Trivia - batting August 1, 2008

# The highest peaks and lowest troughs for batsmen

Brian Lara finished his career with a batting average of more than 50

Brian Lara finished his career with a batting average of more than 50. It is certain that during his illustrious career he would have gone through a few peaks and troughs. Not necessarily a sine-wave pattern but certainly up and down. It is also certain that a few of these would have been way outside his career average of 52.89. This article looks at such peaks and troughs occurring in the careers of Test batsmen.

This analysis will be in two parts. The first looks at the batsman's career in fixed segments. The second is to look at batting sequences, both outstanding and abysmal.

As usual, we have to set some criteria and parameters. As also is normally done, these are common-sense based and will meet expectations of most discerning readers.

1. The number of innings played should be 50 or more. This is a fair requirement since otherwise we will not have sufficient data to analyse. The limit of 50 innings means that an average of 30 Tests would have been played by the batsman. Also the batting average should be greater than 25.0. We are certainly not interested in analysing the batting exploits of Curtly Ambrose, Shane Warne, Harbhajan Singh et al who have played well over 50 innings. I know this will exclude players such as JM Parker (NZl), Nick Knight (Eng), Asif Mujtaba (Pak), Mohammad Ashraful (Bng) et al, all with sub-25.0 averages. In order to complete the analysis properly I have included batsmen whose batting average is less than 25.0 but whose BPA (Batting Position Average) is less than 6.0. Twelve batsmen, including all four mentioned above, have now been included. With this criteria, a total of 299 batsmen get selected for analysis.

2. I will consider a unit of 10 innings [or more], hereinafter called a stretch, as a unit for measuring the average and variation from average. This represents between five and eight Tests, normally spanning across two or more series and is a good measure. We will consider the batting average during this period as that is the most accepted unit of batting measure. Runs per inns and Run aggregate both suffer from significant shortcomings.

3. In the first part, each batsman's peak and trough will be measured against his own career batting average. The need for this method of measuring is best proved by considering the batting averages of two opening batsmen of different eras, of totally diverse temperament, skills and application levels. Herbert Sutcliffe had an average of 60.73 and Kris Srikkanth weighed in with 29.88. If Sutcliffe had a stretch average of 20, he would consider it as a very low period while Srikkanth would find it quite acceptable. Sutcliffe would have to have a stretch average of 75+ to think that he had a very good run, while Srikkanth would be over the moon with a stretch average of 45.0.

4. What is a peak? What is a trough? I have defined a peak or a trough to be 50% on either side of the career batting average. In other words, if a batsman has got a batting average which is above 150% of his batting average, it is considered a peak. If a batsman has got a batting average which is below 50% of his batting average, it is considered a trough. Looks subjective, but has been done based on lot of research.

5. The analysis will be done in two distinct parts. The first is an easier and more understandable method where the batsman's career is split into as many fixed stretches as required (1-10, 11-20, 21-30 et al until career-end) and then the peaks and troughs are determined. The last stretch, if below 10 innings, will be ignored. Because of the fixed interval, it is possible that a run such as Mohinder Amarnath's sequence of 4, 7, 0, 0, 1, 0, 0, 0 might be split into two different stretches. It so happens that Amarnath bookended this horrible run with scores of 91, 81, 54, 116 and 36, 101*, 37, 49 on either side. This is a simple exercise.

6. This is a simple (okay, not so simple) analysis of a player's career performance. No allowance has been made for the quality of opposition, bowling quality, home or away Tests, match results et al. The purpose is not to determine the quality of innings but just to determine deviations away from the mean values. I also personally think that failures against stronger teams cannot be justified nor can successes against weaker teams be derided.

Now let us take a look at the tables for Part 1. The analysis is current upto and including the Colombo match in which the vaunted Indian batsmen were found wanting.

1. Table of Peaks, by % of Batting Average

```No  Cty Batsman          Stretch Ins No Runs Avge CarAvge  %
St End
1. Slk Tillakaratne H.P  91 100 10  6  641 160.25 42.88 373.74
2. Saf Kallis J.H        81  90 10  6  711 177.75 56.28 315.80
3. Slk Sangakkara K.C   101 110 10  4 1036 172.67 54.81 315.01
4. Ind Vengsarkar D.B   141 150 10  4  788 131.33 42.13 311.70
5. Saf Pollock S.M       91 100 10  6  398  99.50 32.32 307.89
6. Slk de Silva P.A     101 110 10  2  961 120.12 42.98 279.49
7. Eng Gatting M.W       61  70 10  4  568  94.67 35.56 266.24
8. Saf Pollock S.M       71  80 10  5  421  84.20 32.32 260.55
9. Aus Trumper V.T       71  80 10  2  774  96.75 39.05 247.76
10. Pak Mudassar Nazar    51  60 10  2  716  89.50 38.09 234.95
```
There is no doubt that the high averages for most of the stretches in the top 10 have been because of the high number of not-outs. That is a parameter we have laid down and there is nothing fundamentally wrong with that. One has to admire Hashan Tillakaratne for his stretch of 55*, 11, 10, 16, 136*, 10*, 105*, 87, 7* and 204* and Kumar Sangakkara for his stretch of 287, 14, 39, 4, 100*, 156*, 8, 6, 200* and 222*.especially for their determination in scoring big centuries and remaining unbeaten. Also Sangakkara exceeded 1000 runs. Jacques Kallis, the unsung South African batsman, has a few impressive runs such as this stretch consisting of 51, 157*, 42*, 189*, 68, 21*, 24, 89*, 5 and 65*.

2. Runs scored by batsman in a stretch

Mohammad Yousuf (1070), Sangakkara (1037) and Viv Richards (1036) are the only batsmen to exceed 1000 runs during any stretch. The year 2006 was a golden year for both Mohammad Yousuf and Sangakkara as was 1976 for the great Richards. As with Lara, Richards has few not-outs, as showed in this sequence. Surprisingly, Mohammad Yousuf also had no not-outs, probably explaining why they dropped down in the previous tables.

At the other end Ian Healy (59), AC Bannerman (72) and Marvan Atapattu (73) have scored the least number of runs during a stretch.

3. Table of Troughs, by % of Batting Average

```No  Cty Batsman          Stretch Ins No Runs Avge CarAvge  %
St End
1. Aus Ponting R.T       61  70 10  1   74   8.22 58.35 14.09
2. Slk Atapattu M.S       1  10 10  0   73   7.30 39.02 18.71
3. Aus Healy I.A        171 180 10  0   59   5.90 27.40 21.54
4. Eng Edrich W.J         1  10 10  0   87   8.70 40.00 21.75
5. Eng Compton D.C.S     61  70 10  1  108  12.00 50.06 23.97
6. Eng Flintoff A        11  20 10  0   86   8.60 32.42 26.53
7. Ind Jaisimha M.L      61  70 10  1   75   8.33 30.69 27.16
8. Aus Waugh S.R          1  10 10  1  125  13.89 51.06 27.20
9. Zim Flower G.W        71  80 10  0   84   8.40 29.55 28.43
10. Nzl Rutherford K.R     1  10 10  0   77   7.70 27.09 28.43
```

During the subject stretch Ponting averaged only 14.09% of his high career average. His miserable run consisting of 14*, 0, 6, 0, 0, 11, 11, 14, 4 and 14 was caused by the Indian spinners in India during 2001 and Darren Gough in England during the unforgettable Ashes tour. Atapattu's "bit pattern" run of 0, 0, 0, 1, 0, 0, 25, 22, 0 and 25 was at the start of his career. Who would have imagined that he would finish with a career average of nearly 40 and score six double-hundreds. Ian Healy's run of 0, 6, 10, 0, 3, 6, 16, 11, 3 and 4 was at the end of his career and hastened his departure. He needed to make this average ten-fold to keep Gilchrist out.

4. Summary of selected players' peaks and troughs

```Cty Batsman             Mats Ins    Stretches
Tot  P  T  A  B
Aus Border A.R           156 265  26  2  0 11 13
Aus Waugh S.R            168 260  26  5  3  8 10
Ind Tendulkar S.R        148 240  24  2  2 10 10
Win Lara B.C             131 232  23  1  0 10 12
Ind Gavaskar S.M         125 214  21  2  2  8  9
Eng Atherton M.A         115 212  21  1  1 11  8
Saf Kallis J.H           121 205  20  4  3  7  6
Pak Inzamam-ul-Haq       120 200  20  0  3 11  6
Nzl Fleming S.P          111 189  19  1  0  7 10
Win Richards I.V.A       121 182  18  2  1  5 10
Slk Jayawardene D.P.M.D   96 156  15  0  0  8  7
Aus Bradman D.G           52  80   8  0  0  4  4

Legend: P-Peaks (above 150%), T-Troughs(below 50%),
A-Above Batting avg (100-150%), B-Below Batting avg (50-100%).
```

Border was consistency personified with two peaks and no troughs. Steve Waugh was just the opposite. Quite a few peaks and troughs. Sachin Tendulkar was somewhat more predictable than Steve Waugh. The surprise is Lara - only one peak and no trough. It shows a facet of his batting which has not been appreciated. Surprisingly Gavaskar's and Tendulkar's distributions are identical. Michael Atherton is somewhat like Lara, with no great variations.

Kallis is similar to Steve Waugh, lots of variations. Surprisingly Inzamam is prone to more losses of form. However this is made up by a very high number of stretches which are above average. Richards has twice as many below-average stretches as above average. Possibly a reflection of the carefree batting he practised.

Finally note Mahela Jayawardene's distribution. He has no peak and no trough. He and Don Bradman are the only batsmen in this list with such consistent batting records.

Part 2: Analysis of high stretch averages and low stretch averages

This analysis is totally different to the first one. The methodology is briefly explained below.

1. The batsmen are selected on the same basis. This time also 299 batsmen are selected.

2. Each innings played by the qualifying batsman is taken as the base and the rest of the career analysed. For each of these innings, the best stretch average is determined. With a minimum of ten innings as a valid stretch, the running averages are computed and the selection is done. Averages above 100.00 and below 10.00 are tabulated.

3. These tables are studied and because of overlapping stretches, appropriate non-overlapping stretches selected and sequenced.

5. Table of high average run scoring stretches

```1.Sangakkara K.C  105 114 10 4 1185 197.50
{100*,156*,8,6, 200*,222*,57,192,92,152}
2.Sobers G.St.A    29  38 10 4 1115 185.83
{365*,125,109*,14, 27,25,142*,4,198,106*}
3.Tillakaratne H.P 95 105 11 7  721 180.25
{136*,10*,105*,87, 7*,204*,96,37,3,19*,17*}
4.Kallis J.H       81  90 10 6  711 177.75
{51,157*,42*,189*, 68,21*,24,89*,5,65*}
5.Bradman D.G      50  59 10 2 1236 154.50
{212,169,51,144*, 18,102*,103,16,187,234}
6.Kallis J.H      118 127 10 3 1065 152.14
{158,44,177,73, 130*,130*,92,150*,40,71}
7.Hammond W.R      88  97 10 4  889 148.17
{87*,29,63*,65, 167,217,5*,0,25,231*}
8.Bradman D.G      18  28 11 2 1327 147.44
{223,152,43,0, 226,112,2,167,299*,0,103*}
9.Vengsarkar D.B  133 142 10 6  584 146.00
{1*,37*,126*,33,61, 102*,38,0,22*,164*}
10.Bradman D.G      63  72 10 3  984 140.57
{56*,12,63,185, 13,132,127*,201,57*,138}
```

Sangakkara's phenomenal run is the best ever and is of recent vintage. Sobers blossomed once he scored his first Test century, which turned to be the world-record breaking one. Tillakaratne had the benefit of quite a few not-outs. But his run was wonderful for a journeyman batsman. Bradman has three distinct stretches. With a career average of 99.96 it is not surprising to see him exceeding 140 three times in his career. There are many overlapping stretches during which Bradman has exceeded averages of 120. Kallis is the only other batsman who has had two separate 140-plus stretch averages. Dilip Vengsarkar is the only Indian batsman in this elite list.

6. The career-best best stretch averages for a few other famous batsmen is given below.

```Lara B.C       164 173 10 1  851  94.56
{68,60,209,10, 80*,29,1,191,1,202}
Tendulkar S.R  105 114 10 3  736 105.14
{124*,18,126*,15, 44*,217,15,61,0,116}
Ponting R.T     10 119 10 2  928 116.00
{169,53*,54,50, 242,0,257,31*,25,47}
Dravid R        65  74 10 3  835 119.29
{28,41*,200*,70*, 162,9,39,25,180,81}
Gavaskar S.M     1  10 10 3  831 118.71
{65,67*,116,64*, 1,117*,124,220,4,53}
Richards I.V.A  27  36 10 0 1093 109.30
{177,23,64,232, 63,4,135,66,38,291}
Javed Miandad   23  32 10 5  654 130.80
{154*,6*,35,100, 62*,81,160*,26,30,0*}
Gilchrist A.C   35  45 11 5  715 119.17
{83*,7,22,30*, 34,204*,138*,24,91,16,66*}
Flower A        82  94 13 4 1243 138.11
{183*,70,55,232*, 79,73,23,51,83,45,8*,142,199*}
```

Lara is the only one who has not exceeded 100. Primarily because he remains not out very few times. Gavaskar's is his debut stretch. Andy Flower has a 13-innings stretch in which he averages 138+. Playing in a weak team, this is a remarkable achievement. Richards has exceeded 100 even though he was dismissed in all 10 of the innings.

7. Table of low average run scoring stretches

```1.Reid J.R          8  17 10 0   36   3.60
{0,3,6,1,9,7,6,0,3,1}
2.Bannerman A.C    27  39 13 1   57   4.75
{8,5,2,15*,4,2,2,0,0,13,5,1,0}
3.Wishart C.B       6  15 10 0   52   5.20
{3,2,25,0,10,0,7,3,0,2}
4.Healy I.A       167 176 10 0   56   5.60
{0,14,5,12,0,6,10,0,3,6}
5.Vettori D.L      13  23 11 1   57   5.70
{0,14*,1,3,16,0,20,0,0,0,3}
6.Kapil Dev N      38  47 10 0   60   6.00
{19,2,7,5,0,0,9,0,4,14}
7.Fletcher K.W.R   19  29 11 1   64   6.40
{4,2,1,28*,1,0,5,2,0,16,5}
8.Knott A.P.E      69  78 10 1   65   7.22
{2,0,0,21,4*,5,0,21,5,7}
9.Atapattu M.S      1  10 10 0   73   7.30
{0,0,0,1,0,0,25,22,0,25}
10.Nadkarni R.G     52  62 11 1   73   7.30
{0,7,14*,9,0,3,15,17,2,0,6}
```

John Reid's stretch is the worst by any batsman in Test history. Ten consecutive single-digit scores is something, a record no recognised batsman has achieved. Ian Healy's poor scoring stretch is towards the end of his career. He has averaged 8.12 in a 17-innings stretch. Atapattu's stretch is on his debut. Fletcher, with an average of 6.40 early in his career, is one of the three recognised Test batsman to have had very low stretches.

I have implemented Daniel Cotton's suggestion of 10 dismissals instead of 10 innings and the results are tabulated below.

```Table of Peaks, based on 10 consecutive dismissals, by % of Batting Average

Batsman          Stretch Ins No Runs StrAvge
St End

Based on running average
Sobers G.St.A      29  42 14  4 1774 177.40
{365*,125,109*,14,27,25,142*,4,198,106*,29,9,44,0}
Flower A           85  99 15  5 1561 156.10
{232*,79,73,23,51,83,45,8*,142,199*,67,14*,28,114*,42}
Bradman D.G        18  29 12  2 1523 152.30
{223,152,43,0,226,112,2,167,299*,0,103*,8}
Kallis J.H         81  96 16  6 1481 148.10
{51,157*,42*,189*,68,21*,24,89*,5,65*,38,99,4,34,3,8}
Sangakkara K.C    109 120 12  2 1433 143.30
{200*,222*,57,192,92,152,1,46,50,21,10,14}

Based on innings played
Tillakaratne H.P   95 113 19  9 1186 118.60
{136*,10*,105*,87,7*,204*,96,37,3,19*,17*,20,
39,20,32*,18,5*,24,27}
Chanderpaul S     176 193 18  8 1044 104.40
{116*,136*,70,104,8,65*,70*,0,23,3,18,86*,118,
11,107*,77*,79*,50}
Kallis J.H         79  95 17  7 1259 125.90
{30*,17,51,157*,42*,189*,68,21*,24,89*,5,
65*,38,99,4,34,3}
Javed Miandad      23  39 17  7 1204 120.40
{154*,6*,35,100,62*,81,160*,26,30,0*,19,16,
129*,19,76,30*,34}
Chappell G.S       59  74 16  6 1031 103.10
{4*,123,109*,13,43,52,182*,6*,4,48*,68,54*,
52,70,121,67}
```
In response to the requests of the readers to do an analysis, not limiting to 10 innings and having a stretch anywhere, not just at 1, 11, 21 etc., I have given below the top 10 entries in this table.

Table of Peaks, with stretches > 10 innings, by % of Batting Average

```Cty Batsman              Stretch Ins No Runs Avge CarAvge  %
St End

1. Pak Mudassar Nazar    42  54 13  4  959 106.56 38.09 279.73
2. Ind Vengsarkar D.B   136 145 10  3  796 113.71 42.13 269.88
3. Slk Tillakaratne H.P  89 100 12  6  665 110.83 42.88 258.49
4. Nzl Greatbatch M.J     1  13 13  4  693  77.00 30.62 251.46
5. Ind Nadkarni R.G      35  45 11  5  378  63.00 25.71 245.05
6. Win Adams J.C         11  21 11  3  781  97.62 41.23 236.76
7. Eng Boycott G         71  82 12  4  890 111.25 47.73 233.08
8. Ind Gavaskar S.M       1  10 10  3  831 118.71 51.12 232.22
9. Aus Taylor M.A       164 173 10  3  701 100.14 43.50 230.23
10. Eng Hick G.A          56  67 12  3  642  71.33 31.32 227.73
```

1. Apologise for mixing up Kallis and Sangakkara sequences. Has been corrected.

2. Very good suggestion on taking 10 consecutive dismissals rather than 10 consecutive innings. Will take it up.

3. A few people have questioned the need for fixed 10-innings stretches (1-10, 11-20, ...) and have suggested variable duration stretches. Let me say that I did all the work in completing the analysis for variable lenth of stretches and my first cut of the article was with 6 tables with these two variations. Then I found that there was not much variation between the two, the article was too long and I was missing an analysis completely excluding the Batting average. Hence I re-did the second part as it stands today. The tables are displayed in the main part of the article.

4. David (Barry) has raised a valid comment on the fact that the number of Peaks outnumber number of Troughs by 2 to 1. My response is set out below.

a. This is not an analysis either side of a a single mean measure (Batting Average), It is based on 10-innings stretches and hence the normal statistical conclusions may not be applicable.

b. Only the Peaks outnumber the Troughs (330 vs 171). However the number of Above-average stretches actually trail the Below-average stretches (1043 to 1334).

c. So the conclusion is that the 50% on either side is probably not equitable. It is possible that a more correct cut-off pair might be 140% and 40%.

5. Every article of mine gets converted into a Lara vs Tendulkar one so much that I will probably do an article analyzing Lara and Tendulkar WITHOUT COMING TO ANY SPECIFIC CONCLUSION. Let readers draw their own conclusions.

6. A valid question has been raised on the methodology in determining the variable stretches. One method is to keep on going until the cumulative average falls below the limit of 150%. In this case the emphasis is on the length of the stretch. The other method is to keep on going until the highest % value is reached. In other words, close the stretch once the % figure drops off. In this case the emphasis is on the % value rather than length.

Both tables were craeted. However what has been presented is the value based one, in other wirds, the highest %. 7. Shishir and Peter have made valid points on the 'point' nature of the stretches. I accept this comment. However it must be remembered that this was only the starting point of the exercise. Please look at the other analytical tables. This problem will disappear since there is no artificial limit of 10 innings in these analysis.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems