SK – Page 120 – Pertinent Observations

Beer numbers

I’ve always wondered why the craft beer at Arbor, a popular microbrewery in Bangalore, is so potent. While I was losing it on one such last night, I made a small calculation (rather simple) which gave me the answer.

The standard serving size at Arbor is 500 ml. The strength of the beers varies from 5.5% alcohol content to 8% alcohol content. While making this calculation last night, I was sipping the one with 8%. 8% of 500 ml is 40 ml, which means that I had 40ml of unadulterated ethanol (combined with 460 ml of other stuff).

Most standard whiskies and hard liquor have 40% alcohol content. So if I were drinking whisky rather than beer (i usually drink whisky and not beer), that one glass of beer was “worth” 100 ml of whisky!

And what about the “regular” beer that I have, which is a 330ml bottle of Kingfisher Premium? That has 6% alcohol content, or 20 ml of alcohol in a beer, which equates to 50 ml of whisky, which is less than one large peg of whisky! To put it another way, one standard unit of beer at Arbor contains about twice the amount of ethanol as one standard unit of bottled beer!

And then it is manufactured right there – because it is a “microbrewery” it is unlikely for each batch to have the precise amount of alcohol. There will be a margin of error. And I’ve been told (verbally, through the grapevine, so this is not official information) that they err on the side of more alcohol – so when the stated alcohol content in something is 8%, they prepare their setup so that the chances of alcohol content being lower than 8% is extremely low. Put that together with the above calculation and you’ll understand why you get so drunk at Arbor!

Tailpiece

Indian Pale Ale is the “beer of beers”. Beer itself is famously an “acquired taste” – I remember being so disgusted when I had my first beer back in 2004 that I didn’t have another beer for another year. Now I’m quite used to the taste of Kingfisher.

But then the taste of IPA is even more “acquired” than that of bottled beer. I had some trouble finishing the IPA I ordered yesterday – what helped me finish it was perhaps the alcohol content which was already working! On a previous occasion I’ve ordered an IPA and only half-finished it. But then fans of IPA swear by it and go all the way to Arbor specifically for its IPA! So it is the “beer of beer”, or perhaps “beerendra beer” (Bikram Shah Dev).

Tailpiece 2

I was there as a part of a really large gathering (some 25 people), with people entering and exiting at random times, so they instituted a good measure to ensure we paid fairly. Every time someone ordered something, the drink would come along with the bill, which the orderer would clear right there.

This way there was no scope for messy calculations on who owed whom how much and all that, and no need for any bill-splitting algorithms!

Which political party to vote for/support/join

If you have any doubts on which political party to join (as a member) or simply vote for, fear not, for there is now a mathematical formula to help you. It’s rather simply, and is given by $A. B$ . Yes, that is it. Notice the dot – however. This is essentially the inner (dot) product of two vectors. So what are the variables here, and how do you construct it?

First of all list out all the “axes” that you think are politically important – anything that you think is relevant for a political party. These axes can include (but are not limited to) “capitalist-communist”, “secular-communal”, “internationalist-regionalist” and so on. Now that you have defined these axes (there is no limit on the number of axes you can define), describe your political position in terms of a vector in the N-dimensional space.

Let’s say that you have defined two axes – economically conservative-liberal and socially conservative-liberal. If you are extremely conservative economically and extremely liberal socially, your political persuasion can be described as say (-5,5). If you are economically centrist and socially conservative, you might be at (0,-5), and so forth (choice of the number 5 above is arbitrary).

Now, take every political party that is in your shortlist (or longlist, if you have that much patience), and define the vector of that particular party. Now, the magnitude of the party vector along each axis should reflect the ability of the party to execute along that axis – for example, if you think a party is socially liberal but is unable to execute on the socially liberal axis (either because of lack of conviction or because the party has minuscule chance of forming the government) you should ascribe to the party a small positive value along this axis. If another party is likely to have regressive views on the social liberal axis, and is very likely to achieve them (good chance of winning combined with conviction to get these policies done), it will have a large negative score along this axis. Once again, absolute numbers don’t matter – your axes may stretch from -10 to 10 or -1000 to 1000, as long as all parties have been graded using the same scale.

So now, for each party, you have an N-dimensional vector which reflects its overall ability to execute. You have your own N-dimensional vector, which represents the combination of policies that you want to push.

All you need to do now is to take the inner product of your vector with each party’s vector. You should vote for / support / join the party with whom the inner product has the maximum value.

The mistake a lot of people do is that they ignore magnitudes, especially that of the party vector, and instead choose the party whose vector forms the smallest angle with their own vector (inner product can also be written as $|A| |B| cos theta$ where |A| and |B| are the magnitudes of the vectors and $theta$ is the angle between them. The mistake people do is to optimize $cos theta$ even if the magnitude of the party vector is small.). This leads to them spending much valuable energy supporting unviable parties (either ones that have a low chance of winning or those that lack conviction to execute on just about anything).

Quite simple, right?

The de facto state

There was a good profile of India’s labour laws in Mint last week. Apart from some absurd regulations, what stood out was the fact that while on paper India’s labour laws are strict, implementation is lax, and that provides flexibility to employers. What that also means (strict rules, lax availability) is increased power and rent seeking capability of the government, since they can choose when they want to throw the rule book at you (and if they choose to, it can hit you very hard).

On a similar note, the Chief Justice of India has slammed the incumbent government for “unilaterally blocking” the appointment of lawyer Gopal Subramanium to the Supreme Court. Here again, it is within the capacity of the government to “unilaterally” block the appointment of a Supreme Court judge – there is nothing to bind the decision of the judicial college on the government. It just so happened that in the past the government would usually not reject the recommendations of the college.

A good place to start reforms (though will to reform these might be weak) would be to get rid of these discretionary measures. If it is prudent that the government and the Supreme Court consult over appointment of new judges, put that down in writing. If it is “known” that labour laws are not going to be enforced, change the laws so that the letter of it is something that is easy to enforce.

One of the reasons we are seeing some friction on these counts is that perhaps for the first time we have an “outsider” government. It is likely that more such frictions will come to the fore in the coming days. From this perspective, it would be prudent of the government to change the laws as necessary so that the letter is in line with the spirit.

Why Brazil is undervalued by punters

When India exited the 2007 Cricket World Cup, broadcasters, advertisers and sponsors faced huge losses. They had made the calculations for the tournament based on the assumption that India would qualify for the second group stage, at least, and when India failed to do so, it possibly led to massive losses for these parties.

Back then I had written this blog post where I had explained that one way they could have hedged their exposure to the World Cup would have been by betting against India’s performance. Placing a bet that India would not get out of their World Cup group would have, I had argued, helped mitigate the potential losses coming out of India’s early exist. It is not known if any of them actually hedged their World Cup bets in the betting market.

Looking at the odds in the ongoing Football World Cup, though, it seems like bets are being hedged. The equivalent in the World Cup is Brazil, the home team. While the world football market is reasonably diversified with a large number of teams having a reasonable fan following, the overall financial success of the World Cup depends on Brazil’s performance. An early exit by Brazil (as almost happened on Saturday) can lead to significant financial losses for investors in the tournament, and thus they would like to hedge these bets.

The World Cup simulator is a very interesting website which simulates the remaining games of the World Cup based on a chosen set of parameters (you can choose a linear combination of Elo rating, FIFA ranking, ESPN Soccer Power Index, Home advantage, Players’ Age, Transfer values, etc.). This is achieved by means of a Monte Carlo simulation.

I was looking at this system’s predictions for the Brazil-Colombia quarter final, and comparing that with odds on Betfair (perhaps the most liquid betting site). Based purely on Elo rating, Brazil has a 77% chance of progress. Adding home advantage increases the probability to 80%. The ESPN SPI is not so charitable to Brazil, though – it gives Brazil a 65% chance of progress, which increases to 71% when home advantage is factored in.

Assuming that home advantage is something that cannot be ignored (though the extent of it is questionable for games played at non-traditional venues such as Fortaleza or Manaus), we will take the with home advantage numbers – that gives a 70-80% chance of Brazil getting past Colombia.

So what does Betfair say? As things stand now, a Brazil win is trading at 1.85, which translates to a 54% chance of a Brazil victory. A draw is trading at 3.8, which translates to a 26% chance. Assuming that teams are equally matched in case of a penalty shootout, this gives Brazil a 67% chance of qualification – which is below the range that is expected based on the SPI and Elo ratings. This discount, I hypothesize, is due to the commercial interest in Brazil’s World Cup performance.

Given that a large number of entities stand to gain from Brazil’s continued progress in the World Cup, they would want to protect their interest by hedging their bets – or by betting against Brazil. While there might be some commercial interest in betting against Colombia (by the Colombian World Cup broadcaster, perhaps?) this interest would be lower than that of the Brazil interest. As a result, the volume of “hedges” by entities with an exposure to Brazil is likely to pull down the “price” of a Brazil win – in other words, it will lead to undervaluation (in the betting market) of the probability that Brazil will win.

So how can you bet on it? There is no easy answer – since the force is acting only one way, there is no real arbitrage opportunity (all betting exchanges are likely to have same prices). The only “trade” here is to go long Brazil – since the “real probability” or progress is probably higher than what is implied by the betting markets. But then you need to know that this is a directional bet contingent upon Brazil’s victory, and need to be careful!

Upside and downside of bankruptcy

I sometimes think of my mobile phone going out of charge as being similar to filing bankruptcy – if the phone is at 1% battery, the loss is “linear” – all I need to do is to plug it back in and once it’s charged again it’ll function as it used to. There is no “non-linear” loss.

Phone going from 1% to 0% changes that, though. Now, even if you were to plug in the phone as soon as it has gone to 0%, you cannot switch it on till it gets back to some level of battery (that’s the case with my current and earlier androids. Not sure about other phones). Thus, you have a non-linear extra cost because you let the phone hit 0%.

It is similar to bankruptcy in that once you file for bankruptcy you are suddenly piled on with additional paperwork and costs and even if you were to “get charged up”, there will be additional costs that you will have to bear that you wouldn’t have to had you managed to find a plug (funding) when you were close to blackout (bankruptcy) but not yet there! This is the downside of bankruptcy – it imposes non linear costs.

But then there is an upside also – maybe this is a different kind of bankruptcy, but this is one that has upside. Maybe the bankruptcy that I’m going to talk about now is what is called as “Chapter 11” in the US while what I described earlier is like “Chapter 7” (do you know that US bankruptcy law is inspired by the Mahabharata? In the great Mahabharata war, the two sides had 7 and 11 regiments respectively. And since it was a disastrous war, the numbers 7 and 11 were picked up by the US bankruptcy lawmakers to name their different kinds of bankruptcy).

So there are times when I have a lot of things to do. I would have bitten off more than I could chew. And I find that I have so many things to do that just thinking about all the things I have to do in that limited time mess up my mind and not allow me to do any of them. It is at such points in time that I sometimes “declare bankruptcy” – declare that I’m not going to do any of the things that I’m supposed to do.

Now, the pressure is off. Since I’ve decided I don’t want to do anything, whatever I do after that is a bonus. Now I can take up these tasks one by one and do more than what I would have had I not decided to declare bankruptcy. There is some downside of course – some tasks might remain incomplete, but importantly more gets done than if I’d declared bankruptcy!

This is the good side of bankruptcy!

Graphing social networks

When I’m meeting a random bunch of people I like to graph out social networks in terms of who knew whom before the meeting happened. For example, I was meeting some friends yesterday – B was in town, and wanted to meet people. He called A and C, who got along D (also known to B). After this meeting B was supposed to meet E, but E landed up anyhow. Based on who knew whom before the meeting this is how the network topology went. People are represented by vertices and if there’s an edge between them that means they know each other.

So it started with A and B meeting, with C supposed to land up in a while. Now, C knows A and B through two different “affiliation groups”, but knows both quite well. So C lands up, but now the question is what do you talk about. The basic structure of the group – where A-B, B-C and C-A know each other through three separate affiliation groups means you can’t talk about people (thankfully!).

Anyway conversation goes on, and then D lands up. When B asked C if they could meet, he said “I’m not in touch with anyone else here in Bangalore. But if you think there’s someone else from our affiliation group who’s here and wants to meet, bring them along”. Thus, C invites D (whom he hasn’t met for ages) and D lands up.

Now, for the first time, the group is not a clique – since A and D don’t know each other. It’s up to B and C now to control the conversation in a way that A or D don’t get bored. People talk about work, careers and all that – where anyone can give gyaan.

After a while, E lands up. Now, E doesn’t know anyone else in the group (apart from B). So now, B becomes a cut-vertex. B starts talking to E. With B and E taken out, in the A-C-D network, C is now a cut-vertex! So it’s up to C to manage the conversation with A and D! C isn’t particularly good at that!

Soon A leaves. Now, the group effectively splits, while sitting at the same table. B talks to E (no one else knows E), and C talks to D. All is well.

The problem with the group was that none of the “connectors” (B, C) were particularly good at connecting people, and keeping one conversation. This, though, wasn’t the case at a drinks session I attended on Monday evening. There, the social network at the beginning of the conversation looked like this (variables here all mean different people, only I was common to both meetings):

The thin lines here indicate that B-F and E-F had met before, but didn’t know each other well enough. As you can see, A is now the cut-vertex here. The difference, though, is that A is a master networker, and has a self-professed interest in “collecting interesting people”. The group for the meeting was also fully curated by A – no one “brought along” anyone else.

So A ensured that the conversation flowed. He made sure people connected, and there was great conversation. At the end of the day the network was a clique!

I’ve never been good at making these connections. I dread gathering where I’m the cut-vertex – forever afraid that someone might be left out. Connecting and collecting people is surely a skill I need to develop!

PS: At a coffee shop in Mumbai eight summers ago, I was at one end of the social network which looked like this. Don’t ask me how it came about!

Hacking life

One of those terms that periodically bubbles up to the top of people’s imagination is “life hacking”. The phrase by itself may or may not make sense – actually looked at the right way, it might. However, the problem with such catchphrases is that they tend to get much abused and people start using them in contexts where they’re not appropriate (think, for example, “big data”. Similarly, I loathe to call myself an “analytics consultant” since that’s much abused. I instead use some variation of “quant management consultant” which is not yet abused).

Coming back to life hacks, the problem with life hacks is that a lot of what goes under the name of life hacking isn’t actually hacks. For example, recently the Mint newspaper (who I write for) published a series on life hacking by this guy called Charles Assisi. The three part series was extremely underwhelming and meh.

Take the first part, for example. It includes supposed “hacks” such as “find yourself” and “get things done”. While I agree that these might be useful principles to live life by, they simply don’t qualify as being hacks.

The basic definition of hacking is to rig up something on the fly. Check out the “hack” page on urban dictionary, for example. Sample some of the (more charitable) definitions of hacking:

A temporary, jury-rigged solution, especially in the fields of computer programming and engineering: the technical equivalent of chewing gum and duct tape. Compare to kludge.

A computerized bartender that automatically mixes your drinks and debits your account? Now THAT’S a hack.

You get the drift right? A hack is something like the Indian “jugaad” – something that’s put together because a mainstream solution doesn’t work. If I buy curtains for my window it’s not a hack. If I cover it up with a bedsheet instead (like I’ve currently done in one of the rooms in my house), it’s a hack!

Coming back to the point, the problem with a lot of “life hacking” discourse is that what it speaks about cannot be classified as hacking (Assisi’s pieces are Exhibits A, B and C of this). The problem, however, is that hacking of any form doesn’t lend itself to newspaper articles, for hacking is always context sensitive.

The reason I’ve used a bedsheet as a curtain is that i have a non-standard sized window and I’m too lazy to go get custom-made curtains – notice that this is a problem unique to me, and hence I’ve hacked together a solution. This, now, cannot be translated to a newspaper piece that says “Home hacks: Use bedsheets as curtains”.

Life hacking, in its traditional form, is rather useful, but doesn’t “travel”. For example, one of the “hacks” that Assisi writes about is “choose focus”. Now, intuitively, there’s nothing “rocket science” about this. For most people, focusing on a task at times can be rather trivial, and thus doesn’t need a “hack”.

But what about people with ADHD like me, who cannot focus? I know that focusing is a wonderful thing, but I can just never get myself to focus. This is where a “hack” (to get myself to focus despite being inherently bad at it) might prove useful – and if the hack proves successful I can “productionize” it. But then, that’s my specific context, and there is no way a newspaper article can address that!

So life hacking exists. Yes, it’s a thing. But it’s a context sensitive thing. A hack that can work for you will not work for me – unless our contexts are extremely similar! Keep that in mind before you profess or import hacks!

Sri Lanka diaries: Hotel of the tour

The “hotel of the tour” award for my just-completed vacation in Sri Lanka goes to Pigeon Island Beach Resort in Trincomalee. Now, it is not that they had the best rooms. It is not that the rooms were the best maintained. It is not that the service there trumped the service at every other hotel that I stayed in. It was simply that they seemed to have given the most thought to the hotel design.

At first look I wasn’t particularly impressed with the hotel. Now, it is a highly rated hotel going by TripAdvisor, because of which we had booked it, but the first impressions weren’t great. The reception area was small – just one table, staffed with people not in any uniform (it’s a beach resort – so I should’ve figured that the T-shirts they were wearing was actually uniform!). The hotel was rather small and narrow, with access to a narrow sliver of the beach. The rooms were big, but the loo seemed uncomfortable, with the way the pot was wedged next to the shower cubicle. And the air conditioning never seemed to cool the room enough!

It was after a trip to the beach later in the afternoon that I figured out the value in the hotel design. Now, when you go to the beach, you can expect to get all dirty and muddy. So resorts usually have a shower installed on the way back from the beach to the rooms. This was there. What really impressed me, though, was the tap in the garden right in front of my room! Now, even after showering on the way back to the room, my feet and slippers had got all dirty and muddy. It would have been a mess to clean up the room had I walked in with my muddy feet. So this tap meant that I could wash my feet once again before stepping into the room, thus saving the hotel the trouble of cleaning all those rooms whose occupants had taken care to wash their feet!

Then there were the clothes hangers outside each room. Now, you don’t expect everyone who go to the beach to be wearing swimsuits, and that means a lot of wet clothes. People usually fill up the bathroom with these wet clothes and it can get uncomfortable! Again, it was great thought to put these clothes hangers so that you needn’t fill up your bathroom with the wet clothes! It was another matter that they didn’t have enough of those, and we had to dry our clothes on a chair outside the room!

The following night we stayed at Hotel Earl’s Regent in Kandy, a new hotel inaugurated by “His Excellency President” Mahinda Rajapakse in January this year. It is a hotel which showed a lot of promise, and we were even upgraded to rooms with Jacuzzis. But the detail in design was missing.

For example, at one end of the bathroom was the Jacuzzi and at the other end the shower cubicle. Now, the towel rack was right above the Jacuzzi, and there were no towel hangers on the doors of the shower cubicle. This meant that once you got out of the shower, you had to get all the way across the bathroom to pick up your towel, thus wetting it in its entirety! Then, despite having bathing spaces at either end of the bathroom, there was only one foot mat. Again, this meant that if you failed to move it to your side of the bathroom when you stepped in, the bathroom was again liable to get dirty!

It is amazing how much people are willing to invest in hotels, without getting these small details that can delight a customer right!

Then there was the issue of the plug points. Sri Lanka uses Indian plug points, which meant that we hadn’t bothered to take adapters along. Both in Earl’s Regent and in Cinnamon Grand in Colombo (a five star hotel), most of the plug points turned out to be British-style! Now, you might get a lot of your guests from Britain and it might make sense to have those plug points, but it is surprising that only one point in each room can take Sri Lankan plugs! Now, when each of you has a phone, and then you have an iPad, all of which need charging, it becomes real hard to manage with such plugs!

I don’t know what it is about five star hotels that they refuse to offer health faucets! Every hotel on tour offered them except Cinnamon Grand (the most expensive), where we were forced to use toilet paper. Now, you might get some Western guests who don’t know how to use health faucets, but having them in the room does no harm, while providing great value to Asian and Middle Eastern guests! On a similar note, the Palm Garden Village Hotel in Anuradhapura (a massive forested resort) didn’t offer a health faucet but instead had a separate arse-washing pot. It was again inconvenient and ineffective design, when a simple health faucet would have done the trick with less real estate wasted! And if they had space for a separate arse-washing pots, they might have as well put Sochi-style adjacent pots – it was after all a romantic hotel, with adjacent showers, etc!

Cinnamon Grand also had the worst showers. They had two taps – one for adjusting the level of the hot water, and one for the cold water, and they were the only two controls you had to adjust both the temperature and the pressure of the flow. So if you finally (after a lot of trial and error) got control over the temperature, and wanted to increase the pressure, you had the unenviable task of adjusting two taps simultaneously! Or if you wanted to stop the shower to soap yourself, you had to again do the trial and error thing of finding the right temperature!

The shower at my home has three controls – one tap each for hot and cold water, and another to adjust the overall pressure of the shower. This third tap can be used to adjust intensity after the first two have been used to adjust temperature! The other hotels on tour offered a single lever – right-left movement adjusted the temperature while up-down movement adjusted the pressure! Worked beautifully. Maybe there is a theorem somewhere that the best shower controls have an odd number of levers!

What’s in a shirt number?

There is a traditional way of allotting shirt numbers to football players. “Back to front, right to left”, goes the rule. The goalkeeper is thus number 1. Irrespective of the system used, the right back is number 2, and usually the left forward/winger is number 11.

Now, the way different teams allot numbers depends upon their historical formations, and how their current formations have evolved from those historical formations. The two historical formations that are the 2-3-5 (mostly played in Europe) and the W-M (which originated in South America).

You can read Jonathan Wilson’s excellent Inverting the Pyramid to find more about how formations evolved. This post, however, is about shirt numbers in the ongoing world cup.

Now, given the way numbering has evolved in different countries, each number (between 1 and 11) has a traditional set of roles involved. 1 is the goalie everywhere, 2 is right back everywhere. 3 is left back in Europe, but right centre back in South America. 4 is central midfielder in England, but centre back in Spain and South America. 6 is a central defender in England, left back in Brazil/Argentina and a midfielder in Spain.

These are essentially numbering conventions based on how numbering systems have evolved, but are seldom a rule. However, such conventions are so ingrained in the traditional football watcher’s mind that when a player wears a shirt number that is not normally associated with his position, it appears “wrong”.

For example, William Gallas, a centre back (and occasional right back for Chelsea) by trade moved to Arsenal in 2006 and promptly got the number 10 shirt, which is usually reserved for a central attacker/attacking midfielder (in fact, the number now defines the role – it is simply called the “number 10 role”). In the last season, West Ham used two successive left backs (Razvan Rat and Pablo Armero) last season, and both were allotted number 8 – traditionally allocated to a central midfielder.

In this post, we will look at the squads of the ongoing world cup and try and understand how many players are wearing “wrong” shirt numbers. In order to do this, we look at the most common roles associated with a particular number, and identify any players that don’t fit this convention.

Figures 1 and 2 have the summary of the distribution of roles according to shirt number.

As we can see, all number 1s are goalkeepers (perhaps there is a FIFA rule to this effect). Most number 2s and 3s are defenders, but there is the odd midfielder and forward also who wears this. Iranian forward Khosro Heydari wears 2, as do Greek midfielder Ioannais Maniatis and Bosnian midfielder Avdija Vrsajevic.

The most unnatural number 3 (in his defence, he’s always worn 3) is Ghanaian striker Asamoah Gyan. Iranian midfielder Ehsan Aji Safi also wears a 3, contrary to convention.

As discussed earlier, midfielders from a few countries wear 4, but there are also two forwards who wear that number – Japanese Keisuke Honda and Australian Tim Cahill. This can be explained by the fact that both of them started off as midfielders, and then turned into forwards, but perhaps wanted to keep their original numbers.

5 is split entirely between defenders and midfielders, who also make up for most of the number 6s. The one exception to this is Russia’s Maksim Kanunnikov, who is a forward. Interestingly, as many as six number 7s (associated with a right winger in both 2-3-5 and W-M systems) are listed as defenders! This includes Colombia’s left back Armero who notoriously wore 8 for West Ham last year. This might possibly be explained by players who started off as wingers and then moved back, but kept their numbers. Two defenders – Costa Rica’s Heiner Mora and Australia’s Bailey Wright wear number 8.

Number 9 is again one of those numbers which is associated with a specific role – a centre forward. In fact, in recent times, there is a variation of this called the “false nine” (there is also a “false ten” now). We would thus expect that all number nines are number nines, but a few midfielders also get that number. Prominent among those is Newcastle’s Cheick Tiote, who wears 9 for Cote D’Ivoire.

10 is split between midfielders and forwards (as expected), but a few defenders wear 11. Croatian captain and right back Darijo Srna wears 11, as also does Greek defender Loukas Vyntra.

Beyond 11, there is no real convention in terms of shirt numbering. The only interesting thing is in the numbers allotted to the reserve goalkeepers (notice that no goalies take any number between 2 and 11). By far, 12 is the most popular number allotted to the reserve goalkeeper, but some teams use 13 as well. Then, 22 and 23 are also pretty popular numbers for goalkeepers.

Finally, we saw that Iran was the culprit in allocating numbers 2 and 3 to non-defenders. Greece, too, came up as a repeat offender in terms of allocating inappropriate numbers. Can we build a “number convention index” and see which countries deviated most from the numbering conventions?

Now, there are degrees in being unconventional, and these need to be accommodated into the analysis. For example, a midfielder wearing 4 (there are 6 of them) is pretty normal, but a forward wearing 3 is simply plain wrong. A forward wearing 8 is not “correct”, but not “wrong” either – this shows that we need more than a simple binary scoring system.

What we will do is to first identify the most common player type for each number, and every such player will get a score of 1. For every other player wearing that number, the score will be the number of such players wearing that number divided by the number of players wearing that number who occupy the most popular position for that number.

I’m assuming the last paragraph didn’t make sense so let me use an example. To use number 2, the most popular position for a number 2 is in defence, so every defender who wears 2 gets 1 point. There are two defenders who wear 2, compared to 29 defenders who wear 2. Thus, each defender who wears 2 gets 2/29 points. One forward wears 2, and he gets 1/29 point.

Taking number 10, the most common position for the number is forward (there are 17 of them), and they all get 1 point. The remaining 15 players who wear 10 are all midfielders, and they get 15/17 points (notice this is not so much less than 1).

This way, each member of each squad gets allotted points based on how “normal” his shirt number is given his position. Summing up the points across players of a team, we get a team score on how “natural” the shirt numbers are. The maximum score a team can get is 23 (each player wearing a number appropriate for his position).

Table 3 here has the team-wise information on correctness of shirt numbers. The team with the worst allocated shirt numbers happens to be Nigeria with 16.13. At the other end, the team that has allocated numbers most appropriately is Ecuador, with 21.

Country	Score
Nigeria	16.13
Costa Rica	16.85
Greece	17.22
Australia	17.45
Iran	17.69
Ivory Coast	17.74
Colombia	18.19
Cameroon	18.19
Argentina	18.29
USA	18.41
Italy	18.63
Portugal	18.66
Algeria	18.68
Honduras	18.69
France	19.02
Ghana	19.06
Croatia	19.08
Netherlands	19.20
Mexico	19.23
Brazil	19.28
Chile	19.37
Japan	19.52
South Korea	19.69
England	19.77
Russia	20.03
Switzerland	20.04
Uruguay	20.25
Spain	20.27
Bosnia & Herzegovina	20.37
Belgium	20.83
Germany	20.86
Ecuador	21.01

This, however, may not tell the complete story. As we saw earlier, conventions regarding numbers between 12 and 23 are not as strict, and thus these numbers can get allocated in a more random fashion compared to 1-11. There are absolutely no taboos related to numbers 12-23, and thus, misallocating them is less of a crime than misallocating 1-11.

Hence, we will look at the numbers 1 to 11, and see how teams have performed. Table 4 has this information:

Country	Score
Australia	7.45
USA	8.04
Iran	8.18
Greece	8.59
Nigeria	8.63
Ivory Coast	8.71
Costa Rica	8.84
Ghana	8.95
Croatia	8.96
Japan	9.06
Colombia	9.27
Brazil	9.29
Spain	9.66
Bosnia & Herzegovina	9.67
Uruguay	9.70
Honduras	9.71
Portugal	9.78
Italy	9.81
South Korea	9.83
Cameroon	9.83
Chile	9.87
Russia	9.94
England	9.97
Argentina	10.03
Switzerland	10.18
Netherlands	10.24
Algeria	10.30
Ecuador	10.34
Mexico	10.35
France	10.53
Belgium	10.88
Germany	11.00

Germany has a “perfect” first eleven, in terms of number allocation. Belgium comes close. At the other end of the scale, we have Australia, which seems to have the most misallocated 1-11 shirt numbers. Iran and Greece, which we anecdotally saw as having high misallocations are at three and four, with the United States at 2.

Note: The data is taken from the Guardian Data Blog. Now, this analysis should be taken with some salt since in the modern game, the division of players into “defender”, “midfielder” and “forward” is not straightforward. Where would you put a “classic number ten”? What about a wing back? And so forth.

Market forces

This morning I refused to board an auto rickshaw since it had one of those old analogue metres. Most autos in Bangalore nowadays use digital metres, which is the regulation. Except a few like the one I saw in the morning.

Now, given that most autos have digital metres people have a choice to choose only such autos. I’m sure the driver I met this morning will realise soon enough that he’s not getting as much business as he can due to his old metre, and make the switch.

It’s similar with usage of metres. In some parts of Bangalore it’s the norm for auto rickshaws to ply by metre. In such areas any driver who tries to make a quick buck by negotiating a higher fare is likely to lose customers. When a customer knows that after letting go of an auto which asked for excess fare, he had a good chance of finding one that will go by the regulated fare, he is less likely to heed to the demand for excess fare.

You can think of this being a case of what Malcolm gladwell calls the tipping point – once markets have tipped to one side (let’s say using regulated fares for auto rides) there is positive reinforcement that leads to an overwhelming move in that direction.

To get back to the metre example, when the fares increased a few months back traffic cops in Bangalore ran a drive where they checked for auto metres and fined those who had not made the switch by a particular date. Maybe that’s led to about 95% of the metres getting recalibrated. The beauty here is that market forces will take care of pushing this 95% to 100% and cops need not spend any more time and energy on enforcing this! Similarly if cops want to enforce usage of regulated fares they would waste time by doing this drive in areas where most rides are by metre – the focus should be on tipping the other areas over!

To summarise, some parts of regulation gets enforced by sheer market forces, and regulators should not be wasting their energies there. Focus should instead be given to those areas where market failure is extreme – for that is where regulation has a role to play.