One day cricket, and the concept of pressure

A well-compiled century by Saeed Anwar took Pakistan to 273 in their crucial World Cup Pool A encounter against India at Centurion on 1 March 2003.

As Tendulkar and Sehwag came out to lead India's chase, the Indian fan was worried. A target of 250 appeared "get-able", but 274 seemed just a little steep. Especially with Shoaib, Wasim and Waqar ready to fire with the new ball.

"I can feel the pressure," Chandu, a loyal Indian fan, told his friend.

Chandu, of course, couldn't measure this pressure. He couldn't say something like: "I can feel a pressure of 123." And even if he did, no one would understand!

We set out to see if we could quantify that pressure, to come up with the sort of number that would have put a measurable face on Chandu's feeling.

Chandu believed that a target of 250 was "fifty-fifty". So if India had to chase 250, he would've felt a pressure of 100, exactly mid-way between its extreme values of 0 (zero pressure; certain win) and 200 (maximum possible pressure; certain defeat).

The Indian start was electric. After watchfully playing Wasim's first two deliveries, Tendulkar cracked him for a four to deep cover and then scampered across for a single. Sehwag guided Wasim's last delivery to third man for another boundary.

Chandu was already feeling better. His pressure had dropped from 123 to 118.

The next over from Shoaib Akhtar to Tendulkar was the stuff that Chandu's dreams were made of. After two singles, Tendulkar cut loose. An upper cut for six was followed by boundaries to square leg and mid on! Chandu was elated. His pressure was now just 102.

Wasim bowled a tight third over to hold India's pressure at 102. But when Waqar brought himself on in the fourth over, Sehwag smacked him for a first ball six. Tendulkar's last ball boundary meant that the pressure had dropped to 95, below 100 for the first time!

Wasim's next over was wayward as he conceded two boundaries to Sehwag. India were now galloping at 50 for no loss after five overs. And Chandu was smiling, because his pressure was down to 85.

But then Waqar hit back, claiming Sehwag and skipper Ganguly off successive deliveries. Chandu's brow was knitted again as the pressure jumped from 85 to 120...

While this account is about India's last World Cup encounter against Pakistan, it's the sort of story that's narrated again and again while talking of ODI encounters. A fan trying to catch up with his favourite team's ODI chase usually needs to ask the following three questions to size up the match situation: how many runs left, how many wickets lost, how many overs left?

(If he's even smarter, he might ask only two: what's the asking rate and how many wickets lost?).

The "pressure index (PI)" that we've introduced here can assess the match situation with just one question: what's my team's PI?

If the PI is above 100, my team is in trouble. If it's well above 100 (140?), the team is in big trouble. Of course, if it's well below 100, Chandu and all other fans will be smiling widely.

In its World Cup 2007 coverage, Rediff will specify the pressure index on its live scorecard on a ball-by-ball basis for all the big matches. So Chandu can now convey, and share, the magnitude of the "pressure" he feels with his fellow cricket fans.

How do we calculate the PI?

The formula isn't easy to explain, but it's based on objective criteria and is mathematically rigorous.

 The process is initiated by asking an expert: "How many runs do you think the chasing team can score if it bats its full quota of 50 overs?"

Thereafter, the pressure index evolves using a new par score model not dissimilar to the models employed by the D/L and Jayadevan methods. In particular, the PI can also be accurately adjusted in case of rain interruptions.

Professor Rajeeva L Karandikar, the well-known statistician and psephologist, has developed the mathematical theory of the pressure index. It has been a pleasure working with him and my other colleagues, Sunil T, Sunil Patil, Debasish Ghosh, Amit Kothiyal and K Anil Kumar, from Cranes Software International Limited, Bangalore, on this project.

Professor M J Manohar Rao, who also developed the Rediff Test and ODI Rankings and Rediff's Most Valuable ODI Player Index, originally conceived the idea of a pressure index.

I remember working with Manohar as he filled up many notebooks, graph sheets and Excel worksheets to examine this theory. It saddens me deeply that Manohar is no more with us; he would have been immensely pleased to see his PI in action.

The pressure index, which will be a live, ball by ball feature of the Rediff scoreboard for the forthcoming World Cup matches, is powered by Cranes Software, Bangalore.