January 15, 2010


Bowling Power Factor: measuring ODI performances

Anantha Narayanan

(This piece has been written in collaboration with Anshu Jain: Updated on Sunday, Jan 16/17)

Based on Alex Tierno's excellent suggestion I had worked on Batting Power Factor - a simple measure to determine the most destructive ODI innings through simple, easy-to-create methodologies. The article was well-received because of the simplicity of the idea. My thanks to Alex.

It follows logically that I should create a similar Power Factor for bowling. I had asked for suggestions. The simplest and most effective suggestion, closest to what I myself was thinking, came from Anshu Jain. My thanks to Anshu.

The requirements are set out below.

1. The methodology should be easy to understand and easy to work out. I have been influenced by Sattvir who mentioned that he wanted to calculate the IPF for each innings as he watches TV. There should be no need to go to the net to get the batsman average or bowler strike rate or whetever. Everything should be available from the Scorecard. A calculator might be needed.

2. The first factor to be recognized is the number of wickets captured. This is the most signicant of a bowler's contributions in a match. It should be recognized that in a 10 over spell, capturing more number of wickets is progressively more difficult. Unlike batting where a batsman can play 150 balls and score 200 runs, here the bowler achieves all in a spell limited to 20% of team overs.

3. The batting position of wickets captured is also important. Not necessarily the batting average.

4. Bowling accuracy is important but only in relation to the team numbers. By itself the bowling accuracy figure means very little as explained below.

India: 150/50 overs (Lee 10-2-25-2,Johnson 10-1-40-2,Watson 10-1-35-1)
India: 250/50 overs (Lee 10-0-45-2,Johnson 10-1-40-2,Watson 10-0-55-1)
Johnson has identical analysis in both matches. However his bowling in the first match is below-par and in the second batch is above-par. Lee has been above-par in both matches and Watson is below-par in both matches.

So the Bowling Accuracy index will be determined based on the bowler's numbers as well as the team's numbers.

I considered briefly and discarded the "% of team wickets" measure since good 4 and 3 wicket performances, where the "% of team wickets" figure was 100, moved up drastically in an unjustifiable manner. This is quite unlike the "% of team score" measure which moves in a 10%-20% band.

Methodology used:

The base is the wicket points. The following are the points allotted. There is a progressive increase for each wicket.

1   2   3   4   5   6   7   8
7  15  25  37  50  64  80  100
To determine the wicket quality, batting position is determined rather than batting average. Anyhow the best batsmen normally bat within no.4. Also if Ponting bats at no.10 his wicket is nowhere as important as at no.4. If a team is reduced to nothing for 3 or 4, it is normally quite difficult to recover. The bowler who captures top order wickets is rewarded and the bowler who captures low order wickets is penalized. This is based on the following formula.
Wickets 1 -  4: 2.0 points
Wickets 5 -  6: 1.5 points
Wickets 7 -  8: 0.75 points
Wickets 9 - 11: 0.25 points
The total for all wickets is added and divided by the number of wickets to arrive at the Wicket Quality Index value. The highest value for WQI is 2.0 (the bowler all whose wickets are 1-4) and the lowest value for WQI is 0.25 (the bowler all whose wickets are 9-11).

The Bowling Accuracy Index is determined by dividing the "Other bowlers' RpO" by the Bowler RpO. The highest ratio value for relevant spells is 10.16 (Walsh's 5 for 1 against SLK). In fact in 3882 such spells only 10 values are above 4 and represent completely bizarre situations, as perfectly illustrated by the Walsh spell. Hence these ratios are first capped at 4.0 and then the square root taken to arrive at the BAI. The index maximum is thus 2.0. This halving is to enure that for a bowler to get a par factor of 1.0, he has to perform at a level twice that of the team. Also to ensure parity with the WQI values. The highest value for BAI is 2.0 and the lowest value for BAI is 0.23.

Now the BPF is determined by multiplying the WP (Wicket Points) by WQI and BAI.

Let us look at the table and the top-20 performances. Only bowlers who captured 3 or more wickets are considered.

No Bowler         MtNo For  Vs  Analysis  WktPts  WQI  BAI   BPF

1 Gilmour G.J 0031 Aus Eng 12.0-6-14-6 64.0 1.71 1.67 182.39 2 Bichel A.J 1976 Aus Eng 10.0-0-20-7 80.0 1.43 1.52 173.32 3 McGrath G.D 1970 Aus Nam 7.0-4-15-7 80.0 1.43 1.41 161.62 4 Johnston D.T 2843 Ire Can 10.0-4-14-5 50.0 1.80 1.79 161.36 5 Mendis B.A.W 2735 Slk Ind 8.0-1-13-6 64.0 1.42 1.77 160.30 6 Muralitharan M 1826 Slk Nzl 10.0-3- 9-5 50.0 1.55 2.00 155.00 7 Imran Khan 0325 Pak Ind 10.0-2-14-6 64.0 1.54 1.56 153.71 8 Bond S.E 1986 Nzl Aus 10.0-2-23-6 64.0 1.58 1.42 143.70 9 Vaas WPUJC 1776 Slk Zim 8.0-3-19-8 100.0 1.41 1.02 143.65 10 Joshi S.B 1504 Ind Saf 10.0-6- 6-5 50.0 1.40 2.00 140.00 11 Edwards F.H 2069 Win Zim 7.0-1-22-6 64.0 1.71 1.28 139.55 12 Simmons P.V 0777 Win Pak 10.0-8- 3-4 37.0 1.88 2.00 138.75 13 Umar Gul 2043 Pak Bng 9.0-2-17-5 50.0 1.65 1.67 137.63 14 Aaqib Javed 0685 Pak Ind 10.0-1-37-7 80.0 1.57 1.07 134.73 15 Vaas WPUJC 1950 Slk Bng 9.1-2-25-6 64.0 1.62 1.28 133.59 16 Wasim Akram 0311 Pak Aus 8.0-1-21-5 50.0 1.90 1.41 133.56 17 Styris S.B 1843 Nzl Win 7.0-0-25-6 64.0 1.50 1.38 132.54 18 Strang B.C 1242 Zim Bng 10.0-2-20-6 64.0 1.62 1.26 131.55 19 Streak H.H 2034 Zim Eng 9.0-3-21-4 37.0 1.88 1.89 131.45 20 Waqar Younis 1724 Pak Eng 10.0-0-36-7 80.0 1.68 0.97 130.43

Gilmour's innspell in the World Cup semi-final, rated by many as the best ever bowling performance of all time, comes in top place. 4 top wickets plus 2 of the next 3, complemented by oustanding bowling accuracy figure, contribute to this top position.

The seven wicket spells of Bichel and McGrath are in the next two positions. Bichel captured wickets 2-8. McGrath's spell included 6 of the top-5. Also note the bowling accuracy of both these spells.

D T Johnston took 5 of the top-6 wickets. Every one knows what Mendis did against India in the Asia Cup Final. He took 3 of the top-6 wickets.

Muralitharan's 5-wkt haul, all in the top-6, coupled with a bowling accuracy which is better than his team's figures by more than 4 times has propelled his performance to the top-5. Imran Khan's 6-14 demolition of India is next, followed by Bond's 6-23 against Australia.

Vaas's best ever ODI bowling effort of 8 for 19 is next. He would have captured all 10 wickets but for the introduction of Muralitharan. Joshi's 5 wickets were in the top-8 and he had an RpO figure of 0.6, way below his team's. This takes him to tenth place.

Note the high placement of Simmons' 4 for 3 against Pakistan. Aaqib Javed's 7 for 30 against India is in 14th position since the bowling accuracy just about matched the rest of the bowlers. Waqar Younis' 7 for 36 finds its way into the top-20.

To view/download the complete 3-wkt bowler list, limited to BPF of 50.0 points and above, please click/right-click here and save the file.

I have created an alternative version of the table based on the suggestion of Unnikrishnan in that I have used the Batting quality total points as it is, without dividing by the number of wickets. This has then been multiplued by the BAI value. The points for the 4 batting groups are 10(1-4), 7(5-6), 3(7-8) and 1(9-11) to get a reasonable final number. To view/download the revised 3-wkt bowler list, limited to BPF of 30.0 points (not comparable to the main table) and above, please click/right-click here and save the file.

I am happy that Gilmour stays on top. A few 7-wkt hauls have been pushed down and great 4-5 wkt spells have moved up because the differential values of the base points has been taken out of the equation.

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

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Posted by Abhi on (January 30, 2010, 5:51 GMT)

Xolile etc. I’m a bit surprised that there seem to be no takers for the “entanglement” theory. Perhaps I was garbled as usual. To explain further then. There seem to be 2 main camps involved: 1)One camp maintains that avg.s inflated by NO.s do not depict the true picture. This is when we use avg.s as a measure of batting quality. So, it is difficult to argue that a Hussey is a better batsman than Tendulkar,Lara,Ponting,Viv. So,this camp desires a modification to the avg. to reflect reality. 2)The other camp insists on treating NO.s as NO.s. The reasoning being that otherwise the batsman suffers both ways. i.e his avg reduces if some modifications are applied and in addition to that his run aggregate also suffers since he has been unable to complete his inn.s

That is why I had mentioned “entangling” both Avg. and run aggregate since they are essentially inseparable.

Posted by Raghav on (January 24, 2010, 11:10 GMT)

I am in full agreement with Xollile. A not out is a not out, nothing less.

In fact, if any adjusments need to be made its in favour of the lower order batsman (need not necessarily be one with more not outs). In virtually every other match, lower order batsmen have to com in after 40-45 overs and take high risks from ball one. Most of the times there is no such pressure on openers.

Secondly, many openers have benefited from easy runs. When playing against weaker teams (Zim, Ban, Nam, Ire UAE, Ken etc...). They get first shot at the weaker bowling attacks and seldom will a Dhoni or Hussey get to bat against them at no. 7. weighing runs with bowling averages does not really compensate fully for lack of opportunity recd. by Dhoni/Hussey.

Posted by Abhi on (January 24, 2010, 6:53 GMT)

On further thought, there is a way out of the impasse, which should perhaps be acceptable to all. Negating all previous comments – it would involve going xolile’s way- with one rider. i.e to treat avg. and total runs scored as “entangled” entitities. Not avg. as an isolated entity.

The"problem" seems to be when we use avg. as a predominant indicator of a batsman’s quality. So if x has a higher avg. than y, x is generally seen to be the better batsman. The “problem” of course is that when a batsman is “Not out” he potentially could have scored more runs. So, his overall run aggregate gets impacted with NOs. So, we simply give equal “weightage” to overall runs scored and avgs. (whatever amount –say 15% EACH). This would effectively “entangle” both entities on an equal footing- and everybody’s happy.

Posted by Ananth on (January 23, 2010, 18:03 GMT)

Let me summarize. 1. Xolile has suggested that all the not outs should be considered as not outs. 2. I have suggested that half the not outs can be considered as outs. I have also suggested an alternative method of considering only not outs below batting average as notouts. 3. Jeff has suggested excluding ducks from average calculations. 4. Abhijit supports my second suggestion. In addition he also suggests ignoring first innings not outs. 5. Finally Unni has suggested that if a batsman remains not out and his team lost, do not give him credit. I am not sure whether this applies to first innings also. Then do we consider poor Coventry's 194 as out. Look at the varied opinions from a group of us, all of whom I think are sound thinkers. Everything is arbitrary or nothing is arbitrary. I am away for 3 days from Monday-Thursday morning and may not be able to look at mails. Ananth

Posted by unni on (January 23, 2010, 14:59 GMT)

Why are we bothered about these numbers? because higher the average for the batsman, we can know that he has contributed to the win. (nothing else. Any other parameters like quality of his shots, aesthetics etc are not captured by stats). If a batsman was not-out and if the team lost, then don't give credit for being not-out. So, consider such not-outs as out. This will ensure that efforts like Hussey's 36* would get the necessary weight-age.

Posted by Abhi on (January 23, 2010, 2:48 GMT)

Xollile: Regret yet another post. But what if we look at it entirely from your perspective? i.e simply extend your logic to its conclusion. 1) Of all the top opening batsmen, the greatest of them all (SRT) avg 48. 2) Hussy avg.55. 3) As per your logic it is easier to bat when opening. Assume that is true. 4) Then it would follow that if Hussey had opened the inn. all along he would avg. higher than he now does. Say 60. Now. Stop right there. Get out of your mathematical straightjacket and use your cricketing brain instead. The question then is – Would Hussey avg. 60 over the hundred or so inn. he has played if he had opened instead? So, you see- your cricketing brain will provide the answer. I think Ananth is simply using common sense when he claims that Hussey’s avg has been inflated by a high no. of NOs. (referring only to ODIs of course). You will find that you can find any number of stats to “prove” just about any claim that you chose to, of course.

Alex Haven’t really studied your comment fully. Will do so later and get back. Just a thought though- getting off a duck and the early part of an innings are one of the basic skills in batting. So, we cannot just ignore them. [[ Look at it from another side. What would have been Tendulkar's average if he had batted two thirds of his career as a 5-6 batsman finishing the innings. It is obvious that his technique would have let him that end-of-the-innings role perfectly. I would not say that of Richards or Hayden or Gilchrist. Ananth: ]]

Posted by Abhi on (January 22, 2010, 16:54 GMT)

Ananth, I posted my comment without seeing your latest reply to xolile! You have effectively said what I wanted to in a much more concise manner, without the round about verbiage I am prone to!

Xolile: You know, when financial analysts finally table an analysis for a company a common practice requires them to state their "bias" towards the company. i.e. whether to start with they liked it, they thought it was a turkey etc. This is because the initial bias will inevitably percolate down to the final "intrinsic value" obtained. So, the investors using the analysis can make due adjustments for this bias. I have stated (often enough!) that I am heavily biased towards Tendulkar.What I wonder is yours? [[ Abhi I am reasonably confident that Xolile's bias is not towards a single batsman but to the entire clan of middle to late order batsmen. I love them, the finishers. After all the adrenaline-charged batting at the top, to see a Bevan or Hussey or Dhoni steer an innings during the last 15 overs with a required rate of 6+, allow it to go tantalizingly close to 7, then pull back, all the while taking singles and then finally moving rapidly, is a wonderful sight for the connoiseur. I am anxiously waiting for Angelo Mathews to take up that role for Sri Lanka. My suggestion is, wait for me to find time to do a comprehensive analysis by Batting position and then resume the dialogue. Ananth: ]]

Posted by Jeff on (January 22, 2010, 16:43 GMT)

Just checked out Husseys figures and they make interesting reading

When Hussey bats at number 4, he averages 54.75 and 14.3% of his inns end not out.

When he bats at number 5, he averages 52.78 and 24% of his inns end not out.

When he bats at either 6 or 7, he averages 54.24 with 43.3% of his inns ending not out

So, the number of innings ending not out increases dramatically as he moves down the order, but his average remains virtually unchanged.

I promise that I won't labour this point anymore !! ;-)

Posted by Jeff on (January 22, 2010, 16:35 GMT)

I've found some of my analysis.

I looked at only the top 20 ODI run scorers of all-time (as of Nov 09) and the analysis showed the following:

When they opened, these players had an average of 40 with 5% of inns ending NO

When the same players batted at 3, they averaged 44 with 11% NO

When at 4, they averaged 40 with 14% NO

When at 5, they averaged 37 with 18% NO

When at 6, they averaged 29 with 22% NO

They had very few inns at number 7 or below.

Remember that these are the same players in all occasions & the top 20 run scorers of all time, so this discounts the "Afridi" factor that Xolile references.

Hopefully it shows that average is not positively correlated to the number of Not Outs - the correlation is between average and batting position. [[ Jeff I think the final point is only to what extent a finisher who remains not out over, say 25%, gains from remaining not out. Let me do my batting position analysis, when I have no idea, I have got so much on my plate, and that would be revealing. Ananth: ]]

Posted by Abhi on (January 22, 2010, 16:32 GMT)

Xolile, I think, as before, you’ve taken a rather narrow band of info/stats and reached rather broad conclusions from them. For eg. in your recent “reasoning” here are just a few flaws: 1) “career stage” has been paid lip service to but effectively ignored. In SRTs case he only opened after his 70th match or so… when he was around 20yrs old. For the first 70 matches SRTs stats are 1758 @ 30.1. This from age 16 to 20. 2) There after he has played 46 inn avg 37, with 9 NO.SR 84 when batting between 3-7. In this period he played a total of around 363 inn. So, some 13% of total inn when batting 3-7. One could say that Tendulkar having opened some 320 times in this period got a bit “used” to it. The batsmen with the higher avg.s who come in late (the Husseys, Dhonis etc) are essentially accomplished “finishers”…etc. - a “different” role, not necessarily a tougher one. 3) Sehwag in Tests (Tests, not ODIs) when batting in the “lower order” avg.38 to his career 52. So, Would you come to the conclusion that opening in tests is easier for All batsmen? Opening may suit the temperament of certain players (which is exactly why they then retain the spot for long periods- not because it is “easier”) 4) Over very long careers like SRTs “peer ratio avgs” would make much more sense. Then we can compare over periods of say 5/10 yrs. Absolute numbers are of limited use. 5)Since the inception of ODIs(1971) the avgs of the Top 10 batsmen( In terms of runs),when opening(From SRT to Astle)-: 48.4,34.7,36.5,41.6,41.4,39.9,42.4,41.8,35.9,34.9. For “lower order” 3-7: (Ponting to Waugh) :42.9,39.3,45.9,39.6,42.6,37.2,35.3,32.2,39.0,32.9. Hardly any glaring difference, If you ask me. Infact if you take out SRT the “lower order” batsmen may have the better stats. The one glaring standout above is SRT at 48.4. Apparently he is not just the Greatest modern day Test batsman and greatest ODI batsman of all time; he is also the greatest opening ODI batsman of all time. And his role (till recently) has been has been that of a classical modern day batsman in ODIs- that of a battering ram and taking it to the opposition- not “finishing”. So: If you could find 1) some batsmen who have more or less equitable spread of inn where they “opened” and played in the “lower order” -For eg. Gambhir when opening (1-2) in 58 inn avg 36.2, batting from 3-7 in 34 inn he avg.39.8. So the inn ration between “opening”/”lower order” = 58:35 i.e. a more reasonable basis for comparison. 2) The above who have played over a decent period of time/matches – A period over an injury free period- then we may have a less flimsy base for comparing. If a “lower order” batsman opens just say 10% of the time or so and does better than his “overall” avg or vice versa it is onerous to arrive at any sweeping conclusions from the same.

If you could get a good sample size of the above, Then we would have less flimsy grounds for any comparisons or conclusions.

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Anantha Narayanan
Anantha spent the first half of his four-decade working career with corporates like IBM, Shaw Wallace, NCR, Sime Darby and the Spinneys group in IT-related positions. In the second half, he has worked on cricket simulation, ratings, data mining, analysis and writing, amongst other things. He was the creator of the Wisden 100 lists, released in 2001. He has written for ESPNcricinfo and CastrolCricket, and worked extensively with Maruti Motors, Idea Cellular and Castrol on their performance ratings-related systems. He is an armchair connoisseur of most sports. His other passion is tennis, and he thinks Roger Federer is the greatest sportsman to have walked on earth.

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