Using DLS to fix NRR

The net run rate has a few disadvantages as a method of comparing performance of teams. There are three that I’ve heard or thought of. 

  1. Team 1 gets bowled out in 33 overs having scored 230 runs. Team 2, while chasing, loses 9 wickets and reaches the target in 25 overs. Intuitively, we would think that this match was close. But because Team 1 got bowled out, its run rate calculation has 50 in the denominator, while Team  will have 25, which means that NRR exaggerates the gap between them. (I think I read of this example in the feed of Twitter user ZaltzCricket)
  2. The bind that Pakistan found itself in recently provides another example. A team that bats first, scores 350 and dismisses its opponent for 150 rightly gets a boost to its NRR. A team that fields first, bowls out the batting team for 150 and then reaches the target in 15 overs has arguably done better than the first team, and this shows up in the run rate difference for that match. But when its net run rate is calculated over the whole tournament, the team that wins by batting second gets a disadvantage in the NRR because only 151 and 15 get added to the numerator and denominator respectively, with the result that the impact of this win is smaller than that of the team that scored 350 in 50. 
  3. A team that scores 300 in 50 overs for the loss of 3 wickets and a team that scores 290 in 50 for 9 wickets will have nearly the same NRR, even though we intuitively feel that the number of wickets lost should also matter. 

Can the Duckworth-Lewis-Stern method help fix the deficiency in the NRR? Prima Facie, it appears that the DLS method, used in its current form, should help with the problems in examples 1 and 2, but not in example 3.  The idea behind DLS is that it considers the overs remaining to play and the wickets in hand as “resources” that are, statistically speaking, proportional to the runs that you can expect to score. To understand this, let’s use this table found in the Wikipedia page for DLS. It says that if your team has lost 9 wickets, unless you have fewer than 7 overs remaining, you have 4.7% of your resources left. This makes intuitive sense, because if you’ve lost 9 wickets at 40 overs, the number of overs left is not much of a constraint on how many runs you are statistically likely to score. If you have scored 200 runs at this point, DLS predicts that you are likely to score 200*100/95.3 = 210 runs. 

DLS Table – Standard Edition. Image Credit: Wikipedia User Chintan9, license: cc-by-sa3.0

To take another example, if, when the rain interrupts play, the team batting first has played for 25 overs without loss of wickets, DLS predicts that you still have 66.5%, or 2/3 of your resources left.  If the score at this point is 125, DLS predicts that the team is likely to have scored 125*100/33.5 had it been allowed to complete its full fifty overs. If the chasing team is also given only 25 overs, it is assumed to have lost the first 25 overs of its innings, which amounts to 100-66.5, or 33.5% of its resources. So the chasing team’s score must be scaled accordingly, which means that we must compare 125*100/33.5 with S*100/66.5, where S is the chasing team’s score, to determine the winner. This is equivalent to saying that the target to chase is 125*66.5/33.5, which is how the target is given. 

Going back to our three examples, it should be clear now why DLS won’t help with the third one.  By definition, a team runs out of resources when it has used up 50 overs or has lost all its wickets. In example 3, both teams are at the same position as far as DLS is concerned. In examples 1 and 2, the DLS method holds more promise. Both of the situations involve a team batting second not having to bat for the full 50 overs because it reached its target score. In the first case, because the team has lost 9 wickets, DLS will predict that it will score only 231*100/95.3 =242 runs, and adjust its run rate accordingly. In the second case, assuming that the chasing team loses 5 wickets in the process of scoring 151 in 15 overs, DLS will predict that it has 48.1% of its resources left and add approximately 300 runs and 50 overs to its run rate calculation. Both these results seem fairer than using NRR as it is. Does that mean that a DLS-enriched NRR is the right option. I will give the case against followed by the case for, and let you decide.

 The case against: In Oscar Wilde’s play “The Importance of Being Earnest”, there is a brilliant line that goes “I do not know whether there is anything peculiarly exciting in the air of this particular part of Hertfordshire, but the number of engagements that go on seems to me considerably above the proper average that statistics have laid down for our guidance.”  The line is funny because statistics are supposed to measure reality, not guide it. It is one thing to use statistical averages as guidance in exceptional situations like rain interruptions. If we start using them for NRR calculations, we will be using them routinely. To use them to predict the score of the chasing team is particularly inappropriate. The canonical team that forms the basis for DLS is a team that is trying to score as many runs as possible within constraints of the number of overs and wickets remaining. But a team that is batting second is not aiming to score as many runs as possible. It is trying to reach its target. A team that needs to reach just 150 runs doesn’t need to bat as if it has 50 overs and 10 wickets. It can adopt a T20 strategy and score them as fast as possible. Going back to our examples, the team in the first example can protest that it is being unfairly penalized for losing wickets, when that was the right strategy in the situation. The team in the second example may benefit from DLS (because more runs and overs are added to the numerator and denominator – I think this depends on how many other matches it has played and how many other runs it has scored)  but it can also argue that it is being unfairly penalized for losing 5 wickets. More pertinently, the introduction of DLS for NRR will make chasing teams completely change their strategy, which is not what  we should be aiming for. 

The case for: Yes, the introduction of DLS for NRR will make teams change their strategy, but that is a good thing, because now this is more of a like for like comparison. To do a perfectly fair comparison between two teams, we must put them in the exact same position. However, in a normal ODI, the team batting first does not know how much it must score; and the situation it is faced with is to score as many runs as possible within the 50 overs it has. The team batting second knows its target,and its strategy must adjust accordingly. For both teams to be in the same starting position, after the first 50 overs are done, we must inject both teams with a drug that induces amnesia and makes them forget the first 50 overs till the next 50 are completed. Unfortunately, anti-doping regulations do not allow that. Therefore, using the DLS to adjust the NRR seems like a good way to level the playing field between the two teams. Hence proved. 

The case against, once again: Using DLS for NRR will slow down the batting of the second team. Any innovation that results in slower batting will never be acceptable to the ICC. Quot Erat Demonstrandum. 

What went wrong with Game of Thrones

Long back, during Doordarshan’s golden era, I watched an episode of a TV series, one those where every episode was a short story. This particular episode told the story  of a novelist who was getting his novel serialized in a magazine. A fan of the novelist comes to meet him and begins discussions about turning this novel into a TV series (or movie, I don’t remember which). As the discussion progresses, it turns out that she is particularly interested in the fate of one particular character and is distraught to learn from the novelist that she was going to die. She pleads with the novelist, asking for the character’s life to be saved, but the novelist refuses, saying “It is not I who is killing her. It’s the logic of the story that is!” The fan and the novelist have more meetings where she continues to implore him to change the course of his story, till finally the novelist relents. He tells her that he had found a way to save his character’s life, but the story would have to be crafted in a particular way and that the producers of the show would have to promise not to deviate from the script. She gladly accedes to the request. The twist at the end was that it turned out that the TV series was just a ruse. In reality, the fan was so interested in the character arc because the character’s story was magically getting turned into the story of her own life, and she naturally did not want to die. 

I remember being fascinated by the idea that the story of a novel is not something that the novelist creates or controls, but something that has a life of its own. I remembered this story in the context of Game of Thrones because it struck me that the essential problem with the series was that there was really no way to end it in a  satisfactory way. 

Game of Thrones is the Mahabharata of Kali Yuga. It is said that the Mahabharata, unlike the Ramayana, prefers realism to idealism. Characters have grey areas, make and morally ambiguous choices. In the Ramayana, Good triumphs over Evil and the story ends in Rama Rajya. The Mahabharata culminates in a great war and the end of the epic marks the beginning of the Age of Kali. This denouement is logical, because unlike in a simple story where good triumphs over evil, in the real world, it is difficult to tie up all the loose ends and come to a tidy conclusion.  There are actually no endings in the real world. A victory in one battle leads to a reaction from someone somewhere. Kill one person and someone from his clan is out there plotting revenge. Get all people in a room and agree on something, and at least one person goes out from the room intending to break the agreement as soon soon as he is in a position to do so. 

Game of Thrones exceeds the Mahabharata in its realism, as befits an epic set in Kali Yuga. It is morally ambiguous. Good people die because of their goodness. Ned Stark got killed because he did the honourable thing. Rob Stark got killed because he married for love. These morally ambiguous events added to the complexity of the story, which branched off in many different directions, making it tougher and tougher to bring them all together. But if Game of Thrones is the Mahabharata of our age, the end of the story must also end Kali Yuga. After the cycle of four yugas is complete, Krta (or Satya) Yuga, the first yuga where righteousness prevails must begin again. The complete inability of the showrunners (and I suspect, Martin as well) to direct the arc of the story towards this ending where Kali Yuga ends and Truth and Righteousness prevails at the end leads me to suspect that the end of Kali Yuga is still far away. 

While the series had many themes and failed to bring any of them to a satisfactory conclusion, the one theme that was of most interest to me was Danerys’ desire to “break the wheel”.  I am not sure how many people noticed the parallel between her desire and Joffrey’s outburst back in season 2 or 3, where, in a conversation with his mother, he expressed frustration that he had to work on the painstaking task of building alliances with all the lords of Westeros if he wanted to assemble an army. It was all so primitive, he exclaimed. Why couldn’t he have an army of his own, answerable only to him? 

The answer to Joffrey’s question is that the medieval economy did not allow such a setup. A medieval monarch faced two choices about where to maintain his army. Should he keep it close, in the capital, or should it be distributed throughout the kingdom? If he opted for the former, maintaining control over the periphery would be difficult. If he chose the latter, given the tyranny of distance in medieval times, maintaining effective central command over the army was difficult. He would have to distribute command by giving autonomy to local leaders. But the latter option meant that the soldiers would be loyal to the local leaders, not to him. 

Modern states maintain large standing armies. A medieval state that tried to maintain a large standing army would face famine because moving young men off farm to the army meant that the fields lay fallow – this would be especially true if it kept this standing army concentrated at some place for purposes of control. A modern state needs a much smaller proportion of its population in agriculture . It can also, because of modern weaponry, maintain a monopoly on use of force with a much smaller and more centralized army.  

For a medieval state, maintaining effective monopoly on use of force was pretty much impossible.  Other than the limit on size of the army, entry barriers to someone else raising an army were non-existent. Raising a modern army requires sophisticated machine guns, tanks and other artillery. In modern day India, if someone began to acquire such weaponry, the state would notice pretty quickly. In a medieval state, if someone decided to acquire spears, bows and arrows and cannon, there’s a good chance that they’d be able to do it without the state noticing.  

If medieval states did not have monopoly on the use of force, how did they maintain political stability? For most part, they did not. There was always palace intrigue, rebellion brewing in the peripheral regions or a foreign invasion going on. To the extent that stability existed, it was built and maintained by the king negotiating coalitions with the various lords and satraps throughout the kingdom. It was the need to do this that so frustrated Joffrey. The need to maintain these coalitions constrained the medieval monarch, preventing him from turning into an absolute ruler.

The more successful states embedded these constraints into customs and traditions that carried on over generations – Game of Thrones was at its best when it depicted this delicate balance in Westeros. The formalization of these customs and traditions, the codification of them in writing (for example, via the Magna Carta), was one of the ways in which democracy began.   

But while medieval kings were not absolute rulers, the economic and social conditions of those times did not actually permit an evolution to real democracy. In a parliamentary system, we know the challenges of having to build coalitions and and governing with the support of many small parties. Imagine having to do that, but with the difference that those parties are not accountable to the people and have armies of their own.  Your attempt to govern for the benefit of the people will be hampered by the fact that your coalition partners want absolute rule over their own jagirs and may want you to run the government for their benefit rather than their subjects’. Your attempt to bring about the rule of law will be stymied by the fact that the government is constrained, not by laws, but by balance of power, and as the balance changes, your coalition partners will want to renegotiate the rules. 

 So here is the paradox. The journey towards democracy may begin with the codification of customs and traditions that constrained kings, but to actually achieve a modern democracy, you need a centralized army with the ability to exercise monopoly over power. One way to achieve democracy is to evolve towards it, slowly changing the rules towards greater and greater participation of the people. The other way, which was Danerys’ preferred way, was to break the wheel – to bring about revolutionary change that blows away the existing power structures in the kingdom. It did help that she had access to the three dragons that, through their awesome firepower, would be able to subdue any opposition to their monopoly. But if you seize power by destroying the existing power structures, you have also destroyed the customary constraints on the autocrat’s power, and now what will stop the military monopoly from sliding into tyranny? 

It is clear that Game of Thrones wanted to conclude the series by coming out in favour of evolutionary over revolutionary social change, but because of the incompetence of the writers and because the showrunners were in a hurry to end the series, they went about it in the dumbest way possible. The worst scene of the worst episode of the worst season of the series is the one that takes place at the dragon pit after Jon Snow has killed Danerys Targaryen. There, the lords and ladies  have gathered to elect the new monarch, and Sam Tarly rather timidly suggests broadening the franchise to include commoners. His suggestion is scoffed at, with the gathered lords arguing that they might as well include dogs in the vote. Quite clearly, this was meant to signal that the socio-techno-economic conditions of the time did not permit a drastic transition to full liberal democracy. 

But the point about evolutionary change is that each step in the evolution needs to be sustainable, possibly over many generations till conditions are ripe for the next steps. The finale of Thrones was a masterclass in papering over the obvious cracks. The surviving dragon, has for some reason, flown away to an unknown location, conveniently doing away with the problem of civilian control of dragonry. But how is this new setup supposed to maintain political stability in its absence? The capital has been destroyed, most of the army has been killed, the military force that conquered the kingdom has been pensioned off, and the one person who is a competent military commander has been sent off to guard against a non-existent threat. Worst of all, the kingdom has installed as ruler a philosopher king who is more philosopher than king, and the philosophy in question being more of the mystic variety than of the kind that will provide guidance in this world. At least, if at the end it had been revealed that Bran the broken intended to use his warging abilities to exercise surveillance over the entire kingdom and use his information asymmetry as power, the series would have been slightly salvaged, but this ending is an unmitigated disaster. 

It’s quite clear that the producers of the series knew that the ending was stupid and that they were airbrushing visuals of loose ends from the picture – Yara Greyjoy, for example, makes some noises about she being still loyal to her old queen, and before she could set out to lead a rebellion to extract vengeance, she is asked to shut up, presumably because the producers were in a hurry to end the series.  This hurry has been visible right from season 6, when they started using their their various dei ex machina to eliminate the complexities in the story. Till that season, all the unexpected twists – the death of Ned Stark, the Red Wedding or the poisoning of Joffrey – had increased the complexity in the story. But when Cersei blew up the Great Sept using wildfire – yes, it led to Olenna Tyrell plotting revenge and joining Danerys, but you have to wonder about the High Sparrow and the Faith Militant. Was there no fallout from eliminating them? Did they not have a following in Kings Landing? Did killing them all not cause any kind of unrest?  In the same season, Dany uses her dragons to burn the slavers’ ships and destroys their fleet. No fallout from that? No one left to plot revenge?  

Evidently, the showrunners were incompetent at plotting the course of the series when unmoored from George R R Martin’s guidance. But Martin himself has been unable to finish writing his books, and while he is good at fleshing out the complexity of the real world, I don’t see any evidence that he has the ability to resolve the complexity and bring the series to a satisfactory conclusion. Which is just as well. A satisfactory conclusion to the series will bring about the end of the cycle of the four yugas, result in Pralaya, and the start of a new cycle. I don’t think we are ready for that yet.  

Should you vote for your PM or your MP?

Many people are arguing that because India is a parliamentary democracy, voters should be voting to elect members of the Lok Sabha, and that it is an error to vote on the basis of whom they want to see as Prime Minister. Such fidelity to the original tenets of parliamentary democracy is touching in a country that has amended its constitution over a hundred times in seventy years and is currently run according to the whims of its judges. This argument also reminds me of one of the two dumbest features of the United States Constitution. 

I am referring to the Electoral College. The US Constitution, as it was originally written (actually, even in its current form) does not provide for direct election of the president by its citizens.  The president was supposed to be elected by an electoral college. Each state would be able to send a certain number of members to the EC, the number being equal to the sum of the numbers of the representative and senators from that state. The method of choosing the electors was left to each individual state. The electors could be chosen by the state legislature, and I believe this was the method adopted by most states during the first few decades of the republic’s history. The electoral college was expected to gather, debate and then vote for their choice of candidate for the president. 

The existence of the electoral college is the reason why the vote of the citizen of a smaller state carries a larger weight than that of a larger state. Every state gets 2 senators regardless of its size and it gets to send at least one representative even if its population may be smaller than the average congressional district, which means that a state that has a population 1/20th of that of a state that sends 20 representatives gets to send 3 electors as against the 22 that the larger state can send. 

But this is not the reason why I believe that the electoral college a dumb idea. To understand why it was unworkable, take a look at how it evolved to its current form. It changed in 3 ways, 2 of which should have been entirely predictable to a political scientist

  1. States began to bind the electors – i.e. they started making laws saying that the electors should vote for particular candidates of their choice.
  2. They started to mandate that all  electors from their state vote for a particular candidate
  3. One by one, all states devolved the “choice” of  electors to the voters of the state. 

The first 2 of these should have been completely predictable. Firstly, why spend time and energy on electing a bunch of people whose only job is to confer among themselves and then elect another person, when you could spend that time and energy in deciding on the person you ultimately want to see elected? Perhaps the founders of the United States believed that discussion and debate among the electors would lead to decisions of better quality, but electing a president is not like writing a constitution, making laws or negotiating some kind of agreement. If you have to do any of those things, by all means delegate the task to your representatives, because there is much scope for discussion debate, give and take, and compromises – all good reasons why it was a bad idea to hold a referendum on Brexit. There is very little scope for compromise on the question of who should be the President – you can’t mix the head of one person and the heart of another and construct a compromise president. Perhaps you can bargain over who should be the vice president, over cabinet positions and over what policies the president should follow, but given that cabinet members can be dismissed at will and policies can be changed at will,  and given that the Electoral College disbands itself after the election, there would be very little scope for the Electoral College to hold the president to any compromises he agrees to. It should have been completely predictable that the election of electors would become an election of the elected. 

The second outcome was also predictable, given the first. In theory, states could have adopted systems where the ticket was split – perhaps in proportion to the votes in the state legislature. In fact, in the early decades of the republic, many states did so. But a state that chooses to split its ticket is much less valuable to a presidential candidate than a state that gives all its votes to one candidate. Once a few states started adopting the general ticket model, everyone else was compelled to follow suit. 

The devolution of the vote to the ordinary citizens wasn’t a predictable consequence of the design of the Electoral College, but seems to have followed from the cultural DNA of the United States. At least in the 19th and till the early 20th century,  that nation seems to have had a strong bias for direct elections.

 I recount the story of the Electoral College of the United States for a couple of reasons. The first is that questions about what constitutes the essence, the basic structure of a republic, is difficult to pin down. You still hear many Americans defend the Electoral College, but when they do, they do not refer to its actual design. Instead, they argue, in rather vague terms, that the College is the reason why the United States is a republic rather than a democracy. It is not quite clear what they mean by that. These days, the design of the EC affects democracy in the US in two ways – first by overweighting the smaller states and second by giving all votes from one state to one candidate or the other depending on who got the majority in that state. There may be some justification for the first. I am not sure why the second is a good thing, but can think of many reasons why it is bad. It must surely contribute to the polarization of politics on geographic lines.  It is rare for anyone to argue that the electors should vote like actual thinking people rather than dummies. Recently, the Americans elected a mentally unstable person as their president, and there were some murmurs that this was exactly the kind of situation for which the Electoral College was designed – that the electors should vote as responsible people and not as bound agents, and override the choice the Americans seem to have made. It should be immediately obvious why that would have been a terrible idea. No matter what the constitution says, the legitimacy of democracy depends on everyone following the rules that everyone agrees are the rules. The voters did not vote for the electors. They voted for the man or woman they wanted as president. A set of essentially random people overriding this choice would destroy the legitimacy of the republic, no matter what the original design of the Electoral College was. 

The second reason is that the experience of the Electoral College has some relevance to our parliamentary system.  Our chief executive is elected by the Lok Sabha. You could say that it essentially functions as a permanent electoral college.  Now, many of you will protest my characterization of the Lok Sabha as a permanent electoral college, and will argue that our Sansad is a legislature, though I am sure you will agree that the lower house also functions as an electoral college. A textbook answer to the question: “What are the functions of our Sansad?” would be: 

  1. Makes laws
  2. Exercises oversight over the executive
  3. Members of Parliament act as a bridge between their constituents and the government
  4. Elects the Prime Minster (Lok Sabha only)

But how is it in practice? Our parliament doesn’t actually make laws in the sense that the Congress of the United States does. That body actually has primary responsibility for making laws. Senators or representatives draft legislation, the Senate and the House form committees to consider them, amendments are proposed, there are negotiations among the legislators, and this back and forth determines the final shape of the law. The executive has a significant say in this process – but it has to exercise its say mostly informally – through its influence over the legislators and by the power of the President to appeal to his popularity. The formal power the President has is the threat of the veto, but the veto power is, by definition, not an agenda setting power.  I think that it is fair to say that no other legislative body in the world, and in particular no legislative body among parliamentary democracies, exercises that kind of power. In most other countries, the government sets the agenda and writes the acts of legislation, the legislature debates them, amends them as needed and passes them into law, or not. In India, a bill not drafted by the government being turned into law is so unlikely that I believe it has happened only once in its history. The parliament has next to no input to drafting or amending legislation, and while members of parliament have a vote, that vote is entirely on party lines. Members of the ruling party support all bills introduced by the government, and members of the opposition oppose it if their party decides to oppose or support if it does. 

The oversight function fares better, if only slightly. Members of parliament do have some freedom to question ministers of their party, especially when it happens behind closed doors in parliamentary committees. 

The only thing that really differentiates our members of the Lok Sabha from electors of an electoral college is the third function – which is to stay in contact with the people, listen to their grievances and communicate these to the government. In fact, India has introduced a weird innovation in the form of the MP Local Area Development Scheme that allocates funds to members of parliament to carry out what are essentially municipal schemes. Many people who believe that we should vote for MPs rather than the PM also believe that the function of a member of parliament is to carry out local development work in the constituency.  Going by the original constitutional design, the latter is just as out of scope of an MP’s remit as is the former.  The only reason MPs are tasked with these things is that our municipal governance is non-existent. 

It is quite clear that the most important task of the legislatures in India is to elect the chief executive, overshadowing their ostensible purpose, which is to legislate. For a voter whose concern is to see certain laws passed and policies executed, the rational thing to do is not to pretend that you are electing legislators, but to model the problem as electing a prime minister, and the members of parliament as members of an electoral college. The alternative model is that of the MP as a feudal patron with the power to dispense government largess and who acts as a conduit for your grievances. The model of an MP as a legislator doesn’t really make sense. For one thing, MPs do not legislate in practice. Secondly, even if by chance one constituency decides to elect an MP who believes that his main task is to legislate, it is pointless unless he is able to coordinate this with a couple of hundred other MPs. 

If you think through this, it should not be surprising – indeed, it should have been completely predictable, as predictable as the evolution of the electoral college was. Some people will argue that the law-making powers of our legislatures began to atrophy due to the anti-defection amendment. I agree that the amendment is a bad idea and did contribute to the worsening of the independence of our legislatures, but the root cause lies with our system of government. If you were designing a system, and you went: “We will have elected legislatures. Their main function is to make laws for the executive to implement. And oh, they will also elect a committee that will actually run the government.” a perceptive political scientist should have been able to point out that this system would inevitably lead to the latter function overshadowing the former, especially in an era where the development of mass communication makes presidential politics possible. The parliamentary system did not come about because someone thoughtfully designed it. In countries where the parliamentary system originally evolved, the monarch held executive power, the legislature slowly wrested law-making powers from him, and eventually evolved to take on executive power as well. There was a path dependency to this. Because the traditions of the legislature had time to evolve before there was a prime minister to exercise executive functions, the legislature in places like Britain does have some independence. India’s Sansad never got time to evolve that kind of independence. It came bundled with a popular prime minister. It is therefore inevitable that it grew to be a kind of glorified electoral college.  If you need that to change, give the voters separate votes – one for a chief executive and one for their representative. If you insist on giving only one vote, don’t be surprised if they decide to use it to choose their chief executive. 

Cash for Votes








The voice in your head










The Pirate Game

  • E: people
  • C: state government
  • D: opposition party in state government
  • B: central government

Thoughts on the GST












In Defence of the GDP













Arya Stark and Advaita






It could get worse after Trump
















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Third Parties in the United States













