The ODI Contributing Average
Let us begin with a fairly simple question  what does a batsman have to do when he walks in to play an ODI innings? Answer: he should score as many runs as he can, and score them as quickly as possible. The rate of scoring is critical; even batsmen who anchor the innings, for e.g. Marvan Atapattu or Yousuf Yohanna, must keep the scoreboard moving, lest they use up too many of the available balls without scoring off them. At the same time, the absolute number of runs a batsman adds is important too; a quick 20 in 9 balls at the top of the order provides only a small boost to the team, very different from a 60 off 27 balls  even though they represent the same scoring rate. So  how many runs should a batsman score, for any given number of balls faced? To determine this we first computed the overall scoring rates for each of the teams that have played one day internationals since this version of the game first appeared. The 'Country' column in the table below refers to the nation in which the match was played, regardless of the teams involved. Scoring rates in different countries Country Matches Runs Balls ScRte 50 Ovrs Australia 427 169503 234100 0.724 217 India 247 108105 132747 0.814 244 England 225 94880 131868 0.720 215 U.A.E. 198 82142 109617 0.749 224 South Africa 181 74181 96037 0.772 231 New Zealand 178 70284 94639 0.743 222 Pakistan 150 61869 76651 0.807 242 Sri Lanka 142 53548 70515 0.759 227 West Indies 118 48477 62666 0.774 232 Zimbabwe 73 31168 39346 0.792 237 Bangladesh 57 24182 30216 0.800 240 Kenya 43 17798 22523 0.790 237 Canada 22 8385 11403 0.735 220 Singapore 14 5212 6011 0.867 260 Morocco 7 3196 4026 0.794 238 Scotland 2 592 938 0.631 189 Ireland 1 365 575 0.635 190 Netherlands 1 305 513 0.595 178 Total 2086 854192 1124391 0.760 227 This table is for all 2086 matches played until January 23, 2004. We see that an average of 227 runs is put on the board across all these games. However, with the success of Sri Lanka's slambang tactics in their winning World Cup campaign, the scoring rates began to rise, and the average figure these days is around 237 for the full fifty overs. This includes a few games with really poor teams, but the number of such games being low, this expectation is largely set by teams with a fairly long history of cricket. For our new measure of contribution, therefore, we have set the par score to be 240. This translates to a strike rate of 0.8. It is important to note an additional point here  the choice of this 'par' scoring rate is not significant to measuring the relative worth of batsmen, those who exceed it or fall below it will be at an advantage or disadvantage to others (respectively) based on any par scoring rate that we choose. The degree to which an individual batsman gains or loses, however, is a function of this par rate, and it is for that reason alone that an appropriate choice is needed. The choice of 240 runs per 50 overs closely tracks the typical rates at which runs are being scored in one dayers. It may be of interest to note that out of the 2004 matches which have been conclusive so far, 906 matches (around 46%) have been won by teams scoring at a rate of 0.800 or lower. This brings us to the core of our new measure. We propose that a Contributing Score be computed for each innings played by a batsman by adjusting the runs scored in two ways  the first adjustment recognizes how far above or below the expected par rate of scoring he scored at during the innings, and the second adjustment recognizes the degree to which the runs he scored contributed to his team's total in the match. This calculation is performed over his entire career to obtain the Contributing Average. Here's the mathematical relationship used to compute the Contributing Score from each innings:Because a par scoring rate (0.8) is set, any score made at this strike rate will result in a Contributing Score that is equal to the actual runs made. When runs are made faster, the Contributing Score will be higher than the runs made, and viceversa. The degree to which such credits and demerits are assigned will depend on the scoring rate as well as the portion of the Team Score made by the batsman; short bursts will add less to the Contributing Score than sustained assaults. We illustrate these factors using two recent strong innings  Yuvraj Singh's 139 and Gilchrist's 95 in the recent match at SCG (match #2086). Yuvraj Gilchrist Runs scored 139 95 Balls faced 122 72 Scoring Rate 1.14 1.32 Par Scoring Rate 0.80 0.80 Gain in Scoring Rate 0.34 0.52 [A] Team Score 296 225 % of Team Score 0.469 0.420 [B] Contributing Runs 22.1 20.7 [Runs * A * B] Contributing Score 161.1 115.7 [Runs Scored + Contributing Runs] This illustrates how individual scores can be compared. Yuvraj's 139 is 46% better than Gilchrist's 95, but when these scored are turned into contributing numbers based on strike rates and their relative importance to the team, the gap narrows to 39% (115.7 versus 161.1). Both batsmen gain over 20 runs in this calculation, but Gilchrist's addition is on a much lower score; his more impressive strike rate narrows the gap between the two performances in our analysis. The Contributing Average, like the Batting Average itself, is valueneutral to the conditions under which the scores are made. This is appropriate; our intent is not to create a ratings scheme where the state of the match will be relevant, but to propose a quantitative measure. Therefore, the facts that Youvraj came in at a difficult situation, and that India lost the match despite Yuvraj's innings, do not come into the scope of this computation. This is the way it is with the Batting Average too. What the Contributing Average does  and the Batting Average does not  is place the duration of the innings and the speed of scoring alongside an expected average, thus allowing the effect of different styles of batting to come through. Contributing Scores for a few interesting innings The highest 15 ODI scores, and their corresponding Contributing Scores (CS) are listed below. The percentage additional credit over the actual score that accrues to the batsman for his innings is also shown (last column). For example, Saeed Anwar's 194 turns into a contributing score of 255, when the adjustments for strike rate and team totals are made; this is 31% better than the score itself will lead us to believe. We've also shown a few other interesting innings in this table  the quick fifties, some cameo efforts, and a few slow hundreds.
HIGHEST ODI SCORES Mat# Year Batsman For Vs Runs Balls CS %credit 1209 1997 Saeed Anwar Pak Ind 194 146 254.9 31.4 0264 1984 Richards I.V.A Win Eng 189 170 229.9 21.7 1652 2000 Jayasuriya S.T Slk Ind 189 161 233.7 23.6 1048 1996 Kirsten G Saf Uae 188 159 230.1 22.4 1523 1999 Tendulkar S.R Ind Nzl 186 151 225.7 21.4 1463 1999 Ganguly S.C Ind Slk 183 158 215.2 17.6 0457 1987 Richards I.V.A Win Slk 181 125 240.0 32.6 0216 1983 Kapil Dev N Ind Zim 175 150 217.2 24.1 1687 2001 Waugh M.E Aus Win 173 148 205.7 18.9 1943 2003 Wishart C.B Zim Nam 172 151 201.5 17.2 2082 2004 Gilchrist A.C Aus Zim 172 126 220.6 28.3 0020 1975 Turner G.M Nzl Eaf 171 178 186.2 8.9 0962 1994 Callaghan D.J Saf Nzl 169 143 203.7 20.6 1009 1995 Lara B.C Win Slk 169 129 212.7 25.9 0831 1993 Smith R.A Eng Aus 167 163 189.6 13.5 Vivian Richards' 181 and Saeed Anwar's 194 have gained the most, but not for the same reason. Anwar's high scoring rate helped him to a Contributing Score that is 31% higher than the runs he scored. His gains would have been even more impressive if his score had formed a more substantial portion of the team's total (327). Richards' 189, on the other hand, did not gain significantly from his strike rate (noticeably lower than Anwar's innings) but instead gained more substantially from his having made a larger share of the team total (272). QUICK FIFTIES Mat# Year Batsman For Vs Runs Balls CS %credit Team Score 1883 2002 Shahid Afridi Pak Hol 55 18 103.0 87.4 142 1090 1996 Jayasuriya S.T Slk Pak 76 28 140.3 84.6 172 1660 2000 Agarkar A.B Ind Zim 67 25 95.0 41.8 301 0630 1990 O'Donnell S.P Aus Slk 74 29 102.9 39.0 332 1763 2001 Boucher M.V Saf Ken 51 20 63.9 25.2 354 Afridi's and Jayasuriya's blazing 50s gain the most because they were made out of low team scores. Boucher's innings, made during a mammoth South African score, does not gain anywhere near as much as Afridi's innings, although both batsmen made similar scores from a comparable number of balls. A FEW CAMEOS Mat# Year Batsman For Vs Runs Balls CS %credit Team Score 0736 1992 Lewis C.C Eng Slk 20 6 23.6 18.1 280 1774 2001 Streak H.H Zim Bng 23 7 27.3 18.5 309 1658 2000 Khan Z Ind Zim 32 11 39.6 23.8 283 1094 1996 Azharuddin M Ind Pak 29 10 34.8 20.0 305 0357 1986 Phillips W.B Aus Ind 23 8 27.2 18.2 262 Also note that the gains for cameos is not very high because their proportion of team scores is low. That is the way it should be. AND FINALLY, A FEW SLOW CENTURIES Mat# Year Batsman For Vs Runs Balls CS %debit Team Score 0632 1990 Smith R.A Eng Nzl 128 168 125.9 1.7 295 1001 1995 Atherton M.A Eng Win 127 160 126.6 0.3 276 1981 2003 Gayle C.H Win Ken 119 151 118.3 0.6 246 These centuries have been scored at below the par rate of 0.80, and at the same time they do not even form 50% of the team totals in those games. Hence these innings have lost in the CA valuation. THE ODI CONTRIBUTING AVERAGEHaving looked at a few individual innings, we now turn our attention to career contributing averages. Once the contributing scores for each innings played by a batsman have been calculated, his Contributing Average is determined by dividing the total of his Contributing Scores by the number of innings played. There are two important gains from this calculation.
Alltime Batting Honours  By Contributing Average
Note some striking facts from this table.
The Contributing Average is an allround measure, and it clearly identifies the players who combine all the important elements of batting in one dayers. It recognizes the value of speed, and removes the effect of more fortuitious matters  like remaining Not Out, or opening the innings, or simply thwacking the ball around for a few deilveries and getting away with it. Who's better than their averages indicate, and who's worse? 1. A few winners: An interesting sidelight to the compilation of this new measure is to identify the players whose standing is most improved by looking at their career in this integrated manner. The following table lists the winners, whose contributions are not adequately reflected in their Batting Averages alone. SNo Batsman Ctry Inns NOs Runs St Rt BA CA %Change 1 Shahid Afridi Pak 171 7 3887 101.62 23.70 24.98 +5.4 2 Gilchrist A.C Aus 177 6 6165 93.76 36.05 37.47 +3.9 3 Jayasuriya S.T Slk 299 13 9166 88.91 32.05 33.08 +3.2 4 Trescothick M.E Eng 75 3 2700 86.10 37.50 37.99 +1.3 5 Gayle C.H Win 82 3 3160 79.18 40.00 40.39 +1.0 6 Sehwag V Ind 79 6 2585 94.86 35.41 35.58 +0.5 The percentage gains when these batsmen's averages are turned into Contributing Averages may seem small (between 0.5 and 5.5%). But keep two important points in mind  (a) these are the only six batsmen in the history of this version of the game whose Contributing Averages are better than their Batting Averages, and (b) For most batsmen, their Batting Average makes them look better than they actually are, for a number of reasons. In this list, Shahid Afridi gains the maximum because of his outstanding Strike rate, noticeably higher than even secondbest Adam Gilchrist. And of these six, all except Gayle have benefited mostly from their strike rate; Gayle's strike rate is close to our par rate, but he gains from contributing more than his share to his team's scores. He also hasn't been not out very much, and doesn't lose much ground from that correction. 2. And lots of others: Here's a look at a few other players. As we pointed out above, nearly everyone is worse than his Batting Average indicates, but some are only a little worse, and some are in fact far less impressive that you would think if you looked at their Batting Averages alone. SNo Batsman Ctry Inns NOs Runs St Rt BA CA %Change 70 Kapil Dev N Ind 198 39 3783 91.24 23.79 20.43 14.2 ... ... ... 107 Martyn D.R Aus 118 38 3346 80.03 41.83 29.35 29.8 108 Harris C.Z Nzl 205 61 4250 66.45 29.51 20.71 29.8 109 Klusener L Saf 124 46 3381 90.62 43.35 28.48 34.3 110 Streak H.H Zim 147 52 2607 74.74 27.44 17.91 34.7 111 Bevan M.G Aus 189 66 6700 74.33 54.47 35.49 34.8 The 6 batsmen who are at the end have lost the maximum for two reasons (and in some cases because of both!)  (a) they have a very high number of not outs, which boosts their Batting Average, and (b) their strike rates and contributions to team totals are not high enough to offset the removal of the notouts' distorting influence. Kluesener's high strike rate, for example, is not enough to hide the fact that his Batting Average is mostly the result of many unfinished innings, many of them low scores. On the other hand, a player such as Kapil Dev, with fewer not outs and an equally impressive strike rate, loses less when his Batting Average is converted into a Contributing Average. Another way oif not losing substantially is to show a fairly high proportion of the team runs as top order batsmen such as Tenudlkar, Inzamam and Gibbs do often, but even here only those with good strike rates can hold their averages high. CONCLUSION The Contributing Average is a more accurate measure of batting value, since it takes into account the runs scored in three different ways  as an absolute number, as a portion of the team's total, and in relation to the balls faced. The Contributing Average also removes the distorting effects of NotOuts, which are strongly related to one's batting position. The CA acknowledges the value of scoring quickly, but ensures that speed alone  without the tenacity to make large scores  is insufficient to be regarded as exceptional. The truly great players are unaffected by these adjustments; their greatness reflects the fact that they rank among the top players of the game by two  if not all three  of the other measures too. Zaheer Abbas, the numero uno thus far, ranks #2 in Batting Average, and #1 in Runs per Innings. The weakest link in his arsenal is his Strike Rate, but even here his 79.98 tops Brian Lara, and that's saying something.
Y. Anantha Narayanan & Ashwin Mahesh
Click here to read Part I  a discussion of the limitations of existing measures, namely the Batting Average, Strike Rate, and Runs Per Innings. A future analysis will also present a discussion of batsmen's records in Test cricket, and Contributing Averages developed for that version of the game.
