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Power Play

Game theory

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Over the last week, cricket blogs have been abuzz with a new cricket ranking system devised by Satyam Mukherjee (below), a scientist at Northwestern University, Illinois. His paper, "Identifying the greatest team and captain - a complex network approach to cricket matches", names Steve Waugh (see list) as the best skipper in Test history. What's new about the theory is its way of looking at the value of a team's victory through relative contests. This could be an iterative method but Mukherjee uses Google PageRank to assess loads of data to compare the performance of captains and teams from 1877 to 2010. The 31-year-old scientist, born in Durgapur (West Bengal), is now a
post doctoral fellow at Kellogg School of Management and Northwestern Institute. His interests lie in complex systems, social networks and statistical physics. And his favourite cricketers: Brian Lara, Sourav Ganguly and Mohammad Azharuddin.

What is the complex network approach? How different is it from the conventional methods of calculating individual or team success?

In simple language, a network is a set of 'nodes' connected by a set of edges or vertices/links. For example, in friendship networks like Facebook or Orkut, a group of users (nodes) are connected to see if they know each other. The subject is almost 15 years old. In recent years, complex network tools have been applied to soccer, baseball and tennis. Thus two soccer players are linked if one passes the ball to another. I have applied these tools to cricket teams and skippers. Conventional methods of ranking teams are based on the number of wins. I have applied the Google PageRank algorithm - used for ranking a web page - to rank the quality of wins. So if a weak team wins against a relatively stronger team, it gains points but if it loses to a strong team it's not penalised much. Traditional ranking schemes are more biased towards the number of wins.

What's wrong with the methodology adopted by the International Cricket Council?


I'm not saying the ICC ranking scheme is wrong. It's just opaque. The methodology is not available anywhere and ranking is based on points. Such points are prone to bias. If we are asked to rate Sachin and Bradman in terms of votes, Sachin would emerge winner purely in terms of votes given by modern age viewers. Network theory doesn't include these 'external factors' and yet provides consistent ranking.

Many might have a bone to pick with you about your Test captains list. Even if one accepts Steve Waugh was the best in history, how is M S Dhoni placed at No 9 and why doesn't Mike Brearley find a place?


The skippers and teams are connected based on the fraction of wins against each other. Unlike in the early days, Test matches now end in results. Then we'd see more draws. One of the reasons why Steve Waugh is the greatest is that he was consistently successful for a long period of time. Dhoni's rank is bound to change when you take into account the recent back-to-back series defeats. This study was conducted in mid-2011 and so I had considered matches played till the end of 2010. Dhoni is high up the order because he had till then never lost to Ponting, who in turn is a successful skipper. Dhoni suffers a big fall in his rank as skipper if 2011 data is applied. Remember he lost to comparatively weaker skippers in England and Australia. Mike Brearley falls short of Waugh, Dhoni or Clive Lloyd's success. Hence, even though he has been widely praised as an inspiring leader, particularly in the 1981 Ashes, his name doesn't feature in the Top 20.

Indian captains like Pataudi, Kapil Dev and Sourav Ganguly have done a lot too in inspiring their teams ...


Pataudi, Kapil Dev, Ganguly and Dhoni are charismatic leaders and known for their leadership skills. But to quantify the 'influence' of a captain and modify the algorithm is not easy. So this research is still open to further analysis which I would like to pursue in the long run.

Why is Clive Lloyd placed lower? Could it be that his team was too good?


Lloyd isn't placed very low, he's placed 6th. But Steve Waugh's quality of wins makes him more successful. Let's also note that the ranking scheme depends on the concept 'a skipper/team is successful if it defeats a successful skipper/team'. I believe this wasn't the case with Lloyd.

What about a captain who saves a match by fighting for a draw?


Initially I did consider including these cases, but from the scorecard database it's not possible to determine how a team or its captain is salvaging a draw from the jaws of defeat. Also imagine a skipper who drew matches and never lost a game, but never won a game either. Here there could be two reasons: a) He's an attacking skipper who pulled his team away from the verge of defeat, and b) He's a defensive skipper who is looking to 'save' a match rather than 'winning' it. But it would only be logical to consider the wins . . .

What about relative individual strengths of teams?


I don't know if anyone has tried that. In the present paper, I haven't taken into account the team's individual relative strength. That again isn't a straightforward parameter but it's not impossible to handle. I may try that in future.

Can the algorithm determine who is better - Sachin or Bradman?


There is no direct application of this algorithm to determine the greatness of Bradman versus Sachin. The PageRank gives a score for games which involves winning or losing in direct contests. It can be applied to tennis where Nadal is facing Federer or in soccer where, say, France is playing Spain. In cricket, one can't have a direct Sachin-Lara or Bradman-Sobers encounter, since batsmen are pitted against bowlers.

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