Monday, May 14, 2012

the Toss - Probability and the uniqueness of IPL


In the sport of cricket, a coin is tossed to determine which team  gets the option of deciding on batting or bowling. This is known as the toss.   In many games, the toss decides the option as to who would start – though not all of them involve the ‘tossing of a coin’.

Most of the ardent fans would like to be in the Cricket stadium, hours before the match starts.  It would be electrifying to be in with lots of expectations.  It is to be seen and experienced to be believed.  At Chepauk, for Test matches, we used to wait patiently and suddenly you can hear the crowd coming alive – as you watch you would see two white hats appearing near the sightscreen at the pavilion.  The two Umpires would enter the ground, greeted by roaring applause of the  cheering crowd – then the fielding team captain would enter with his men – some would loosen themselves with some body exercises, whilst the fast bowler likely to open the attack might start running a few paces – crowd running more.  Then you have the sight of two openers – generally the Senior walking first  towards the end to take strike [may be if you had Srikkanth, you could see him twirling his bat, looking at the Sun chanting something !]

Much before all this was the all important toss – those days there were not this fanfare attached. Usually it was only the two Captains walking along with Umpire to the middle; the Home Team Captain would toss a coin, the visiting Captain would call and the correct call would give them the right to opt for Batting first or Bowl first – known as ‘putting the opponent in’.   A lot has changed now – it is the Match Referee, the two Captains and host of camera including the spider descending on the Captains – noisy crowds [as against the ones which were silent when coin went up for toss] and even TV anchors – those days there used to be only gestures – now, you have the losing Captain talking and the winning Captain announcing his decision instantaneously to the TV commentator……….    The toss generally occurs ‘half an hour’ before schedule commencement of play.  

It is the toss – a coin which goes up on air, necessarily falling on one of its sides, which would determine the immediate action and sometimes even the end result.  – the all important toss.  It could be any coin – coin with two sides ‘a Head and a Tail’ – ‘Heads you win – tails you lose’ !!  - generally it is the standard coin of the host country – though there have been some special and some commemorative coins used in the history of Cricket.

When a coin is tossed up, there are only two possible outcomes – it can be Head or a Tail [crooked possibility of coin standing up removed]  - the possibility of somebody determining the outcome, scientifically, is  not probable – yet when it occurs in sequence by chance, some Captains are touted as intelligent when calling them ‘lucky’ would have been more appropriate.  

When we toss up, there can be a head or a tail – so the possibility of your calling it right is 50% ?  - if that logic were to be correct, then you should be calling right one out of 2 – that does not happen – some Captains lose tosses in row.   That takes us to the ‘probability theory’ -  Probabilities are written as numbers between zero and one. A probability of one means that the event is certain. If you toss a coin, it will come up a head or a tail. So there is a probability of one that either of these will happen. A probability of zero means that an event is impossible. If you toss a coin, you cannot get both a head and a tail at the same time, so this has zero probability. Anything that can happen but is not certain is written as a number less than one.

To understand ‘Probability theory’ – the primary thing is that they do not tell you what would happen – merely what is likely to happen.  So if the probability is say 4 out of 10 and you toss a coin 20 times, still you may not get even once right !! – might startle you but that is real.  The odds stay the same, of Head or Tails  at 50% - but each  toss being 'independent events' they are not bound by logic or statistics.  In effect the potential 20th time, has the same odds of 50% and it might still turn to be Head or Tails

So, thus individually you might still end up losing or winning all the time, if one were to record and analyse all the tosses, at a larger representative numbers, it is most likely to represent the probability theory.   Theoretically, when  a coin is tossed up, the no. of possibility is 2 and the outcome to get  head is 1 so it ½ - 50%.  If you flip a coin 200 times and get 80 heads, then the estimate should be 80/200 = 0.4.  

More of controversies on tosses in another post….  Before that the coin you use for toss should be clear –  Indian coins have ‘lion headed Ashoka lion emblem’ on one side and the numeral + rupee written on the other – the former is ‘Heads” and side having the numeral is ‘Tails’.  Some coins have the Ashoka lion and the numeral on the same side and map of India on the other – and if such a coin were to be tossed, what would be Heads is to be pre-determined, though most would say that the side with Lion is always the Head !!

Indian Premier League is a different league on its own – unique in many ways.  Read that for each match a coin made specially with distinct print of ‘DLF IPL – Match No. – details of playing Teams and word H on one side and T on the other’ are used.  No confusion !! 

Here is a coin used in the match between ‘Pune Warriors and Chennai Super Kings” on 14th April 2012.

Photo courtesy : www.iplt20.com

With regards – S. Sampathkumar.

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