Saturday, November 27, 2010

On Risk, Return and Batsmanship

In Finance, one of the cardinal sins is to undertake an investment decision without assessing the forecasted return in the context of the risk exposure. Risk and Return are inextricably linked. I'd rather have my money earn 3.5% in the Savings account if an alternative market investment promises a 10% return with a standard deviation of 50%!

A common metric often employed to evaluate portfolio performance is the Sharpe Ratio, which is basically the premium return that is offered by an investment for each unit of risk undertaken. No wonder "risk-adjusted return" is a hackneyed phrase one hears from portfolio managers.

How is all this related to Test Match Batsmanship? Very closely related as we shall see.

Batsmen in Test Matches are often judged on the basis of their "batting average". An average of 50+ is usually regarded as outstanding and is often the figure that most Test batsmen aspire for. Ofcourse, one needs considerable skill to maintain an average of over 50. But more than skill, I think the key is to understand risk-return dynamics well.

There are two components to the batting average that ought to be understood if one wishes to optimize it:

Component A : Time Spent in the Middle i.e the No of balls that one lasts on an average per innings

Component B : The ability to force the pace while in the Middle. This component is better known as "Strike rate" i.e the No of runs that one scores per 100 balls faced.

Batting Average = F(Component A, Component B)

Sounds too obvious, yes. But this is not exactly a simple plain-vanilla two-variable function. What's often overlooked by batsmen and cricket pundits is that A and B are not independent variables. A is a function of B and vice-versa.

In fact, the two components influence each other negatively. Typically, a batsman with a high strike rate spends less time in the middle, because of the risks involved in trying to force the pace. Similarly, a batsman who bats for long periods of time tends to have a lower strike rate, for reasons that are obvious.

So what should one do to optimize the Batting Average? Should the batsman adopt a risk-averse style by concentrating only on putting away the rank bad ball and defending the rest? The likes of Hutton, Gavaskar and Dravid have achieved great Test records by optimising Component A, without overly worrying about Component B. Nevertheless, for every Gavaskar, there are a dozen other fine technicians who couldn't reach the magic figure of 50 despite their excellence at Component A. Geoff Boycott is a name that readily springs to mind.

There are others who have Test records just as enviable as those of a Gavaskar or a Dravid thanks to their extraordinary strike rates. Viru Sehwag is an obvious example. Here's a guy who is a very limited batsman in many ways, with serious technical deficiencies against the short rising ball. A guy who lasts only 64 balls each time he comes in to bat (that's probably about half the number of balls per innings faced by someone like Gavaskar). And yet, he has a brilliant batting average of 54, significantly better than Gavaskar's 51!! The secret of his success is that he manages to maintain a strike-rate of 80 and yet lasts 64 balls per innings!

There have been several daredevil strokeplayers in the past who have graced the game of cricket. Think Gilbert Jessop, Kris Srikkanth and more recently Shahid Afridi. All of them had batting averages significantly below 40. This is because their high-risk approach to the game significantly reduced their average duration at the crease.

The reason why Sehwag is such a great treasure is not because he is a great strokemaker (there have been several such players in the past) or a great technician (which is hardly the case). Sehwag's greatness lies in his ability to understand the dynamics of risk and return. He is able to play his normal game without taking undue risks that were the bane of players like Afridi or Yuvraj Singh.

It is vital for batsmen around the world to grasp the importance of maximising risk-adjusted returns. The tradeoff between risk and return may vary among batsmen depending on their skill level. Yet, the magnitude of the tradeoff can be minimised only if you are aware of the tradeoff in the first place!

Take Dravid for instance. The man averages a fantastic 53 with a strike rate of about 42 per 100 balls faced. He roughly faces 110 balls each time he visits the crease in a Test match. I'd like to argue that he has not consciously thought about the tradeoff during his career. For a batsman of his ability, the tradeoff between strike-rate and duration at the crease shouldn't be too large.

Mathematically, the tradeoff can be stated as shown below :

d(No of Balls per innings)/d(Strike Rate) <= 0

The objective should be to minimise the absolute value of the above differential!
Cutting down the aerial strokes to the extent possible and running well between the wickets are some of the ways of achieving this objective.

Let us suppose Dravid had been a little more aggressive during his Test career and maintained a strike-rate of 50 instead of 42. This might have reduced his "No of balls per innings" figure from 110 to perhaps 100. Nevertheless, it is a great trade-off. His hypothetical batting average in this case is 56.5, a good three runs higher than his current average! (Note: I'm assuming the same no of "Not out" innings as before)

The man widely regarded as the greatest batsman in Test history is ofcourse Sir Donald Bradman. People often have endless debates on what made him so special. The Don was a somewhat frail man with poor eyesight. In fact, he came perilously close to losing his life on account of poor health during his career. By most accounts, he wasn't a particularly "correct" batsman, with a very unusual grip and a notorious tendency to play across the line. Yet, he averaged 99.94 in Tests and more astonishingly 95.14 in all first-class cricket!

The secret to his success is that like Sehwag, he understood the risk-return tradeoff probably better than most people. No wonder he was a professional stock-broker off the field. The Don managed to maintain a strike-rate of 60 in Test matches (astonishingly high back in the thirties) and lasted about 145 balls per innings.

The figure of 145 is not as exceptional as his batting average. It's still probably better than the Component A of most other batsmen in Test history. But I'm sure there are several bastsmen who are running him close. What made him special was his ability to score at a strike rate as high as 60 without compromising on the time spent in the middle.

I know this post may sound a tad too obvious to a lot of people. But I think it bears repeating. The Risk-return tradeoff is something we're all aware of, yet we don't always consciously think of optimising it in the daily business of life!

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Saturday, November 20, 2010

Ranji - the most underrated cricketer of all time?

The name Ranji immediately conjures up a smallish brown man of royal lineage who lit up the English cricket fields with his brilliantly unorthodox strokeplay about a hundred and ten years ago. He is widely regarded as one of the game's great early innovators and a very popular cricketer in England at the turn of the century.

But pundits don't normally invoke Ranji seriously while discussing all-time greats. Recently, Cricinfo picked an "All-Time XI" for each of the major international Test playing countries. I was flabbergasted to learn that Ranji was not even nominated as a middle-order choice for the All-Time England XI!!

English cricket lovers are not exactly known for their ahistoricism, unlike Indian fans who tend to focus on the here and now. It is very hard to find any English cricket writer who hasn't turned in a few lines on the likes of WG Grace, Sidney Barnes, Gilbert Jessop, Jack Hobbs among others. In fact, Wisden went to the extent of picking Hobbs as one of the five greatest cricketers of the Twentieth century!

Being an Indian with a fair share of interest in English cricket, I wondered - Where does Ranji rank in the pantheon of great English cricketers? Is he widely known today primarily on account of his exotic Indian origin? Are we guilty of overrating his stature in the context of English cricket history? After all, he was the first person of colour to play Test match cricket.

I turned to Cricinfo Statsguru to better understand Ranji in terms of hard numbers. The idea was to move beyond the romantic prose penned by the cricket writers of his time and judge the man using figures alone.

What one discovers is a true cricketing colossus!

Here is a man who played First class cricket in England for 25 years spanning from 1895 to 1920. A man who scored nearly 25,000 First class runs at an average of 56.37!! (yes, you read that right) These figures are very impressive even by today's English first class standards, notwithstanding the fact that English pitches in Ranji's time were a lot livelier by most accounts, even when unaffected by rain. Just to put that average into perspective, Graeme Hick, the most prolific English first class batsman of the past 20 years averages 52.

During his time, Ranji played Test match cricket with/against names like Grace, Trumper, Jessop, Fry and Hobbs among others. All these guys represented the cream of talent the world had on offer during that period. How does Ranji compare with each of them?

I must say Ranji trumps them all going by the first class averages. In fact, he is miles ahead of the rest.

First-class Averages of Ranji and his Contemporaries
Ranji 56.37
Jack Hobbs50.70
CB Fry50.22
Charles MaCartney45.78
Vic Trumper44.57
Clem Hill43.57
Frank Woolley40.77
WG Grace39.45
Archie MacLaren34.15
Gilbert Jessop32.63

It is a very revealing table! Ranji is about 6 runs ahead of the next best batsman. That's a really huge margin. The most striking revelation is that Ranji averaged a good 17 runs more than the great WG in his First class career and about 12 runs more than the celebrated Australian legend - Vic Trumper.

The two guys who approach him in consistency are Jack Hobbs and CB Fry. However, Hobbs scored the bulk of his runs post WW-I during the twenties, when batting became a lot easier thanks to the improved pitches of the time. It is quite likely that Hobbs averaged well below 50 if one considers only his pre WW-I record. CB Fry had an outstanding First class record, but disappointed in Test cricket with an average of barely 32.

How does Ranji rank among all the great first-class cricketers of the past 150 years?
To attempt an answer to this question, I looked at the top 10 batsmen with the highest first-class averages in cricket history (with a minimum run aggregate of atleast 20,000 runs). Ranji ranks sixth in this list.

Highest First-class Averages of all Time (Qual.criteria : 20,000 runs)
Don Bradman 95.14
Sachin Tendulkar59.63
Darren Lehmann57.83
Geoff Boycott56.83
Ricky Ponting56.73
Bob Simpson56.22
Wally Hammond56.10
Rahul Dravid55.89
Len Hutton55.81

Ranji is the only person on this list who made his first-class debut prior to 1920. In fact, he played nearly all his cricket before World War I. Now that was an era when an average of 35-40 used to be regarded as a very good record in first-class cricket.

I think these tables ought to be better known. Ranji was so much more than a mystical Oriental talent who played unorthodox strokes. He was, without doubt, the foremost batsman of his generation. In fact, it can be argued that Ranji was the most dominant and consistent batsman the world had seen until Bradman came along in the thirties.

Surely it's a career that deserves more recognition by cricket historians and greater mindshare among cricket fans (especially English cricket fans)!

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Saturday, November 06, 2010

On Income "Inequality"

I stumbled upon an article lately on my Google Reader feed that ranted somewhat predictably about how income "inequality" has risen significantly in the United States and how the middle class in the US has stagnated over the past 2-3 decades. Here's the link

It is a very provocative article as most poorly reasoned articles are. The worst part of it is that the author attempts to place the blame for "inequality of incomes" on Corporate America without rhyme or reason. In this post, I ponder on the possible reasons for stagnation of middle-class incomes. There are several of them and the most obvious ones have nothing to do with Corporate America or conservative economic policies.

Let's look at certain portions of the article that are worthy of repudiation.

globalization's significant profits were captured by a small corporate elite in the U.S. and a new corporate elite and rising middle class in China and India. The American middle class got very little of it. No wonder people are mad.......Americans accept income and wealth inequality to a much larger degree than Europe........... Looking at the stats on inequality gives us an idea of why so many are angry at the business elite — it's the highest since the 20's and getting worse

Okay. So the moot point is that while incomes have soared in the top bracket, the "median" income of the "representative" Middle American has stagnated over the last few decades notwithstanding the outstanding economic growth during the same period.
I checked up the income stats on wikipedia and it appears that this contention is quite compelling on the surface.

Sluggish Growth in Median American Incomes
Data 20031979
Median (50th)$43,318$38,649
95th percentile$154,120$111,445

We observe that while the 95th %ile income has risen by nearly 40% between 1979 and 2003, the median incomes have remained quite stagnant. On the surface, this might seem like an indictment of Reagan era deregulation and the increasing preponderance of economic conservatism in the US since the late seventies.

But there are several problems with this story.
Think about Individuals and not some mythical "Middle American" : Anybody with an iota of sense can readily see that the 50th %iler who earned a median income of $38,649 in 1979 is not necessarily from the same household as the 50th %iler who earned $43,318 in 2003. It is quite possible that someone who was at 50th %ile in 1979 now has a gainfully employed son who is closer to the 80th %ile on the income distribution curve.

The American Middle class has changed in constitution since the late seventies. Several households have moved up the economic ladder as one would expect in any society bustling with private economic activity. Then, the natural question is that if most households have been upwardly mobile over the past three decades, why have median incomes remained stagnant?? The answer could well be immigration.

Immigration likely to push down median Incomes: A lot of people emigrate to the US with the hope of working their way out of poverty in their native lands and entering the "middle class". These immigrants are often unskilled and poorly educated and hence unlikely to land up with jobs that fetch them more than the median US income.

Households that have immigrated in the eighties and nineties did not feature in the dataset that generated a median income of $38,649 in 1979. Which is why it is highly irregular and inappropriate to compare two very distinct datasets from 1979 and 2003 and make sweeping statements about stagnant "middle class" incomes in the country.

So, does that mean the US should place restriction on immigration to help solve this "problem" of seeming income inequality? No. Reducing inequality of incomes should never be an end in itself. Most recent immigrants to US earning less than the median income are quite happy with their adopted country and wouldn't want to return to their roots. Take for instance a waiter in an ethnic Indian restaurant in NYC (Saravana Bhavan for eg). The guy probably earns $20,000 in his present role which perhaps places him at the 40th %ile on the income distribution curve. It is quite likely that percentile-wise he was much better off in his native country, prior to immigration (given that median income in India is barely $500 p.a). Yet, immigration makes sense for this guy as he is better off being a 40th %iler in NYC than an 80th %iler in Trichy, TN.

The Tamil waiter's immigration to US has contributed to a drop in the median American income. Nevertheless, it is welcome as the waiter's immigration was a personal preference and leaves him better off than he otherwise would've been in his native town.

"Inequality" could be an outcome of personal choices : Let's consider Bob, a successful corporate executive of yesteryear who used to earn the equivalent of $300,000 back in 1979. He has a daughter - Alice who has led a rather comfortable life thanks to her father's affluence. Unlike her father, Alice has little aptitude for business. She has always evinced keen interest in Native American history and wants to specialize in the same and eventually end up as a professor of Native American history in one of the eastern colleges. Alice is 30 years old now in 2003 and is well settled in a Boston college enjoying her role thoroughly. Her annual income is in the vicinity of $50,000, not even one-fifth of what her father used to earn in 1979!!

Is this an instance of downward intergenerational mobility? Yes. Nevertheless, it is an outcome of personal preferences and shouldn't be bemoaned. Alice is less well off than her parents in terms of monthly cash-flow. But she loves her job and probably enjoys more leisure than her father ever did in all his working life!

This little story emphasises an important point that's often overlooked by liberals who bemoan income inequality :

"It is quite likely that the 50th %iler enjoys more leisure and leads a less stressful life than the 95th %iler!"

Distribution of Leisure fairer in recent decades : Back in 1900, the distribution of Leisure was terribly unfair in the Western world. The rich were not just wealthy in terms of cash but also leisure, with little accountability. The workers who slogged 18 hours a day in unwholesome sweatshops, had neither the income nor the leisure to compensate for the lack of income.

Today, the distribution of leisure is distinctly fairer. The clerk in a Federal office may languish at the 50th %ile of the income curve, but he is quite probably placed much better (perhaps 90th %ile+) on the leisure distribution curve! The corporate executives of today enjoy far less leisure and peace of mind than the landed gentry who constituted the affluent class in the 19th century.
Disclaimer : This is only a hypothesis. But I do wish someone undertakes a study that examines how the distribution of leisure has shifted over the past 100 years in favour of the lower income groups.

Writers in the press who talk about rising income inequality in America seldom think about the points discussed in this post because of their obsession with aggregate nation-wide statistics and an indifference to what the statistics actually mean in the context of average individuals and households. Which is why we keep reading pieces where "pundits" use statistics such as the ones used in this post to launch a tirade on outsourcing and corporate executive compensation.

Inequality of outcomes need not necessarily always be a plot hatched by Wall Street wolves or neo-conservative policy makers. People who think so misunderstand not just economics but also human nature. Economics is a social science that concerns real people gifted with a free will. To reduce these people to a statistical abstraction is not just downright unfair, but bad science.

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