This is the second of three very important and significant articles on batting performances against differing conditions and players. The first did a revised take on the Bowling Quality Index. This one covers the Pitch Quality and the third one would combine both and do an analysis of runs scored by batsmen.
Over the past two weeks, the six of us have shared the work and downloaded over 600 scorecards. I have incorporated the balls played information for all these and also took the opportunity to post the 4s/6s information also. Now my database is looking wonderful with 1374 scorecards (68% - a far cry from 37%) containing balls played and 4s/6s data. From match no 1070 (1987), I have an unbroken sequence of 957 scorecards with complete data. This opens up many new avenues of analysis, especially in the analysis of boundaries hit.
Once again my heartfelt thanks to Raghav, Boll, Rameshkumar, Ranga and Anshu, who spent hours during the holiday season. May their tribe flourish.
There is nothing to be gained by looking at history to determine the quality of pitch. The following example will convince anyone on the futility of such a view. Let us look at happenings in the same ground, Hamilton, in two matches played within 12 months of each other.
Tale of two Tests at Hamilton
2003: Ind 99 ao & 154 ao. Nzl 94 ao and 160 for 6. 36 wkts at 14.1.
2003: Nzl 563 ao & 96/8. Pak 463 ao. 28 wkts at 40.1, despite the last innings.
India at Ahmedabad within a 18-month period
2008: India 76 ao against South Africa. RpW: 33.2.
2009: India 760/7 against Sri Lanka. RpW: 76.1.
Instead I am going to look only at the specific match. I am not also going to make the mistake of going down to innings. The recent match from "The Twilight Zone" at Cape Town is enough reason to stay away from this. 284 ao, 96 ao, 47 ao, 236/2 neither indicates a horror pitch of RpW (Runs per Wicket) of 7.2 considering the middle two innings nor a very comfortable pitch with an RpW of 43.3 looking at the first and fourth innings. This is a match with a RpW value of 20.7. A difficult pitch but not an impossible one to bat on.
Thus it is clear that the overall match RpW seems to be closer to the actual pitch condition. This will take care of many a match in which the innings scores change significantly. Four innings and five days present us with a chance to come very close to determining the way the match went.
I will only consider the first 7 batsmen. The last four batsmen will distort the picture. Thus I am going to look at a maximum of 28 innings and determine the average. This is called T7-RpW.
Now we come to a different problem. The RpW works well in most cases. However there are some matches in which the extremely low rate of scoring means that very few runs were scored but quite a few balls were faced. This indicates not a diabolical pitch but only a difficult pitch. To a considerable extent the ultra-defensive approach of the batsmen would have contributed to this situation.
First let us see two examples, at either end, where the RpW and BpW (Balls per wicket) are in sync.
Match 216: Scores 36 ao, 153 ao & 45 ao. RpW: 8.5. BpW: 22.3.
Match 1374: Scores 537/8 & 952/7. RpW: 113. BpW: 215.
Now let us take a look at three matches, taken as two comparisons.
Match 1037: Saf 109 & 101, Aus 230. RpW: 14.1. BpW: 33.7. RpO: 2.50
Match 0438: Saf 164 & 134, Eng 110 & 130. RpW: 14.3. BpW: 60.8. RpO: 1.40
Match 0438: Saf 164 & 134, Eng 110 & 130. RpW: 14.3. BpW: 60.8. RpO: 1.40
Match 0782: Pak 417 & 105/4, Nzl 157 & 360. RpW: 33.8. BpW: 60.7. RpO: 3.23
I am sure the readers are going to say that the period, viz., the 1950s, when Test no 438 was played, was a defensive one and teams did not think twice about scoring very slowly, irrespective of the situation. The slowest Test innings ever is New Zealand scoring 69 for 6, during 1955, against Pakistan in 90 overs: Yes, it is correct, not a misprint. In fact it is this very trend which has to be taken care of. New Zealand lost only 6 wickets in 90 overs, leading to an innings RpW of 90. Was it a 11.5-RpW quagmire of pitch. No, certainly not. It was probably a 30-RpW wicket. It is this adjustment I am referring to.
After trying out a few scenarios I have hit upon a simple method. One which would be clearly understood and accepted by all. I have realized that both RpW and BpW are important. Hence I have determined the Pitch Quality Index by adding the two values together. However I feel that the RpW value is more important. Hence the RpW gets three-fourths weight and the BpW value, one-fourth weight.
This is not as arbitrary as it looks. With an overall RpO of 3.0 across all matches, the BpW value is around twice that of the RpW value and 75-25 looks perfect. 67-33 will make this skewed too much towards the BpW value. As an example, take RpW of 30 and BpW of 60. 67-33 takes PQI to 40 (20 + 20). 75-25 comes out with a PQI of 37.5 (22.5 + 15). The final PQI values do not matter. The almost equal weight, as shown in the first case, negates my requirement that RpW should have a higher impact.
Again readers should realize that the seemingly arbitrary nature of this does not matter since it is only a derived interim index value. It is also applied across all matches. I will call this composite value PQI (Pitch Quality Index).
I can anticipate a question why the BpW has been taken and not BpI since that seems to make more sense. However since I am adding two disparate figures, it is not correct to have one based on wickets and the other based on innings. If a top-7 batsman could not be dismissed, then to that extent the pitch has to be related to that. If Lara's 582 balls are not included in the computation of the BpW (as against the BpI) figure at Antigua, that would correctly increase the BpW value by about 35 (since 16 top order wickets fell in that match), bringing to light the true dead nature of the pitch.
It can be seen that the period in which the match is played does not have any relevance since only what happened in the match is taken into account. For instance take two Tests in 2001: Test# 2021 (Aus vs Nzl) has a PQI of 27.2 (PG-5), Test# 2016 (Saf-Aus) has a PQI of 27.7 (PG-5). Now look at Test# 2008 (Slk vs Aus) with a PQI of 77.6 (PG-1) and Test# 2009 (Pak-Slk) with a PQI of 77.6 (PG-1). Such examples abound even during the notorious batting-friendly periods. Readers should never forget that this is a post-match actual measure.
Given below are the matches with extreme PQI values. Teams are all out if not mentioned otherwise.
The top-10 and bottom-10 Tests in PQI table
MtId Year Hme Awy< ------Top-7 Batsmen------ > Ins No Runs BpW RpW PQI Grp Innings scores
Three of the low PQI matches were played during before WW1 and two during the 1930s. On the other hand the high PQI Tests have been distributed over the years. The PQI runs from 10.1 for the 1888 Test through 11.9 during 1932 at MCG and through 157.4 at New Delhi during 1955 and finally 157.5 during the run-deluge at Lahore during 2006.
A brief referral back to the three matches we had considered earlier.
1037: 14.1 & 33.7 lead to 20.6 (Group 5 - but lower)
0438: 14.3 & 60.8 lead to 29.8 (Group 5)
0782: 33.8 & 60.7 lead to 42.8 (Group 3).
The distribution is quite skewed. This is confirmed by the statistical measures. The distribution has a mean of 48.5 and a Standard Deviation of 16.6 which means the Coefficient of Variation is a rather high 0.34.
The range of the PQI is so wide that all calculations go awry. Remember that this is post-match measure, unlike the BQI which is a pre-match expectation. Hence it was possible to put limits on BQI. Here nothing like that can be done. The distribution is also not a Normal one like the BQI. There are only 80 matches between 86 (half of 172) and 172. So the PQI cannot be allocated blindly or by making standard assumptions. Hence I have done the following. The 27 is a starting point determined by looking at low RpW and BpW values. Then reasonable gaps are allowed for subsequent groups. It is possible that some fine-tuning will be done when I do the Batsmen analysis, especially in the formation of groups.
Summary of PQI Grouping
Finally while the memory is fresh, let me show the relevant values for the two Tests which finished a few days back.
Below 27.0: Group 5 - 101 ( 5.0%) A nightmare for the batsmen 27.0 - 37.0: Group 4 - 388 (19.2%) Difficult to bat on 37.0 - 47.0: Group 3 - 563 (27.8%) Good pitch - slightly favouring bowlers 47.0 - 60.0: Group 2 - 576 (28.4%) Good pitch - slightly favouring batsmen 62.0 - 80.0: Group 1 - 313 (15.4%) A belter (I have had too much of Shastri!!!) Above 80.0 : Group 0 - 85 ( 4.2%) Where "open season" is declared on bowlers.
Boxing Day Tests
Match 2025: Scores 333, 282, 240 & 169. RpW: 25.6. BpW: 52.9. PQI: 32.5 Match 2026: Scores 338, 168, 279 & 241. RpW: 29.0. BpW: 57.6. PQI: 36.1
To download/view the document containing the complete PQI tables please click/right-click here.
In the next article I will form a composite of BQI and PQI for each innings and arrive at a Bowling-Pitch Group. This would be a true indicator of the conditions the batsmen played in and the attack he faced. I will do a analysis of the runs scored by batsmen against different combination groups.
Revision of PQI calculation based on Arjun's alternative method.
Given below is the revised Pitch Group allocation based on MT10 (Top 10 innings of match) values. This was suggested by Arjun Hemnani. This has a lot of pluses going for it, mainly the inclusion of all performances irrespective of the batting position.
Match# 684 is a perfect example of why we should not take Average but Runs per Innings.
Win 363 ao. Ind 376 ao. Win 307/3. Ind 123/0.
The third and fourth innings had two high score not outs. The first two innings had a high score not out each. Net result is 754 runs in 4 (10-6) innings leading to a MT10-Avge of 188.5, the third best. A total farce. This is the only Test with 6 MT10 not outs. 5 not outs, there are two matches. One seems okay. The other not. Then come the matches with 4 not outs, led by two matches with the highest MT10-Avge of 191.0 and 190.3. Only the later, Match# 1426 truly deserves this number. This is the Taylor-334 match.
So taking average is truly out. The current match, with 3 top innings already as not outs, would also go that way. One possibility to is to limit the number of not outs to 3. Works well but rather artificial.
Finally the simplest and most elegant solution is to take the MT10-RpI. After all these are the top-10 innings of the match. So remaining unbeaten does not mean that much of a difference. What does it matter whether we take 400*/329* or 400/329. The RpI has worked out very well.
For the T7-PQI I used the BpW as an additional measure. However here there is no need to do that for reason given below.
The 28 innings used to determine the T7-RpW had a number of small innings, with varying balls played associations. Hence I used the BpW measure to smoothen these wide variations within a match and across matches. However in this case we would select only the top-10 innings of the match. As such I have found that the MT10 Runs have a strong correlation to the MT10 Balls played. Hence there is no need to incorporate the Balls played information, which anyhow gets determined on a pro-rata basis for a third of the matches.
Summary of PQI Grouping - Based on Top-10 innings in match
Below 40.0: Group 5 - 112 ( 5.5%) A nightmare for the batsmen 40.0 - 52.5: Group 4 - 358 (17.7%) Difficult to bat on 52.5 - 65.0: Group 3 - 490 (24.2%) Good pitch - slightly favouring bowlers 65.0 - 80.0: Group 2 - 599 (29.5%) Good pitch - slightly favouring batsmen 80.0 - 95.0: Group 1 - 342 (16.9%) A belter (I have had too much of Shastri!!!) Above 95.0 : Group 0 - 125 ( 6.2%) Where "open season" is declared on bowlers.
Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems