Today one more record in the Test cricket's history was made, or broken, depending on your point of view. Jayawardene and Sangakkara, best buddies on and off field in the Sri Lanka cricket team, scored 624 runs together for the 3rd wicket against South Africa, a record for any partnership by any team. In the process, Jayawardene achieved the personal milestone of scoring 4th highest individual aggregate of 374 runs (highest by a Sri Lankan). The partnership total overtook the earlier record of 576 set nine years ago by another Sri Lankan duo of the great Jayasuriya and Mahanama for the 2nd wicket stand against India (Jayasuriya scored the highest, until today, Sri Lankan individual score of 340 in that match). This is the recurring theme in cricket records, or any sport record for that matter. You create one record today that instantly propels you to cloud nine, and poof it goes tomorrow and you are another been-there-done-that fellow ruminating on past glory. There are statistical outliers - records so spectacular they stand the test of time - like Bob Beamon's world long jump record in 1968 Summer Olympics that stood for 23 years; or, more relevant for this topic, Bradman's career Test batting average of 99.94 that will probably remain unsurpassed. (These two performances have since been immortalized in the sports lore by two new adjectives "Beamonesque" and "Bradmanesque".)
So, how close are the current top cricket records to being toppled? Below are two small tables, for Test and ODI formats of the game, where I pulled together some of the commonly quoted world records and the number of performances that are within 5%, 10%, 15% and 20% of these records. I have included all present and past cricketers (except Bradman) to show the "clutter factor" of a record, which attempts to make the point that unless the record is an outlier (like Bradman's average) or a close one, it is likely to be broken sooner than later. I have disregarded names and other details about the results (they can be found here). For the Test averages I considered only those cricketers who played at least 20 Test matches; likewise, for ODI averages I included those who played at least 50 ODI matches.Test Record <=5% <=10% <=15% <=20% Batting score 400 1 5 6 13 career tot. 11505 1 3 4 4 career avg. 60.97 8 14 21 35 100's 35 1 3 4 4 innings tot. 952 0 1 2 3 partnership 624 0 1 1 1 Bowling career wkts 685 0 1 1 1 career avg. 15.54 0 2 3 3 ODI Record <=5% <=10% <=15% <=20% Batting score 194 4 9 17 24 career tot. 14146 0 0 0 1 career avg. 53.58 0 0 3 9 strike rate 108.16 2 3 9 24 innings tot. 443 2 2 5 16 partnership 331 1 1 2 3 Bowling career wkts 502 0 0 0 2 career avg. 18.84 0 1 2 8
If we had listed Bradman's average 99.94 instead of Graeme Pollock's 60.97 in the third row of the Test table, succeeding numbers in that row would be all zeros - Bradman's record has a zero clutter and is a true outlier (Pollock's average, which is the next highest, barely makes the "<=40%" column). There are couple of close ones in the ODI table, for example Tendulkar's career aggregate of 14146 runs (and he is still playing), or Akram's aggregate of 502 wickets. They will eventually be surpassed, but may take quite awhile. By contrast, Saeed Anwar's highest ODI score of 194 runs has lot of clutter - there are 4 scores within 5% of it and 9 within 10% - and it may not be long before this record tumbles. Same is true for Afridi's ODI strike rate of 108.16, with the increasingly specialized techniques used today for power hitting. On the other hand, Pollock's Test average of 60.97 runs presents a conumdrum - on the face the record has the largest amount of clutter, but Pollock played only 23 Tests in his entire career before retiring in 1970. Today's cricketers often play more than 100 Test matches, and sustaining such high averages is quite difficult after so many games (the more matches one plays over a prolonged career, more he plays when out of form, which pushes his career average down). It is a testament to Dravid's stupendous consistency that after 104 Tests his average of 58.75 finds a place within 5% of Pollock's record, besides being a record itself among current batsmen (followed closely by Ponting's 58.22 after 105 matches, with Tendulkar's 55.39 after 132 Tests not too far behind). So, there is indeed a point to the cliché "records are meant to be broken". Today's tech-savvy coaches and managers with a slew of support staff and ultra-modern gadgetry have considerably narrowed the gap between the prodigy and the merely good, thereby creating a level playing field, and what is record today will be commonplace tomorrow. Or maybe not. Surpassing a record 20 or even 10 years later assumes that the format of the game stays the same. There used to be only Tests being played in Graeme Pollock's time, now ODI taps the pulse of the crowd, and it already looks like Twenty20 holds the promise of the future.
Saturday, July 29, 2006
Another cricket record "made to be broken"
Saturday, July 15, 2006
Golden Ratio - how ubiquitous is it?
I recently read "The Da Vinci Code" by Dan Brown, and was reminded of the so called "power of Φ (Phi)". The story begins with the curator of Louvre Museum leaving a code scrawled on the museum floor just before he was murdered. The code has a jumbled set of numbers, which when unscrambled gives the first few elements "1-1-2-3-5-8-13-21" of the famous Fibonacci series, discovered by Leonardo Fibonacci in the 12th century. The obvious thing about this series is that each number is the sum of the preceding two numbers. Its less obvious feature is that, as the series progresses, the ratio of a number and its immediate predecessor approaches another famous mathematical entity, the Golden Ratio Φ = (√5+1)/2 = 1.61803398874989...(the 1.5 billionth significant digit can be found here). The golden ratio has a much longer history, and is believed to have been first defined by Euclid in 300 BC. Of course, mere deciphering of the numbers does not reveal the cause or the perpetrator of the murder in the story; there are wheels within wheels, or rather, codes within codes, and you can read all about them in the rest of the 450-page novel. My interest here is in the claim often made about the surprising ubiquity of Φ in nature around us.
In the story itself, the male protagonist Robert Langdon recalls his favorite Harvard lecture in which he talks to a bunch of thoroughly impressed students about the instances where this "divine proportion" shows up:
1. Ratio of female-to-male honeybee numbers in a beehive.
2. Ratio of diameters of successive spirals in the shell of Nautilus (a marine mollusk).
3. Ratio of diameters of successive spirals in a Sunflower seed pattern.
4. Pinecone petals, leaf arrangements on plant stalks, insect segmentation,...
In a human body too, one sees Φ in the ratio of the lengths of
1. Head-to-toe and navel-to-toe.
2. Shoulder-to-fingertips and elbow-to-fingertips.
3. Hip-to-floor and knee-to-floor.
4. Finger joints, toes, spinal divisions,...so on and so forth.
But the novel is about a fictional story (barring "all descriptions of artwork, architecture, documents, and secret rituals"), and who chases facts in a fiction! However, there are numerous places where such evidences are talked about (just do a google on "golden ratio in nature", or click here for one such example). Leonardo Da Vinci was apparently so impressed that he himself discovered the list of Φ hidden within the human body.
While the list is certainly impressive, the claim is at best only approximately true, contrary to the exactitude typically associated with a mathematical number. Nature does not follow Number Theory, and natural systems always have wide variations around some mean value. Take the human body for example. No two human beings have identical lengths of the same part of their body, and these lengths are in fact continuously varying parameters of human anatomy (in evolutionary biology this is an example of a quantitative phenotype). The ratios mentioned in the above list can only approximate the value of Φ. But if this is true, then what about, say, the ratio of shoulder-to-elbow and elbow-to-fingertips? Suppose this ratio is some μ. If one looks hard enough, I am sure μ can be found to roughly hold in several other parts of the human body. In other words, Φ is about as fundamental to human anatomy as any μ, σ or ω.
Now take the first item in the list: the number of female and male honeybees in a beehive. There is interesting biology involved with this example, and Fibonacci himself supposedly noticed it. If an egg laid by a female bee hatches without being fertilized by a male, it produces a male bee (by a process known as parthenogenesis). On the other hand, if the egg is fertilized by a male bee, it hatches a female. Let us track the genealogy of a male bee. It has a single parent (1 female bee and 0 male bee), which has two parents (1 female and 1 male). The male again has a single female parent, and the female has male+female parents (2 females and 1 male). Each of the two females has a male+female parent pair and the male has one female parent (3 females and 2 males). Three females again have male+female parents each, and the two males have single female parent each (5 females and 3 males), ad infinitum. Going far back into the 
ancestry, we recover the golden ratio from the female-to-male numbers. Mathematically interesting, but again biologically approximate! In all beehives there are a large variation in the actual male-female ratios due to any number of stochastic factors. What about the other entries in the list? Same argument holds without exception: shell of a Nautilus or seed patterning in a Sunflower never describes perfect spirals, and their diameter ratios give only approximate Φ. These rough spirals are no mere coincidence though, but give evidence to Mother Nature's efficient design, for instance to optimize seed spacing in the Sunflower (see picture).
While writing this post I came across Devlin's Angle, and most of what I said here, he said only better. It is an interesting coincidence that we both start our piece with the same novel, which speaks of its popularity (thanks partly to the transatlantic copyright controversy that made national headlines not so long ago). My advice on if you should read the book: if you like thrillers that are thicker than your pinkie, get it from your local library (as I did) or get your dumb friend to buy it (I do not have dumb friends), but do not waste your dough.
