Too much time on hand and too little work to do these days after getting placed ( and with the placement season in full swing) meant that I can do a little research on one of my favorite areas: "CRICKET".
I have been trying to understand Duckworth-Lewis rules which were framed for this game in times yore. Though there is no information about the algorithm they used on the internet, I could find a paper submitted by Duckworth and lewies. I was curious to find the function used by them to calculate the percentage resources available at any point in the game.After some research I found that they used a non parametric asymptotic function in two variables, which has an exponential decaying constant.
Z(u;w) = Z0(w)[1 - exp{-b(w)u}].
This raised a lot of questions in my mind
1) why asymptotic function, when every match has fixed no of overs for a team , especially in One days where D/L method is used more frequently ?
2) How can the resources be considered to be same for every wicket! Common, a school kid in India also knows that Sehwag who opens is far more dangerous than an Ishant Sharma for sure while batting!
3) The table uses the above mentioned Function to fit the curve on data of all the cricket matches . But wouldn't it be more practical to plot the curve or fit it depending on the data of just that particular ground or based on the the matches played between those two participating teams instead of generic stats of all matches?
So I am thinking on those terms. As of now, I figured out tentatively that, Weightage has to be given to each player based on his previous record and then incorporate that probabilistic variable in the function to differentiate a Sehwag from Ishant sharma or a Petersen from Anderson.
The Function can actually be calculated real time by having the previous data of the teams on hand while the match is being played and various projective techniques can be fitted (which would then be dynamic) during the match using Excel tools like what if analysis or Solver.
The second Issue to be blogged on is Umpire referral system. I fail to understand why is all the fuss about the probability of Technology not identifying the unnoticeable things on the ground. The name ‘UDRS’ is clumsy, and the UDRS implementation has been just as clumsy.
UDRS for those who don't know is short for ‘Umpire Decision Review System’. This system allows the batting and fielding side the opportunity to challenge the decision of the on-field umpire. But there is a proviso: you cannot challenge after two failures! Why two? What is so sacred about two? The argument for limiting the failed challenges to two is that every decision would otherwise be challenged, and this would unnecessarily delay the game. It is also intended to appease on-field umpires who might ask: “what the hell am I doing out in the middle?” Restricting referrals to two is actually making things worse. For example, one of the two Indian referrals would perforce be reserved for Virender Sehwag if he is playing; and the second might be held back for Sachin Tendulkar. This is ridiculous. We have also seen situations where a blatant umpiring error could not be contested because both the referrals had been used up. Indeed, we also know of instances where a batsman has abused a referral: he knows that there is a faint nick, but he also knows that technology is unlikely to spot it! So instead of walking, he asks for a review.
Today’s avatar of the UDRS is essentially a compromise. We want to use technology, such as Hawkeye, Hot Spot, Snickometer and Super Slo-Mo, but we don’t want to offend the umpires. This can’t go on. We have to quickly choose one of the ‘umpires only’ or ‘technology only’ options.The latter is much more likely because cricket is, what mathematicians would call, a ‘discrete’ game: the game moves forward step by step, or ball by ball. Tennis is discrete too, as indeed is American football. Football, on the other hand, is ‘continuous’.If we reflect for a moment, we will realize that technology is easier to implement in discrete games than in continuous ones. The next ball in cricket can be delayed to confirm an lbw decision, but a football game cannot be halted to verify if a player was really offside or not!
That’s why the future is much more likely to be ‘full-blown’ UDRS. In this set-up, the best umpires are not in the playing field … they are seated next to technology-based outputs. Every appeal will be reviewed; every decision will be technology-driven. The umpires in the middle will essentially be lackeys: they will call ‘play’, count the six balls that make up the over, ensure good on-field behaviour, signals boundaries or dismissals (after hearing from the chief umpire indoors), peer at light meters, hold the bowler’s cap and, if they feel like Billy Bowden, do a little jig to amuse the crowds. But they would still be required to call no balls (because that’s a real time decision).
The ICC tells us that the best umpires get 93% of their decisions right, while UDRS-assisted decisions are 97% right. These statistics try to impress, but ignore that one of the 7% wrong decisions could completely change the course of the match. A better way to estimate performance is to ask how little did the umpire’s performance affect the eventual result of the match … and it is here that UDRS will perform much more impressively.
The trouble with ICC is that it is fearful of technology. A decade and more ago, ICC asked Duckworth-Lewis (D/L) to come up with rain rules that could be computed on the back of an envelope, because they feared that a ground in some corner of Bulawayo might not have access to a computer. This meant poorer targets not because the D/L model was deficient but because ICC’s mindset was flawed. Today, ICC has similar fears about UDRS technology and its costs. But they will eventually discover that full-blown UDRS is indeed the way to go. I am in for UDRS, join the brigade if you are with me.
I have been trying to understand Duckworth-Lewis rules which were framed for this game in times yore. Though there is no information about the algorithm they used on the internet, I could find a paper submitted by Duckworth and lewies. I was curious to find the function used by them to calculate the percentage resources available at any point in the game.After some research I found that they used a non parametric asymptotic function in two variables, which has an exponential decaying constant.
Z(u;w) = Z0(w)[1 - exp{-b(w)u}].
This raised a lot of questions in my mind
1) why asymptotic function, when every match has fixed no of overs for a team , especially in One days where D/L method is used more frequently ?
2) How can the resources be considered to be same for every wicket! Common, a school kid in India also knows that Sehwag who opens is far more dangerous than an Ishant Sharma for sure while batting!
3) The table uses the above mentioned Function to fit the curve on data of all the cricket matches . But wouldn't it be more practical to plot the curve or fit it depending on the data of just that particular ground or based on the the matches played between those two participating teams instead of generic stats of all matches?
So I am thinking on those terms. As of now, I figured out tentatively that, Weightage has to be given to each player based on his previous record and then incorporate that probabilistic variable in the function to differentiate a Sehwag from Ishant sharma or a Petersen from Anderson.
The Function can actually be calculated real time by having the previous data of the teams on hand while the match is being played and various projective techniques can be fitted (which would then be dynamic) during the match using Excel tools like what if analysis or Solver.
The second Issue to be blogged on is Umpire referral system. I fail to understand why is all the fuss about the probability of Technology not identifying the unnoticeable things on the ground. The name ‘UDRS’ is clumsy, and the UDRS implementation has been just as clumsy.
UDRS for those who don't know is short for ‘Umpire Decision Review System’. This system allows the batting and fielding side the opportunity to challenge the decision of the on-field umpire. But there is a proviso: you cannot challenge after two failures! Why two? What is so sacred about two? The argument for limiting the failed challenges to two is that every decision would otherwise be challenged, and this would unnecessarily delay the game. It is also intended to appease on-field umpires who might ask: “what the hell am I doing out in the middle?” Restricting referrals to two is actually making things worse. For example, one of the two Indian referrals would perforce be reserved for Virender Sehwag if he is playing; and the second might be held back for Sachin Tendulkar. This is ridiculous. We have also seen situations where a blatant umpiring error could not be contested because both the referrals had been used up. Indeed, we also know of instances where a batsman has abused a referral: he knows that there is a faint nick, but he also knows that technology is unlikely to spot it! So instead of walking, he asks for a review.
Today’s avatar of the UDRS is essentially a compromise. We want to use technology, such as Hawkeye, Hot Spot, Snickometer and Super Slo-Mo, but we don’t want to offend the umpires. This can’t go on. We have to quickly choose one of the ‘umpires only’ or ‘technology only’ options.The latter is much more likely because cricket is, what mathematicians would call, a ‘discrete’ game: the game moves forward step by step, or ball by ball. Tennis is discrete too, as indeed is American football. Football, on the other hand, is ‘continuous’.If we reflect for a moment, we will realize that technology is easier to implement in discrete games than in continuous ones. The next ball in cricket can be delayed to confirm an lbw decision, but a football game cannot be halted to verify if a player was really offside or not!
That’s why the future is much more likely to be ‘full-blown’ UDRS. In this set-up, the best umpires are not in the playing field … they are seated next to technology-based outputs. Every appeal will be reviewed; every decision will be technology-driven. The umpires in the middle will essentially be lackeys: they will call ‘play’, count the six balls that make up the over, ensure good on-field behaviour, signals boundaries or dismissals (after hearing from the chief umpire indoors), peer at light meters, hold the bowler’s cap and, if they feel like Billy Bowden, do a little jig to amuse the crowds. But they would still be required to call no balls (because that’s a real time decision).
The ICC tells us that the best umpires get 93% of their decisions right, while UDRS-assisted decisions are 97% right. These statistics try to impress, but ignore that one of the 7% wrong decisions could completely change the course of the match. A better way to estimate performance is to ask how little did the umpire’s performance affect the eventual result of the match … and it is here that UDRS will perform much more impressively.
The trouble with ICC is that it is fearful of technology. A decade and more ago, ICC asked Duckworth-Lewis (D/L) to come up with rain rules that could be computed on the back of an envelope, because they feared that a ground in some corner of Bulawayo might not have access to a computer. This meant poorer targets not because the D/L model was deficient but because ICC’s mindset was flawed. Today, ICC has similar fears about UDRS technology and its costs. But they will eventually discover that full-blown UDRS is indeed the way to go. I am in for UDRS, join the brigade if you are with me.
