Computations for Ball Difference

***

Update: In February 2012, Anantha Narayanan, in his  ESPNcricinfo statistics blog about ‘ODIs: a blue-print for the future‘ recommended giving higher weight for away results. To implement that suggestion,we can award +1BD for an away win for every 10 overs, that is, +2BD for a T20 match and +5BD for a 50 over ODI.

Anantha Narayanan, included this post in his final version as suggestion #7 on match level changes under the heading “Tie resolution in leagues

***

Here we continue from an earlier post to describe the various scenarios and computing ‘Ball Difference (BD)’ in an interrupted game. Ball Difference uses the actual match data to determine the precise ball when one team outscores another in a completed game. We can’t use the ball by ball match data to determine BD in an interrupted game because the side batting second may outscore the winning side but still fall short of the revised D/L target.

The various scenarios for Ball Difference are described here:

1. Side that bats first wins

  • Team A bats first and set a target of 287-6 off their full quota of fifty overs. Team B fail in their run chase, early losses causing them to struggle to 243-8 in their 50 overs. Team A scored 244 after 43 overs and four balls. So their Ball Difference is 6 overs and two balls i.e. 38balls.
  • Team A’s BD for this game is 38. Assuming this was the first game of the season, their BD for the league table would be +38.
  • Team B’s BD for this game is −38. If this was the first game of the season, their BD for the league table would be −38.

2. Side that bats second wins

  • Team A bat first and set a target of 265-8 off their full quota of fifty overs. Team B successfully chase, getting their winning runs with sixteen balls (2.4 of the 50 overs) remaining.
  • Team A’s BD for this game is +16.
  • Team B’s BD for this game is −16.
  • Assuming that Team A and Team B had previously played as in the game in scenario one, the new BD for team A would be 38+16=54.

3. Side that bats first is bowled out. Side batting second wins.

  • Team A bat first and are skittled out for 127 off 25.4 overs. Team B reach the target in 25.5 overs.
  • Team A were bowled out effectively scoring 127 after facing 50 overs. Team B actually scored at a slower pace. However they managed to protect their wickets and win with 24 overs and 1 ball remaining. So the BD for team B is +145 balls.

4. Side that bats second is bowled out. Side batting first wins.

  • Team A bat first and set a formidable 295-7 off their complement of 50 overs. Team B never get close, being bowled out for 184 off 35.4 overs.
  • Suppose, Team A reached the score of 185 after 35 overs. The next scoring stroke was played after 4 dot balls. The furthest point where Team had scored 185 was after 35.4 overs. So the BD in this case will be 14 overs and 2 balls. Thus BD for Team A is +86 balls.

5. Both sides are bowled out, the team batting first therefore taking the points.

  • Team A bat first, and manage 117 off 24 overs on a difficult playing surface. Team B fall agonizingly short, reaching 112 off 23.3 overs.
  • Assuming Team A reached 113 at the end of 23 overs before getting bowled out six balls later, we have a Ball Difference of +6.balls.

6. The game ends in a tie

  • Both teams have scored same number of runs at the end of 50 overs. There is no victory and hence BD is zero for both teams.

7. Abandoned games recorded as No-Result

  • Abandoned games are not considered, whatever the stage of the game at stoppage may be, and the scores in such games are immaterial to BD calculations.

8. Interrupted game where side batting first wins

  • In matches where interruptions reduce the number of overs bowled, the revised targets will be used to calculate Ball Difference.
  • For example, in a 50-over World Cup first-round group match, Team A score 226/3 in 42 overs when play is halted due to rain.
  • Four overs are lost due to rain and the match is reduced to 46 overs. After resumption of play Team A reaches 250/9 in 46 overs.
  • The target is revised as 267 due to 4 overs lost and Team B must score 268 to win instead of 251 in 46 overs.
  • Team B is bowled out for 234.
  • Ball Difference is computed in three steps:

Number of balls required to win = Runs required to win * Total number of balls in interrupted innings / The revised target

Interrupted Ball Difference = Total number of balls in interrupted innings – Number of balls required to win

Ball Difference = Interrupted Ball Difference * Total number of balls in scheduled innings / Total number of balls in interrupted innings

  • Team B is bowled out for 234. Team A wins by 33 runs using the Duckworth-Lewis method. Runs required to win the game for Team A are 235. Thus BD = 35.955056 as shown below:

Number of balls required to win = (234+1) * (46*6) / 267 = 242.92135

Interrupted Ball Difference = 276 – 242.92135 = 33.078652

Ball Difference = 33.078652 *300 / 276 = 35.955056

9. Interrupted game where side batting second wins

  • ‘Total number of balls in scheduled innings’ of a 50-over ODI is 300 (120 for a T20 match).
  • In matches where interruptions reduce the number of overs bowled, the revised targets will be used to calculate Ball Difference.
  • For example, in a 50-over World Cup first-round group match, Team A are dismissed for 165 in 33.5 overs.
  • Team B progresses to 120-0, but play is halted after 18 overs due to rain.
  • Six overs are lost, and the target is reset to 150, which Team B reach comfortably after 26.2 overs with only 2 wickets lost.
  • The two step formula for BD is:

Interrupted Ball Difference = Total number of balls in interrupted innings – Number of balls required to overhaul the revised target

Ball Difference = Interrupted Ball Difference * Total number of balls in scheduled innings / Total number of balls in interrupted innings.

  • Because the target was revised, 6 overs were lost and Team A were bowled out, Team A’s total is reset to 149 after 44 overs, thus BD = 120.4545 as computed below:

Interrupted Ball Difference = (44*6) – (26*6 + 2) = 106

Ball Difference = 106 * (50*6) / (44*6) = 120.4545

10. A game with result after multiple interruptions

  • If the game is interrupted more than once, Ball Difference is computed, ignoring intermediate targets, using the final values only.
  • For example, in a 50-over World Cup first-round group match, Team A score 265/7 in 50 overs.
  • Team B scores 137/6 in 31.3 overs when rain stops play.
  • Match is reduced to 46 overs when the play resumes with the revised D/L target of 260.
  • Rain halts play completely when Team B has reached 142/6 after 32.5 overs.
  • The revised D/L target at this stage of the match is 191. Team A wins the match by 48 runs.
  • In this case ignore the intermediate D/L target of 260 in 46 overs and use only the final values to compute BD as described earlier.
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9 thoughts on “Computations for Ball Difference

  1. alokjoshi

    Kudos to you – ball difference is indeed a better measure than NRR because it reduces the variable that separates teams to just one, given that runs scored is made to be a constant (plus 1 to decide winner notwithstanding) and wickets lost are rightly considered irrelevant.

    It is logical that difference between two sides is only calculated in terms of # of balls, and it is time to make NRR redundant.

    I’ve a question for you – can the target for interrupted matches be set differently, rather than through D/L (which has wickets as one of the variables)?

    Reply
    1. pandimi Post author

      Any fair method to determine modified targets after a rain interruption must be based on wickets and overs.

      I am suggesting that at the end of an inning the one thing that matters is runs scored. Hence we can ignore wickets in hand to devise a tiebreaker for league matches.

      Reply
  2. pandimi Post author

    Thanks Dr Bhogle.

    I am repeating here what I mentioned elsewhere in the posts and comments.

    Why combine runs scored by a team in various matches, the way Eng in CWC11 was involved in two 300+ maches against Ind and Ire and a low scoring thriller against RSA, to form the basis of a measure. Run Rate, Net Run Rate and Run Difference treat runs scored in various matches uniformly.

    Use actual match data instead of a modelled value for what the winning team batting second would have scored.

    Wickets should not be used in a measure for a limited overs match.

    Finally in an interrupted match, the measure should be scaled up using the full allocation of scheduled overs.

    Reply
  3. Srinivas Bhogle

    Ken: Your method is exactly what Duckworth-Lewis have been recommending for a long time! They even talk of it in their book.

    In fact we should use this difference, instead of the net run rate (NRR), as the tie-breaker in ODI tournaments.

    It is trivially obvious that NRR gets messed up when D/L is used. ICC currently has a rather ridiculous work-around.

    Reply
  4. pandimi Post author

    Ken, in the computations for ‘ball difference’ for interrupted games, the final step of:

    Ball Difference = Interrupted Ball Difference * Total number of balls in scheduled innings / Total number of balls in interrupted innings.

    is precisely to ensure that all match results are compared using the full quota (i.e. 120 balls for T20 and 300 for F50). This is a measure for multiple matches played in round-robin league and all results should have the common denominator. A win by 20 balls in F50 is actually ’20 out of 300′ balls which compares with winning a T20 by 8 balls.

    Personally, I *too* would scale up both teams’ scores to what they would have made from 50 overs.

    Reply
  5. pandimi Post author

    Ken, I like your method and must admit that I had tried my hand at ‘Run difference’ in ’90s. Unlike you, I did not work on all possible alternatives. I used to think about an alternative during every CWC. Since ‘runs’ are the natural currency, I tried to ‘extrapolate’ runs to derive a ‘Margin of Victory by Runs’. Of course, full credit to you for explaining the system for all possible scenarios.

    On the eve of world cup 2011, or maybe during the Sehwag show in the opening match, I thought of using ‘Balls Remaining’ instead. I prefer this method because:
    i. Simple method. No calculations other than sliding down the scoreboard in completed matches.
    ii. Uniformly treats the victory margin for both high scoring games and low scoring thrillers. I discarded the measure based on RUNS primarily for this reason.
    iii. A team scoring 300/2 loses to 301/9. A test match is won by claiming 20 wickets and scoring an additional run. Balls do not matter. But a limited overs match is won by scoring an extra run within allotted balls, irrespective of wickets. Both D/L and VJD (let me disclose my bias to VJD as a better alternative to D/L) are models, they have both improved in the last ten years, and of course a new method can be developed to make use of the available resources to mathematically derive revised target ‘during the match’. This is a ‘post-result’ measure and hence wickets remaining should definitely not be taken into account. It does not matter how many wickets were lost at the end of first innings. That is to say that wickets in hand are important only during the play not in the final outcome. That is why a strong batting side can win LOIs with a weak bowling attack unlike Test matches.

    In my main article where I described this idea, I touch upon the reasons why I like this method. Not because ‘I’ stumbled on this idea, but mainly for its elegance and use of ‘actual match data’ – i.e. no extrapolations.

    Reply
  6. Ken Butler

    Interesting. For some time, I have been thinking that net run-rate is excessively complicated, and this is one way around that.

    An idea I had is to calculate a “run difference” by converting any win by wickets into a faked-up win by runs, by using Duckworth-Lewis to figure out how many runs the team batting second would have made, if they had had the chance to bat out their overs. (That is, you work out what % resources the second team had left when they won, times that by 235, add that on to the score they actually made, and then take the difference of runs.)

    I’m using a 2002 D-L table for this.

    Let’s see how that works with your examples:

    1. A 287-6, B 243-8: A wins by 44 runs. (Obviously!)

    2. A 265-8, B ? Let’s say 266-6 with 3 overs left. With 6 wickets down and 3 overs left, B has 9.5% of resources left; 0.095*235=22, so B would have made 266+22=288 and win by 23 “runs”.

    3. A 127 (25.4 overs), B ? say 131-3 in 26 overs. With 24 overs left and 3 wickets down, B still has 54.7% resources left; 0.547*235 = 129, so B would have made 131+129=260 and win by 133 runs.

    Notice how in 2 and 3 it matters for me how many wickets were lost on reaching the target, because that affects the resources left.

    4. A 295-7, B 184, A win by 111 runs.

    5. A 117, B 112. A win by 5 runs. (When a team wins by runs, no conversion is needed).

    6 & 7. same as you.

    When D-L is used, it makes most sense to me (like you) that the *final* target is the one that counts.

    8. A 250-9 (46 overs) after interruptions, revised target 267 in 46 overs, B 234. A wins by 267-234=33 runs.

    9. A 165, revised target 150 in 44 overs, B 151-2 (say) in 26 overs. 18 overs left, 2 wickets down = 48.6% of resources left. 0.486*235=114, so B predicted to make 151+114=265 and are awarded a win by exactly 100 runs.

    9a. Suppose as in 9, B reached 120-0 in 18 overs and no further play is possible. B had 26 overs left with 0 wickets down, so they lost 68.3% of their resources. Team A’s score (which we’re pretending is 150) is multiplied by (100-68.3)/100 to give 48 to give the par score for B. B win by 120-48=72 runs. (This is exactly the amount by which B would have been declared the winner under D/L.) [Personally, I would scale up both teams' scores to what they would have made from 50 overs, but D/L does it the way I did above and I'd rather be consistent.] Note that it’s easier to win by more if you bat longer, because in 9a both teams’ scores were effectively scaled down from what they would have made in 50 overs.

    10. same as you: A wins by 48 runs.

    In short, by using run difference you convert any win by wickets to an “equivalent” win by runs by using the resources “lost” to the second team for scoring runs by virtue of their already having won the game.

    What do you think?

    Reply

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