The ODI Contributing Average
A new perspective on batting combines different measures of a player's worth into a single index.
Part I: Click here to read our arguments for this new measure

How good is your favourite ODI batsman? In the first part of our discussion we looked at the different measures available currently, and understood the problems with each of them. In this concluding part we present our new measure - the "Contributing Average". This indicator overcomes the limitations of the other ones already discussed, and is a fairer reflection of the relative contributions of different players across thousands of games.

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 slam-bang 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.

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 value-neutral 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.

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).

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.

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.

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.

Having 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.

• Unlike in the case of the Batting Average, the effect of not-outs is removed in the calculation of the Contributing Average. This makes the comparison between lower order batsmen (who remain not out more often) and higher order batsmen truer than when using Batting Averages alone.

• The contrasting styles of play demanded by the team's needs at various stages of the game are factored in. The Batting Average ignores the rate at which runs are made, and the Strike Rate doesn't distinguish between innings based on the actual score. The Contributing Average, on the other hand, provides credit (or penalties) based both on the total runs scored as well as the rate of scoring.

All-time Batting Honours - By Contributing Average

SNo Batsman             Ctry  Inns  NOs  Runs   StRt   Avge   %Change

  1 Zaheer Abbas         Pak    60    6  2572   80.0  47.63   - 6.49
  2 Tendulkar S.R        Ind   315   31 12878   86.6  45.35   - 4.63
  3 Richards I.V.A       Win   167   24  6721   88.7  47.00   - 8.21
  4 Gayle C.H            Win    82    3  3160   79.2  40.00   + 0.97
  5 Lara B.C             Win   220   23  8443   79.3  42.86   - 6.49
  6 Ganguly S.C          Ind   232   20  9133   75.1  43.08   - 6.99
  7 Greenidge C.G        Win   127   13  5134   66.3  45.04   -11.69
  8 Jones D.M            Aus   161   25  6068   73.2  44.62   -14.78
  9 Trescothick M.E      Eng    75    3  2700   86.1  37.50   + 1.32
 10 Hayden M.L           Aus    81   11  2959   77.3  42.27   -11.00
 11 Gilchrist A.C        Aus   177    6  6165   93.8  36.05   + 3.92
 12 Saeed Anwar          Pak   244   19  8823   80.7  39.21   - 4.63
 13 Kirsten G            Saf   185   19  6798   72.0  40.95   - 9.68
 14 Yousuf Youhana       Pak   150   23  5449   73.9  42.91   -13.98
 15 Ponting R.T          Aus   187   26  6763   77.2  42.01   -12.53
 16 Waugh M.E            Aus   236   20  8500   76.8  39.35   - 6.95
 17 Kallis J.H           Saf   176   31  6497   70.4  44.81   -18.29
 18 Marsh G.R            Aus   115    6  4357   56.4  39.97   - 8.67
 19 Knight N.V           Eng   100   10  3636   71.5  40.40   -10.04
 20 Dippenaar H.H        Saf    56    9  2066   65.3  43.96   -17.98
 21 Haynes D.L           Win   237   28  8648   63.7  41.38   -12.90
 22 Sehwag V             Ind    79    6  2585   94.9  35.41   + 0.47
 23 Bevan M.G            Aus   189   66  6700   74.3  54.47   -34.84
 24 Smith R.A            Eng    70    8  2419   69.8  39.02   -10.48
 25 Sidhu N.S            Ind   127    8  4414   70.0  37.09   - 6.49

    CA

  44.54 
  43.25 
  43.14 
  40.39 
  40.08 
  40.07 
  39.77 
  38.02 
  37.99 
  37.62 
  37.47 
  37.40 
  36.99 
  36.91 
  36.74 
  36.62 
  36.61 
  36.51 
  36.35 
  36.05 
  36.04 
  35.58 
  35.49 
  34.93 
  34.69 

Note some striking facts from this table.

• The list excludes some players who figured in the Top 25 when we looked only at Batting Average. Lance Kluesener and Damien Martyn, both of whom were present in the Batting Average table (see Part I) are absent from this new table. Their batting averages are hugely boosted by their large Not Out percentages, and when that effect is removed, they no longer figure among the top, in Kluesener's case despite his fairly impressive strike rate. Michael Bevan makes it to this list despite losing the boost from his not-outs, but this time he's at more credible position.

• While thwacking the ball around is a valuable skill in the limited form of the game, this too cannot by itself guarantee a place among the all-time greats. Shahid Afirdi's phenomenal strike rate (27% better than our par rate) is still inadequate for him to make it to the Contributing Average list, because he's typically unable to sustain his powerful hitting very long, and is instead dismissed after cameo efforts. In contrast, the 'anchor' type of batsmen - such as Youhana, Kallis and Haynes - lose over 15% when their batting averages are adjusted to determine the worth of their contributions relative to the par scoring rate. This happens because we have now integrated into our measure one of the key elements of ODI Cricket - the ability to score quickly.

• Geoff Marsh, whose RPI is high enough to feature in the top 20 by that criterion - also figures in this list. While his moderate strike dropped his contributing average a few points below the batting average, nearly all the runs he scored were earned in completed innings - he has only 6 not outs.

The Contributing Average is an all-round 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 second-best 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 not-outs' 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 Not-Outs, 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
January 2004.

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.