Expert Blog

Friday, February 26, 2010

The cricketer’s new face

Ever wondered if cricket data can be “visually” represented? Here’s a look at how Chernoff faces can do so.

While browsing the Internet for innovative statistical analysis in sport, I stumbled upon an April 2008 article in the New York Times, titled “Professor puts a face on the performance of baseball managers”.

I was pleasantly surprised because we had done something very similar – and a year earlier – during the 2007 Cricket World Cup. We had put a face on the performance of cricketers!

It is common knowledge that while looking at huge multivariate data sets – such as cricket data sets – it is not easy to quickly identify similar and dissimilar data subsets. Looking at the data, can we say if it is related to a batsman or an all-rounder? Or, looking at the data of two batsmen, can we say who is performing better?

One particularly elegant idea, first employed by Chernoff, is to use cartoon faces to represent many variables. This graphical tool works because the human eye finds it easier to spot similarities between faces, rather than cold data sets.

We used Chernoff faces, using the SYSTAT software, to depict the most valuable players of the 2007 Cricket World Cup featuring over 200 cricketers.

We created Chernoff faces for each player based on the following assignment of variables to facial features:

Here are the Chernoff faces of the nine most valuable players of the 2007 World Cup.




If a layman sees these faces, he will discover that “Matthew Hayden” and “Ricky Ponting” have striking similarities. Both have rounded faces, wide noses and big smiles, although “Hayden” is smiling a little more.

 If we now look at our variable assignments we see that the smile is because the number of runs is linked to curvature of the mouth (variable 1); the wide nose is because the number of runs is also linked to the width of the nose (variable 3). So both “Hayden” and “Ponting” have offered immense value as batsmen, although Hayden’s wider smile suggests a slightly greater batting value (659 runs at a strike rate of 101.1, in comparison to Ponting with 539 runs at a strike rate of 95.4).

If we continue looking, we’ll find that “Hayden” and “Hogg” are very dissimilar. Hogg has no smile (didn’t score runs), and has a tall, thin nose. Hogg also has massive ears and a tapered face. Hogg’s tall nose (variable 4) and big ears (variable 19) suggests that he has taken a lot of wickets (21). This is further confirmed by Hogg’s tapered face (imagine that the face is made up of an upper and lower ellipse) because wickets are linked to the eccentricity of the ellipses (variables 16, 17).

We also discover that “McGrath” is very similar to “Hogg” (26 and 21 wickets respectively).

Next, we find a lot of similarity between “Jayasuriya” and Styris”. This duo looks slightly different from “Hayden” – in comparison, they have a taller nose and bigger ears – but sufficiently dissimilar to “Hogg”. We guess – correctly – that they are batting all-rounders.

Finally, don’t be surprised by Jayasuriya’s big eyes. He was responsible for quite a few run outs (variables 10, 11).

Friday, February 19, 2010

Defining a paisa vasool index

How do you judge a cricketer’s “worth”? Srinivas Bhogle has an interesting perspective on the subject. Read on…

We live in times when a Shane Watson is “bought” for US$125,000 and Rohit Sharma for $750,000. So someone’s surely going to ask what the return on this investment is, i.e. is this a paisa vasool investment?

Answering such questions isn’t easy. Obviously, the answer would depend on the player’s on-field performance … and things are trickier in T20 cricket because, apart from runs and wickets, strike rates, economy rates and fielding ability also enter the calculation.

Thankfully, the Castrol Index (CI) could do the job of measuring the player’s on-field performance rather well. The CI judiciously combines a player’s batting, bowling and fielding effort into a single number.

While the CI is an interesting concept by itself, it doesn’t answer that key question: which player is paisa vasool and which player isn’t? However by dividing the money paid to a player so far (if the player has been available for 9 matches so far out of 14, we assume that he has received 9/14th of his total payment) by his CI, we obtain an index (that we could call the Castrol Paisa Vasool Index) that will do the job very adequately.

When we attempted such an analysis, a handful of interesting observations tumbled out of the cupboard:

# It is unwise to pay too much for single cricketing skills. A good ‘pure bowler’ could at best command a price of $500,000. Paying Ishant Sharma $950,000 is a big waste of money. Even Rohit Sharma wouldn’t be worth $750,000 if he didn’t bowl a bit too (and a hat-trick, as in IPL2, would be a real bonus!)

# A player possessing explosive skills that can turn a match around is good value for money … that’s why a Virender Sehwag, Tillakaratne Dilshan, Ross Taylor or Kieron Pollard is still a coveted catch … they could single-handedly win you 3-4 of the 14 or more IPL matches. To appreciate this better, read Ananth’s masterly analysis of JP Duminy’s knock in the Champions League for Cape Cobras.

# If the pitches are batsmen-friendly, pick bowling all-rounders; if they are bowler-friendly, pick batting all-rounders. Jacques Kallis is a fine example: he flopped in batting-friendly IPL1, but was immensely successful in bowling-friendly IPL2.

# Specialist wicket-keepers are not worth the money unless they bat well too. So if you can’t be an Adam Gilchrist, at least try to be a Kamran Akmal. And Brad Haddin can go home!

But the most significant finding of the analysis was that franchise owners accorded equal or more weightage to a player’s off-field value. Mashrafe Mortaza’s price of $600,000 didn’t make any sense … till you factored in the fact that, by playing him, Kolkata Knight Riders bought the loyalty of the whole of Bangladesh. Kevin Pietersen’s cricketing worth could certainly not be worth $1,550,000 … till you recognized that he was a great choice to walk down the ramp with Deepika Padukone.

So how do we set up the complete model of a paisa vasool index? The Castrol Index will estimate the on-field performance admirably. To couple on-field performance with off-field worth, we will need a more complicated hedonic pricing model – that could someday form the basis for a future Interpreter blog.

Wednesday, February 03, 2010

The idea of the pressure index

After the par score in ODI cricket, our expert shares his insight about another concept: the pressure index.

Last time we talked of the par score in ODI cricket: it is the score that a team chasing must make to tie the match based on the Duckworth-Lewis method.

A typical ODI match has ups and downs: sometimes you think India is winning and at other times you think that Sri Lanka is more likely to win.

This feeling about which side is winning is based on our general appreciation of an ODI game. If India is chasing a huge target and loses quick wickets you feel India is losing. If India is chasing a modest target and Sehwag and Gambhir are on the rampage, you feel India is winning.

Can we quantify this feeling? Can we come up with a number that measures the probability that the team chasing will win the match?

Some years ago, I collaborated with two professors: MJ Manohar Rao – now, alas, no more – and Rajeeva L Karandikar to define the pressure index ‘experienced’ by a team chasing a target in an ODI match. This index would range from 0 (if the side chasing wins) to 200 (if the side chasing loses). If the match was evenly placed, the chasing team’s pressure index would be exactly 100.

If India lose their openers while chasing 350, their pressure index might be as high as 150. If Sehwag and Gambhir blaze to 100 for no loss in 12 overs while chasing 225 in 50 overs, the pressure index could be well below 50.

Our building block for the pressure index was the par score. If the team chasing was well ahead of its par score then it had a higher probability of winning – and therefore a pressure index below 100.

The key idea – although it wasn’t as simple as that – was to look at the ratio of the par score and the actual score. If this ratio was less than 1, i.e., if the par score was lower than the actual score then the team chasing felt less ‘pressure’ and had a pressure index less than 100. If there were now a flurry of boundaries, the pressure index would drop even lower; but if there were a flurry of dismissals, the pressure index could quickly become greater than 100.

That was the approximate idea: keep tracking the pressure index ball after ball! It was a great way to know at a glance which team was ahead, and by how much. The ball-by-ball pressure index could also be plotted graphically to produce a ‘pressure map’. This pressure map provides a wonderful instantaneous appraisal of how the ODI match went.

We reproduce below the pressure map of the India-Sri Lanka game in the 2007 World Cup. India lost this match and suffered a quick exit when they failed to overcome Sri Lanka’s target of 255. The map shows that India had some sort of a chance in their first 5 overs when the pressure index was just above 100. But the loss of quick wickets – Ganguly and Tendulkar in quick succession – sent India’s pressure index up to 144 at around the 12th over.




The Castrol Index provides another way to quickly discover which of the two teams is faring better at every point of time. Read Arvind’s article to know more.

Wednesday, January 13, 2010

The idea of the par score

If you have wondered how the Duckworth-Lewis method makes or breaks a game, look no further. Our expert tells you more.

Let’s suppose that India score 275/5 in 50 overs in an ODI game against England at Leeds. Suppose England have reached 98/2 after 22 overs in their chase when run (or even snow!) stops the game.

Who’s winning at this stage?

This is where we use the idea of the par score, now used by the Duckworth-Lewis method. The par score is the score that England must make to tie the match. England win if they score at least one run more than this par score.

To be sure, the par score is not unique. It depends on how much the team batting first has scored, the overs remaining in the innings and the wickets lost by the chasing team. For the same number of overs remaining, the par score is lower if fewer wickets are lost, and higher if more wickets are lost. In our example if 98/2 is the par score, then 88/1 or 121/3 may also be par scores (they are not actual D/L par scores, I’m just guessing).

On most English grounds, the par score is displayed on the score board – well, sort of … what score boards actually display are numbers like +11 or -5. The display ‘+11’ means that the side batting second is now 11 runs ahead of the D/L par score; ‘-5’ would mean that the side chasing is five runs behind the D/L par score.

Remember that the par score is not static. It keeps changing from ball to ball. Let’s suppose that, in our example, England’s 98/2 was the par score after 22 overs. Let’s suppose that the first ball of over 23 is a dot ball … and then it starts raining or snowing! Then in all probability, England have lost the match because that dot ball may have pushed the par score up to 99/2.

Amazingly enough this was how South Africa probably got knocked out of the 2003 World Cup that they were hosting. Chasing Sri Lanka’s 268/9, South Africa were 216/6 when Muralitharan started bowling the 45th over – which was almost certain to be the last with rain turning heavier. The par score at the end of that over was 229/6; so the batsmen in the middle – Boucher and Klusener – were told that they had to get to 229 by the end of the over without losing their wicket. Boucher hit a six off Murali’s fifth ball to take South Africa to 229/6. Happy to reach 229, and perhaps not wanting to take a risk and get out, Boucher quietly defended Murali’s last ball.

When the match was called off after over 45, a jubilant South African team thought that they had won! They hadn’t! They had merely tied the match because South Africa needed to score one run more than the par score to win. The loss of two points because of the tie finished off SA’s World Cup campaign. The story could have been very different if Boucher had played the last ball for a single. Sadly, the South African team management confused the par score with the winning score.

Some six years later, it was again some confusion around the par score that gave England a shock victory over West Indies. With light fading at Guyana, West Indies were ahead of the D/L par score at 244/6 when Broad trapped Ramdin lbw. The loss of the 7th wicket meant that 244 was no longer the par score; it had gone up to 245!

Not realizing this, the West Indies coach John Dyson called his team in when the umpires offered lights. West Indies could have won if they had walked off after the new batsman had scored a single or two off the next ball.

The par score is an interesting idea: it measures the difference between two teams after every ball in terms of runs. In the Bangladesh-India ODI on January 11, 2010, India overtook Bangladesh’s score of 247 in 43 overs. The record books will say that India won by 6 wickets with 7 overs to spare. But what was India’s victory target in terms of runs? Let us suppose that the D/L par score while chasing 247 with four wickets lost and seven overs remaining was 187/4 (again, just guessing). We could then say that India won by 60 runs.

The par score can also be used to define an interesting concept called the ‘pressure index’. We will talk about the pressure index in the next blog.

Wednesday, December 30, 2009

Revisiting team ranking schemes

What must be the criteria to accurately define a team’s standing in world cricket? Our expert looks at existing schemes and analyses them

I know of a lot of team ranking schemes in cricket: some are mighty complicated, and many are duds.

It’s quite a puzzle actually. A lot of people can recognize a good team performance in cricket, but few seem able to encapsulate it in an appropriate mathematical model.

Let’s look at ODI cricket, and let’s list some of the popularly touted criteria, in no particular order:


1. If you win more matches, your ranking should be higher

2. If you defeat stronger teams, you must get more weight

3. If you win ‘away’ matches, you must get more weight

4. Recent wins must get more weight, and this weight must steadily decline over time

5. Winning by bigger margins must fetch more credit

6. Winning a series or tournament must fetch extra credit

7. Winning when your top players are injured must receive more recognition.


About half of the existing ranking schemes only consider criterion 1. They give one point for a win, 0.5 for a draw or tie, and 0 points for a loss. Then they choose a time window (typically a calendar year or a moving 12-month window) and start calculating!

It’s easy to pick holes with this scheme: play 20 matches with the weakest available team and win all of them! So if Bangladesh plays 20 ODIs against Zimbabwe and wins all of them, Bangladesh could become the ‘best’ team in the world.

This isn’t making much sense. In fact, it’s pretty clear that a ‘good’ ranking scheme must use as many of the above criteria as possible.

How many of these criteria are feasible? Most would say criterion 7 is subjective. They might also argue that criterion 5 is a little hard to model.

Let’s therefore look at ICC’s ODI ranking scheme (that we’ve written about earlier). It considers criteria 1, 2 and 4. In particular, the ICC scheme models criteria 2 and 4 rather elegantly. I won’t go into details, but criterion 2 is handled really neatly. My only grouse with criterion 4 is the choice of August 1 as the cut-off date to reduce weights: this makes a win on August 2 relatively more valuable than a win on July 29.

The ICC scheme can, in an awkward sort of way, accommodate criterion 6 (the ICC Test cricket ranking scheme does consider criterion 6; the awkwardness in the ODI ranking scheme is because of tournaments involving several teams). It also seems feasible to bring in criterion 5 via the Duckworth-Lewis method, because D/L can quantify every ODI win in terms of a run margin.

The inability to accommodate criterion 3 is a serious weakness although it can be argued that the ‘home-away’ variation is less pronounced in a 50-over match, especially with pitches everywhere now being prepared to favour batsmen.

The ODI ranking scheme published on rediff.com for 8 years is of comparable pedigree: it accommodates criteria 1, 2, 3 and 6, but fails to consider criterion 4, although there is a reasonably easy way to do it.

There is, of course, a completely different way to look at team rankings: suitably add up the individual rankings of the players making up the team! This is the Castrol way, and it was very encouraging to note that the Castrol Index correctly spotted the semi-finalists in the recently concluded Champions League.

Monday, December 14, 2009

Revisiting the Duckworth-Lewis method

When it rains, remember Messrs. Duckworth and Lewis. Their method of calculating targets in rain-affected ODIs has always been a little complex to understand. Our expert sheds some light on the same.

The D/L rationale

To win an ODI match, the team chasing requires two ‘resources’: ‘wickets in hand’ and ‘overs remaining’. Everyone knows this. We knew this even 20 years ago!

But the rain rules in 1989 were strange: they only considered the ‘overs remaining’ resource.

So if India scored 250 in 50 overs (O1=50) and then a rain interruption left India’s opponents with only 25 overs (O2=25), they had to score 250*(O2/O1)+1 = 250*(25/50)+1 = 126 runs to win with all 10 wickets in hand!

The option of using all 10 batsmen even when the overs were reduced offered a considerable advantage. No wonder all captains wanted to chase if they won the toss on a cloudy day.

The Duckworth-Lewis (D/L) method corrected this anomaly. D/L came up with a mathematical model that combined these two resources into a single ‘combined resource’. D/L said that it’s more appropriate to use the ratio of the ‘combined resource’ instead of just using the ratio of ‘overs remaining’.

In our example, therefore, India’s opponents will be required to score 250*(R2/R1)+1 to win, where R1 is India’s combined resource, and R2 is the combined resource of the opposing team.

To understand this R1, R2 business, look at the illustration below:

The x-axis is a countdown of the 50 overs in an ODI game. You start the innings at the origin, and after every ball you take one step to the right, till you reach the right extreme with ‘0 overs remaining’ when the innings must end.

The y-axis shows the ‘combined resources’ percentage. When all 50 overs remain, you have 100% of the resource percentage. After every ball is bowled, the combined resource reduces a little, and when all 50 overs are bowled, the resource percentage drops to 0%.

We also see ten coloured curves in the illustration – all of them start off from somewhere on the y-axis and eventually merge into a single curve at the ‘south-east’ extreme corresponding to 0 ‘overs remaining’.

Each curve corresponds to the ‘wickets in hand’. The top most curve corresponds to ’10 wickets in hand’, while the bottom most curve (barely visible) corresponds to ‘1 wicket in hand’. These curves indicate how the combined resource depletes as the ODI innings progresses.

A team starts its innings by travelling right along the curve corresponding to ’10 wickets in hand’. When a wicket falls, the team drops to the curve below (corresponding to ‘9 wickets in hand’) and continues its 50-over journey. So after every ball, it is possible to track the combined resource percentage used by the batting team.

Illustrative examples

As an example, suppose Pakistan has scored 128/3 in 30 overs chasing India’s 250 when rain ends the match. Who wins? If we go by the 1989 rain rule – that only considered ‘overs remaining’ – India wins, because the Pakistan target was 250*(30/50) + 1 = 151. But would Pakistan win based on the D/L method? Let’s check.

Since India batted all its 50 overs, India used up 100% of its available combined resource (R1=100). How much of its available combined resource has Pakistan used up when rain ended the match? Let’s look at our illustration. Move your finger right on the x-axis till you reach ’20 overs remaining’ (remember 30 overs have been bowled). Then track the curve corresponding to ‘7 wickets in hand’ (because Pakistan lost 3 wickets). You’ll find that Pakistan at that point had used up about 50% of its combined resource (R2=50). So Pakistan’s winning target at this point was 250*(50/100) + 1 = 126 and, therefore, Pakistan wins!

Let’s now suppose that India was cruising at 200/2 in 40 overs, when rain ended the Indian innings. The 1989 rain rule would have required Pakistan to score 201 in their 40 overs. Was this fair?

If we look at the curves again, we’ll find that India had over 30% of its resource remaining (look at the yellow ‘8 wickets in hand’ corresponding to ’10 overs remaining’), so it had used only about 70% of its combined resource (R1=70). Pakistan, on the other hand, had the opportunity to use up to 90% (R2=90) of its combined resource (look at the ’10 wickets in hand’ curve corresponding to ’40 overs remaining’). Clearly this was unfair; that’s why the D/L target for Pakistan would have had to be higher than 200.

If we use the formula we used earlier, the reset target would be 200*(90/70) + 1 = 258, which, at first sight, appears unreasonably high. Duckworth-Lewis knew that such scale-ups could give very unreasonable results; that’s why they introduced the G50 turn-around, which set a more reasonable target of about 230-240. The G50 criterion says that if R2 is greater than R1, it is better to use an additive formula to determine the elevated reset target instead of a multiplicative scale-up. This made the D/L formula less elegant mathematically, although it still gave very reasonable targets in most cases.

As these examples illustrate, the D/L method indeed appears to be fair, with the reset targets appearing reasonable in most cases.

D/L glitches

However, there were two glitches that some of us had identified (that Duckworth-Lewis were aware of, even if they were a little reluctant to publicly say so in the early years).

#1 While chasing big targets, the D/L method seemed to favour the chasing team if they didn’t lose too many wickets.

Even a cursory glance at the D/L curves tells the story. The top three curves (corresponding to 10, 9 and 8 wickets lost) show that a team is sitting with just under 60% of its combined resource intact even when just 20 overs remain. So a team with a score of 160/2 after 30 overs wins even if the target is about 350.

Put another way, the top three D/L curves don’t come down quickly enough during the first 30 overs, and this anomaly can be successfully exploited by the chasing team.

#2 In low-scoring games (less than 150 runs scored), if a lot of overs (20 or more) were lost, the D/L target was unreasonably high for the chasing team.

This anomaly was linked to the ‘G50’ criterion of the D/L method. The G50 criterion, which assumed an average ODI score of 225 or 235, was a flawed instrument; Duckworth-Lewis knew this, but couldn’t fix it as long as their Standard Edition was being used.

Towards perfection

In the early years, the ICC’s mandate apparently was that the D/L method must be simple (back of the envelope calculations only), and must not require a computer.

But as ODI scores started climbing (300 is pretty common today), Duckworth-Lewis realized that glitch #1 could create a potentially difficult situation, especially in big World Cup matches – there was a brief moment during the 2003 World Cup final when India appeared to have a small chance of gaining a thoroughly ill-deserved victory against Australia, but India then lost a couple of wickets and the big rain never came.

The way to correct the glitch was to ‘play’ with the shapes of the D/L curves – especially those corresponding to 10, 9 or 8 ‘wickets in hand’ – so that they drop sooner and steeper. While the curves would still start from the same point on the y-axis, we now have a kind of knob at the south-east extreme (corresponding to ‘0 overs remaining’) that can be turned to make the curves tauter. As long as the team batting first scores 235 or less (G50=235), we don’t turn the knob. As soon as the score crosses 235, we start turning the knob: the higher the score above 235, the more we turn the knob and the tauter the curves get.

This seems to be the general idea in the new Professional Version that is used for the international matches. The Professional Version also does away with the G50 criterion by successfully managing scale-ups, although I haven’t understood how Duckworth-Lewis have achieved this – and they aren’t sharing this information in the public domain yet.

With these corrections, it would be fair to say that D/L is now very close to the ‘perfect’ rain rule for ODI cricket, although – ironically – this seems to be happening just when the 50-over version seems threatened.
 
What about T20?

Sadly, the D/L method for T20 cricket is still far from perfect. The general idea is to pretend that a T20 match is actually a 50-over match with the first 30 overs lost: we operate only with the segments of the curves to the right of the ’20 overs remaining’ vertical line.

This has to be considered to be a make-shift ‘fix’ because the dynamics of a T20 game are very different from the last 20 overs of an ODI game; for example, field restrictions during the first 6 overs will make quite a difference to the run-scoring and wicket-losing pattern.

It is also easy to see that all curves start strongly overlapping beyond the ’10 overs remaining’ stage and are practically indistinguishable in the last five overs. This means that the ‘wickets in hand’ resource is practically ignored from this point.

The real solution is to completely redraw the curves for 20 overs, with the combined resource diminishing from 100% to 0%. To do this, Duckworth-Lewis need more data points – this will come only when more T20 matches are played. Till then, we must wait … and not grieve too much if England is wrongly declared a loser in a match it should have won against the West Indies.

Friday, November 13, 2009

Sachin Tendulkar’s ODI career

Our expert analyses the Master Blaster’s achievements in different phases and tells you why there is only one Sachin Tendulkar.

There will never be a better ODI batsman than Sachin Tendulkar: 436 matches, 45 centuries, over 17000 runs, over 20000 balls faced … no one can scale those peaks!

But while it is easy to agree that Tendulkar is the best, a more interesting question would be: when was Tendulkar himself at his best?

We’re going to argue here that there have so far been six phases in Tendulkar’s ODI career.

The first phase (Dec 1989 - Mar 1994) was characterized by uncertainty – almost as if the team didn’t know what to do with this young bundle of talent. In 66 innings, he got 12 fifties, 13 sixes, but not a single century! His batting average was 30.8 and strike rate was 74.4. While that might have been better than Sanjay Manjrekar’s strike rate, it still wasn’t good enough.

The second phase (Mar 1994 - Dec 1997) – a phase of discovery – began with Tendulkar offering to open the innings against New Zealand at Auckland after Sidhu was injured. Taking advantage of field restrictions, and short square boundaries, Tendulkar scored a blistering 82 in 49 balls – and left everyone wondering why he hadn’t been asked to open before. In this break-free phase, Tendulkar’s average jumped to 43.4 in 101 innings and his strike rate climbed to an impressive 86.6. He also started scoring centuries – in fact 12 of them.

The third phase (Jan 1998 – Dec 1999) was explosive. Tendulkar was batting with the sort of aggression and authority never seen before in ODI cricket. In just 24 months, he scored 2737 runs in just 2805 balls. A strike rate close to 100 was considered beyond the reach of mere mortals those days. In 55 innings, Tendulkar averaged 55.9 and slammed 12 more centuries, including those two magical hundreds against Australia in the Sharjah desert storm.

Tendulkar was masterly during the fourth phase (Jan 2000 – Dec 2003) but always stayed a notch below his Mount Everest. He still averaged 50.8 over 90 innings, he again scored 12 centuries, he could still briefly climb the top peak – as he did when he scored 98 against Pakistan in that World Cup game – but the smallest of dips in form was now apparent. His strike rate dropped to 86.3 – unarguably excellent, but no longer superlative.

The fifth phase (Jan 2004 – Dec 2006) was the most trying in Tendulkar’s ODI career. As injuries hit him in quick succession, the great player was driven by doubt and ravaged by pain. For a small – and mercifully brief – period, Tendulkar batted like a mere mortal: he scored 1852 runs in 53 innings to average 37.8 with a strike rate of just 78.4 and with just 4 centuries. It was painful to watch – and when Ian Chappell suggested that the master’s time was up, we felt the aching grief that accompanies the impending departure of someone truly beloved.

The sixth phase (Jan 2007 – Nov 2009) has been magical – some might even call it miraculous. The real Sachin Tendulkar is back again! He may not be atop Mount Everest, but most would agree that he’s on Mount Kanchenjunga. In 60 innings, he has scored 2641 runs in 3018 balls for a strike rate of 87.5. His average is up to 47.2 and while he has 5 centuries, he has missed 7 more by falling in the 90s.

We hope there will be a seventh miraculous (?) phase, which will end with the maestro leading India to another World Cup victory in 2011.

The cutting edge with numbers: The return of Sachin Tendulkar

Interpretation: Sachin Tendulkar reached the peak of his powers in 1998-99. Even a decade later he continues to be very, very good. Genius never quite goes away.

Friday, October 09, 2009

This ICC team ranking business

Srinivas Bhogle explores the pros and cons of the ICC rankings system.

“What’s India’s current ranking in ICC’s Reliance Mobile ODI Championship?”

“At the moment, India is second with 124 points.”

“But, wait a minute … wasn’t India first a little while ago, and then wasn’t it third too a little while ago?”

“Yes, India was indeed first and third very recently. And did I hear you say ‘Jack Robinson’? If yes, India must now be second!”

So what’s going on? It really has to do with the way the ICC rankings are defined, as we shall soon see.

Let us look at the current rating of Australia (128), India (124) and South Africa (121). This rating is computed by dividing the team’s total points by its total matches (see table below).

Now suppose India wins the first match in its forthcoming 7-match home series against Australia.

Because India beat Australia, it wins Australia’s rating (128) plus 50 points. So India gets 128+50 = 178 points.

Because Australia lost to India it wins India’s rating (124) minus 50 points. So Australia gets 124-50 = 74 points.

If we now do the arithmetic, India’s new rating is now (3852 + 178)/(31+1) = 4030/32 = 126 (125.94) and Australia’s new rating becomes (4234 + 74)/(33+1) = 4308/34 =  127 (126.71).

So just one point (actually 0.77 points) now separates the two teams.

If India also wins the second match, it will again be No. 1 with a rating of 127 (127.48), 2 points above Australia’s 125 (125.26).

We expect the series to be close … so expect the ICC rankings to go up and down like a see-saw, and expect Ponting and Dhoni’s teams to keep exchanging the top crown after every other match.

This happens because the ICC rating formula – admirable in many ways – has a worrying middling propensity.

We’ll end off with a final Q&A:

“I presume that Australia is now the ICC ODI champion because it won the Champions Trophy?”

“Not really … it’s more because Australia defeated England 6-1 in a ridiculously listless ODI series!”

The cutting edge with numbers: The ICC ODI ranking’s middling propensity

If we see the progress of the ICC ODI Ranking Championship (plotted on the y-axis) during the first 9 months of 2009 (1=Jan, 2=Feb … 9=Sep), we see that the three rating worms keep getting entangled with one another.

Australia’s steep climb is only partly due to its victory in the final of the Champion Trophy; the real reason is the 6-1 England whitewash. Notice therefore that the rating does NOT give greater weight to ‘big’ matches.

Interpretation: The ICC rating scheme has two weaknesses. It tends to cluster teams with similar performances into a tight embrace and fails to adequately reward wins in the big ODI contests.

The scheme is otherwise elegant; especially in the way it builds in the opposition’s strength and progressively reduces weights for older matches.

Saturday, September 26, 2009

G versus V

How do we capture the true essence of a winning performance? Let’s explore and enjoy the fascinating interaction between cricket and numbers.

When we were young, the enduring debate used to be: who’s the better batsman, Sunil Gavaskar or Gundappa Viswanath?

With a Test career average of 51.1, 34 centuries and 10122 runs, Gavaskar seems to have clearly won that contest because Viswanath ended up with a Test average of 41.9, 14 centuries and 6080 runs.

But, being Gavaskar, he’ll always throw in new variables! At the Castrol Cricket Awards function the other night, Sunny claimed that Viswanath was the better batsman because only he could hit the good ball for a boundary.

In a sense, that’s the problem. So many variables, so many criteria… how the devil do we get to the truth? And can numbers alone point to the truth? How does one quantify the sublime beauty of a Viswanath square cut?

In response, I’d like to point towards the unmatched elegance of a Gavaskar straight drive, but that’ll get us nowhere. Let’s therefore stick to numbers, and let’s show how they can indeed unravel the big puzzles.

Of course the biggest puzzles today show up in one-day international cricket. How do we capture the true essence of a winning performance? We know it’s not enough to just score a lot of runs in ODI cricket; we must score them quickly too. So, how about an index that judiciously combines batting average with the strike rate? Well, that’s exactly what the Castrol Index does.

Since I am a diehard Gavaskar fan, we won’t use our index to compare G vs. V in ODI cricket. In any case, Viswanath played very little ODI cricket and Gavaskar… well back in 1975 he once took 173 balls to score 36 runs at a strike rate of about 21. But we can certainly compare Yusuf vs. Irfan or Sachin vs. Jayasuriya or Sehwag vs. Afridi.

These comparisons are fun. Cricket analytics is fun. I hope this column too will be good fun as we set out to explore and enjoy the fascinating interaction between cricket and numbers.

The cutting edge with numbers: Gavaskar wins the race because of his away performances

In the Gavaskar vs. Viswanath debate, it is fashionable to say that Viswanath won matches for India, while Gavaskar merely saved them

Let us plot the number of Tests played by Gavaskar and Viswanath to their cumulative batting average. To get an idea of the timeline, the 20-Test mark is around 1977, the 30-Test mark is around 1979 and the 40-Test mark would be just after 1981.

If we look at Tests played outside India (‘away’), Gavaskar was decidedly superior with a significantly better cumulative batting average than Viswanath.

If we look at Tests played in India (‘home’), Viswanath was well ahead of Gavaskar in their first 20 home Tests together (till about 1977 or so). Thereafter, they were almost at par – with Viswanath continuing to enjoy a slight edge almost till the end.

Interpretation: Since most of India’s victories came at home – and at home, Viswanath was arguably the better player – everyone associated Viswanath more with Indian victories.