootball.ap.org ' ' '