Ball Difference

It has been universally agreed that the matches contested in the first 4 weeks of ICC Cricket World Cup 2011 have limited appeal. With four out of the seven teams in each pool qualifying, who needs so many games to reveal the identity of the eight quarter-finalists? Viewers may as well tune in at the knock-out stage. While the identity of the eight quarter-finalists may not surprise many, the QF lineup will be of considerable interest. Net Run Rate (NRR) will be used as tiebreaker when two or more teams will have equal number of points.

World’s most popular sport is played week after week in a league format. ‘Net Goal Rate’ is a common term known to all football fans which is used as a tiebreaker. TV cameras frequently zoom to the notepads of relegation threatened football managers furiously scribbling Net Goal Rate calculations after a goal is scored. A vital skill for every manager is his ability to compute Net Goal Rate using the number of goals scored for and against his team using the number of matches played until that point in the league.

Sorry, I made that up. Football Managers are actually very poor at maths. Hence they use calculators.

Oops! So you do know that ‘Net Goal Rate’ does not exist because football fans think that division is a term used for separating leagues. Also it is a shorter game without frequent interruptions. Cricket fans get plenty of free time between two overs to compute (Required) Run Rate which involves division. So no wonder then that Football uses ‘Goal Difference‘ (that is, goals scored minus goals conceded) but Cricket uses ‘Net Run Rate‘ (that is, total runs scored/total overs faced – total runs conceded/total overs faced).

With IPL starting soon after ICC Cricket World Cup 2011, we get plenty of ODIs and T20 matches played in the league format. Can we find a simpler measure which deals with Integers, does not involve division and uses a currency understood by all fans (Runs, Wickets or Balls) but does not convert it into a rate?

The most obvious candidate is Runs and Net Run Rate is already in use. The won’t do candidate is Wickets. Wickets matter the most in Test matches which can’t be won without getting the opposition out twice. But Test matches are played between two countries, not in a league format. Also an ODI or a T20 game, played in a league format, can be lost by a team even when a team scores all its runs without losing a single wicket but the other side outscores after losing a bucketful.

That leaves Balls. The Margin of Victory in a limited overs game is already measured by the number of balls remaining. But this is restricted to the games where side batting second wins. The game stops as soon as the side batting second outscores the losing side. If only the game continued beyond that point and the side batting second posted its own total! The Margin of Victory could be calculated using Run Difference – the fairest measure possible. We know that will not happen. Instead we determine the precise ball when side batting first outscored the losing side and calculate the number of balls till the end of that innings as the Ball Difference(BD). If the side batting first wins but is bowled out, then end of the innings will be the final ball faced by that team and not the scheduled end of the innings.

The number returned by BD will be an easy to understand integer (unless the game is interrupted and Duckworth-Lewis method comes into play.). Unlike NRR, which is likely to be a decimal, BD will be a round number representing the number of unused balls for the winning team irrespective of which side bats first.

So when a team batting second wins, ‘Ball Difference’ equals the much used term ‘number of balls remaining’. The scorecard for ODI 3085 reads ‘New Zealand won by 9 wickets (with 196 balls remaining)’. The BD in this case is 196. Now Consider ODI 3090 where ‘Pakistan won by 43 runs’ batting first where NZ scored 250. Scorecard reveals Pak reached 251 after 46 overs and 3 balls after which 21 balls were bowled. So the BD is 21 and the scorecard can be altered to read as ”Pakistan won by 43 runs (with a difference of 21 balls)’.

Net Run Rate computation relies on 4 variables – runs scored, overs faced, runs conceded and overs faced – and a formula including division must be used at the end of every game to derive its new value. Ball Difference is an integer that can be added or subtracted to the running total at the end of each game to determine its new value.

It is common to find multiple teams fighting for the last qualifying spot in the latter stages of round robin league. The precise qualification parameters are usually not known until the end of first innings owing to the number of variables in NRR. With BD, teams will know in advance how many ‘balls to save’ in the win to qualify for the next round. If team A needs to save 12 balls, then the match must be won by the end of 48th over while chasing or defending the team score at the end of 48th over.

The Margin of Victory should remain unaffected when neither side has won. A Tie in Cricket is not as common as a draw in football where the Goal Difference remains unchanged. Net Run Rate will change for both teams after a rare thrilling Tie but Ball Difference won’t.

BD is described in the next post using various match scenarios including the computations required for an interrupted game where revised D/L target comes into play. Details about using BD to uniformly determine which games in ICC CWC 2011 recorded the largest margin of victory can be found in this post. An Alternate Points Table for World Cup 2011 displaying both Net RR as well as BD is here.

4 thoughts on “Ball Difference

  1. Stephen Channell

    Thanks for the post.. I’d never shown enough interest in Cricket to know how it is scored! I guess the formula to decide when to declare assumes a downward sloping curve of run-probability from first to last batsman for each team.. with the declare point being before the integral of team-2 curve exceeds the integral of team-1.. I kinda like the idea that stochastic maths is needed because it gives more scenarios for augment/debate.

    What is more interesting though is applying duality of your Cricket model to football, because a tie is much more common to Football than in Cricket. Football becomes more entertaining once a team has scored.. but a measure that divided goals, by time (since start, or possession) would be more far moving.

    1. pandimi Post author

      Castrol sponsors Indices in Football and Cricket to analyse player performances and rank them. We can put ‘Cricket’ and ‘Markov chain methods’ in the same sentence. There are papers for simulation of a cricket match based on Bayesian latent variable model. I am not sure whether gambling sites already combine live ball by ball data with Monte Carlo simulation to maximise odds.

  2. Alok Joshi

    I would ideAlly like 6 variables to be used in deciding who moves fOrward. Wickets are also a vital aspect of the sport. Avg runs scored per wicket per ball less avg runs conceded per wicket per ball should decide standings. BD formula that you have suggested is exciting. But it’s too simplistic and does not appear to take a holistic view unless i have understood it wrong. Imagine a league of 3 teams. Team A scores 330 losing 7 wickets to win against team C with 3 balls remaining. Team B scores 345 losing 4 wickets to beat team C with BD of 2. Assume further that match bet A and B is washed out. Then A will win tthis league despite losing more wickets and scoring fewer runs. Divisions are essential to get a ruling about who rules!

    1. pandimi Post author

      It is a simple measure. It is also fair. In a limited overs match, the primary objective of both teams is to score one additional run. Teams chasing have a pretty good idea how much is enough and are willing to lose wickets as long as they win quickly. It is tempting to accumulate runs scored in different games but even if the unit is same we are in fact adding apples to oranges because a 370 or 338 at more than 6 & 7 is not comparable to chasing 207 or 189. If teams are level on wins, balls remaining should be used to compare the performance ignoring both wickets and runs.


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