April 12, 2014

Team performance analysis in T20 internationals

Who defends well and who chases a target better?

Sri Lanka - perched at the top of the performance table - are the most successful team in T20 internationals © ICC

I do not like the IPL. The reasons are mostly non-cricketing in nature. Regular readers will know the reasons since these have been expounded often in these columns. This will be the only negative reference in this article. Let us move on.

However, the T20 internationals are something else. Money does not drive teams and players there. What drives them is their national pride. No scandal of any sort has been associated with T20Is. Most matches are great contests between teams. Of late, the bowlers, especially the spinners, have had their days in the sun and under the moon. So the bottom line is that I have a lot of time for T20Is. The icing on the cake is that the five World T20s have been won by different teams. None of the teams have dominated the game for long. The timing is just about perfect. A World T20 has just about finished and around 400 matches have been played.

Another aspect of T20Is is also the precise nature of the game. As someone who has analysed almost every aspect of all the three formats, I find the T20I format is the one that lends itself to clarity of thinking and almost perfect analysis. I have not been wholly fair to this format. During the past 12 months at the Cordon, I haven't done a single article on T20Is. It is time to redress the balance now. And the fact is that as I went deeper into the analysis, I was amazed at the way the colour of my analysis kept changing. Even purists will find the analysis very interesting and meaningful.

First let me outline some of the facts that are special to the game. In all the examples I have taken that the first batting team scored 160 runs.

1. The two types of wins: the win by the first batting team by runs and the win by the second batting team, normally by wickets, are like chalk and cheese.

2. The First batting team's win is easier to analyse. The margin of victory, by runs, is clearly defined. It does not matter how many wickets are lost. It is what is achieved in 20 overs that matters. If the second batting team scores 120 runs, the win is by 40 runs and the win margin is 25%. If the second batting team scores 150 runs, the win margin is 6.67%. If the second batting team scores 159 runs, the win margin is 0.67%. A 161/1 win against 160/9 will have a margin of 0.67%. A 161/9 win against 120/1 win will have a margin of 25%. Probably obvious to all.

3. D/L interruptions could still lead to wins by runs. If the D/L target is 120 and the second team's innings was terminated at 102, the win margin is 15%. If the D/L target is 120 and the second team's innings was terminated at 132, the win margin is 10%. No problems there also.

4. Now we come to the much more complex situations in which teams win by chasing targets. The problem is that there are two independent resources available: ten wickets and 120 balls. I will show later that one of these resources is a far more limiting and difficult resource to handle than the other.

5. There is a fundamental weakness in the way these wins are reported. When we read that a team won by eight wickets, we think the win was quite comfortable. When we read that a team won by two wickets, we think the win was tough. While this could be true, it need not necessarily be the case. It is my considered conclusion that T20 wins by teams batting second should be reported as "Australia won by six wickets and three balls", or "England won by two wickets and 14 balls" and so on. Why? Please consider the following fairly loaded statement. Let us assume that the winning stroke was a single.

6. I would very confidently say that "161 for 2 in 20 overs" is a tighter win than "161 for 4 in 19.5 overs" which, in turn, is a tighter win than "161 for 7 in 19.4 overs". It is simple. If that single had not been scored off the last ball, the first match would have been a tie (and possibly a Super Over). In the second match there was another ball and in the third match there were two more balls to achieve that single. Now tell me, which win was more nerve-wracking. But the report says "win by eight wickets", "win by six wickets" and "win by two wickets".

7. The ball resource is the far more limiting one than the wicket resource. I am not saying that wickets are not important but it is more likely that the ball resource would prove to be an exhausted resource than the wickets. Proof?

8. The basic fact is that there are only 120 balls. The average balls per wicket value for 400 matches is 17.6. Thus only 6.8 wickets could be captured, on an average, in a 120-ball innings. Considering only second innings in a match, since the first innings always goes on to 120 balls (and over 90% of the innings last this long), there have been 74 all-out situations and 194 120-ball situations. The all-out number is well below half of the 120-ball number.

9. I also believe, after viewing a number of T20Is, that there is no clear home advantage. The format is such that such advantages are negated. Mitchell Johnson is king in Australia but then he is allowed to bowl only four overs. The recent breed of players - the T20-adapters-cum-specialists - have also gone a long way in negating these benefits. Finally the fact that an extraordinarily high 192 matches, out of 400, have been played on neutral grounds should settle the home/away issue once and for all.

The reason why I have gone into such detail is because the analysis uses all these facts and conclusions.

Since we have not yet captured the ball-by-ball data, I can go only by my notes, inferences, common sense and knowledge of the game. It is my firm belief that the T20 game is split into three parts: the first-six Powerplay overs, the nine middle consolidating overs and the finishing five overs. My rough calculations lead me to work on the basis that during the three phases, equal resources are expended. That means that 66.67% of resources are available at the end of Powerplays and 33.33% of resources are available at the end of the 15th over. If you take a typical T20 innings, this pattern is repeated. The team would score about 50 runs in the first 6 overs, 50 in the middle phase and round off with 50 in the last one. Of course Netherlands scored 80 odd in the PP and West Indies scored 80 odd in the last five overs. But these are outliers.

This information is essential since I have to determine the resource available at any time in the innings, in the case of second team wins. The other important conclusion is that there is no great change in the scoring pattern in the first two phases. The first over is likely to yield as many runs as the third over. Similarly one does not expect a spurt between the 10th and 13th overs. So these over resources are linearly decayed. But clearly each of the overs after 15 is likely to produce more runs than the previous one. So the resource during this period is geometrically decayed. This has been done using a decay value of 0.986578 from balls 91-120. This sets the resource available at the end of 120th ball at 0.0 and 90th ball at 33.33%.

The graph below is self-explanatory. It can be seen that the decay in the first and second segments is straight and the third one is geometric.

Now, some important facts on the T20I game as it stands now.

1. Out of the 400 matches, two matches were washed out after the toss without a ball being bowled. Of these, ten ended in no-result situation, including four early matches where a Super Over was not used to decide the winner.

2. Out of the other 388 matches, 200 matches were won by the team batting first and 188 matches were won by teams batting second. Thus there is a slight edge (3%) in wins to the teams batting first.

3. For the second team wins, the wicket resource available is calculated using the values 82.5%, 61.1%, 54.6%, 42.0%, 31.2%, 22.6%, 15.6%, 9.8%, 4.7% and 0.0% as the resources available at the end of the fall of the first to tenth wickets. These are derived from the matches.

4. Out of the matches decided on D/L basis, eight were won by teams batting first, all by runs. The other eight matches were won by the second batting teams. Three of these wins were by the normal method of winning by wickets. However the other five matches present a peculiar occurrence. The rain cut short the matches and the D/L were decided afterwards. All were wins by runs, by the teams batting second.

5. The point I had already made regarding the limiting factor of ball-resource as against wicket-resource can be best demonstrated using one stunning fact. Out of the 188 matches that were won by teams batting second, there is only one match in which the wicket-resources available at the end of the match was lower than the ball-resources. This is the match between UAE and Zimbabwe in the recently concluded World T20. The scores were UAE: 116 for 9 in 20. Zimbabwe: 118 for 5 in 13.4. The wicket-resource available was 31.2% and the ball-resource available was 38.3%. In the other 187 matches, the wicket-resource available was higher than the ball-resource. I do not think there has been a more emphatic statistic to decide a point of view.

6. Eight teams, batting first, won by one run. The highest victory margin was Sri Lanka's 172-run win over Kenya in the 2007 World T20.

7. Teams that batted second won on the last ball of the match on 19 occasions. Since no ball was left in the match to determine a win resource available value for these teams, the margin of victory has been taken as one ball. The wicket resource remaining does not mean anything, as we have already seen.

T. The biggest unutilised ball resource was during Sri Lanka's recent demolition of Netherlands in the World T20 - they still had 90 balls left: a whopping 72.2% of resources were still available.

Resource determination

The methodology for the win margin percentage is summarized below.

- First batting team wins: The formula 100.0*run margin/target is used. This applies to the D/L matches also.

- All wins through a tied match and Super Over are treated as x-run wins where x is the single over difference in runs. This information is available for two matches. For the other two matches the run margin is taken as two.

- Second batting team wins: The values of the wicket resource and the ball resource available at the end of the match are determined and the lower of these two values is taken as the win margin. Enough explanation has already been given on this. Whichever is the limiting resource is used.

- For D/L wins by the second batting team by runs, the formula 100.0*run-margin/second-innings-score is used.

I have given below the win margin percentage for the last-three matches of the World T20, matches which are still fresh in our memory.

- SF: SL won by 27 runs (D/L). SL - 25.2% (27/107)
- SF: Ind won by 6 wkts and 5 balls. Ind - 6.5% (100.0*(1.0-0.986578^5))
- F : SL won by 6 wkts and 13 balls. SL - 16.1% (100.0*(1.0-0.986578^13))

Let me put these numbers in another way. What could Sri Lanka have chased? This is one occasion when it is necessary to consider the number of wicketa in hand. They had enough. My projection for them is 160 (134/(1.00-.161). So it is clear that Sri Lanka could easily have chased a target up to 155, it would have been a toss-up for targets between 155 and 165 and anything above 165 would have made India favourites. This is one nice fall out of this analysis.

This is possibly the longest preamble I have ever done. But I am certain this will not have put any reader to sleep. It took me three days just to write this. So do not expect to assimilate this in three minutes. Now let us go on to the tables.

1. Team Performance summary (Min 30 matches)
Team Matches Wins N/R Losses Perf % Avge Margin
Sri Lanka664212368.2%19.18%
South Africa704212760.7%15.52%
West Indies633033052.4%19.04%
New Zealand753543649.3%16.41%
Zimbabwe31 612421.0%21.32%

Sri Lanka lead the Performance table, based on the tried and trusted 2-1-0 points allocation, with an additional tweak. The World T20 winners get an additional three points and the runners-up get one point. Sri Lanka have a very good 68.2% performance index value, above the outstanding two-thirds achievement mark. Pakistan are next, some distance behind. India follow closely behind in third position. These three teams, and South Africa, have a performance index exceeding 60%. Ireland are a welcome top-five entry. Despite their single World T20 win, England have been ordinary.

The last column is the average of the margin achieved in the matches won. This an indicator of the comfort with which wins were achieved. Australia are in the lead by a huge margin. Their average margin is a huge 24.9%. This indicates that when they win, they win well. If we ignore Zimbabwe, with their high average, albeit in six matches, Ireland are right at the top, with 19.1%. Then come West Indies and Sri Lanka. India are in the last position, with 14.5%. This means that they had more narrow wins than other teams.

2. Team Results summary - First Bat & Second Bat (Min 30 matches)
Team Matches Wins FB Wins FBW % SB Wins SBW %
New Zealand75351748.6%1851.4%
South Africa70422559.5%1740.5%
Sri Lanka66422559.5%1740.5%
West Indies63301963.3%1136.7%
Bangladesh4011 436.4% 763.6%
Ireland3620 735.0%1365.0%
Zimbabwe31 6 350.0% 350.0%

This table splits the wins into first batting and second batting classifications. The table is ordered on the number of matches. Pakistan are a very strong defending team with 62% of their wins having been achieved batting first. West Indies have a still higher first batting win percentage. South Africa and Sri Lanka also have first batting wins of around 60%. These are the four teams which have excellent bowling combinations and this is borne out by these numbers.

Bangladesh and Ireland have had a lot more chasing wins. The other teams are around the middle. India have a 10% edge in chasing wins.

3. First Batting Results analysis (Min 10 wins)
Team FB Wins Tot Mrgn Runs Avge Mrgn Runs All-10-wkts LT-10-wkts Avge Margin %
Australia18 819 45.510 824.19%
England15 582 38.8 51021.69%
West Indies19 668 35.2 81021.32%
Pakistan311094 35.3121820.49%
Sri Lanka25 834 33.4 91620.34%
India14 388 27.7 6 816.60%
New Zealand17 477 28.1 41215.36%
South Africa25 525 21.0 42113.34%

When Australia won, they win very well. Their average margin is 24.2%, Also look at their average run-margin: a whopping 45. England have similar numbers. And West Indies too. Pakistan have had a lot of first-batting wins and have average run-margin in excess of 35 and win margin exceeding 20%. South Africa is at the bottom of the table with 21 and 12.9%.

Australia dismissed teams on ten occasions and contained them eight times. England could dismiss teams only five times. West Indies are approximately even in this. Pakistan have contained more than dismissed teams. The same applies for the other teams. Come to think of it, only Australia have had more wins by dismissing the opposition batsmen than containing them.

4. Second Batting Results analysis (Min 10 wins)
Team SB Wins TotWkts AvgeWkts AvgeWktsRes% TotBalls AvgeBalls Avge Margin %
Ireland13 745.744.1%24018.519.92%
South Africa171136.653.6%29817.518.72%
Sri Lanka171015.945.3%25114.817.47%
New Zealand181015.643.8%27215.117.40%
West Indies11 696.346.4%13111.915.10%
Netherlands11 575.236.5%13412.213.56%

Australia are again the leaders by a country mile, with an average margin of 25.7%. Their average win has been by 6.7 wickets and by 24 balls. Very impressive figures, indeed! India and South Africa have average wins by 6.6 wickets. Ireland are right at the top. If anyone says they did not face top teams, let us agree that they faced teams of matching strength, as all Test-playing teams did. Pakistan have had low average margin percentage. Interesting fact is the average win by only 11 balls for India and Pakistan.

T20 World Cup 2014

Two teams entered the World T20 with huge albatrosses around their necks. One succeeded in sending off the bird and the other did not.

South Africa had the big white bird emblazoned "semi-finalists" around their collective necks. At the end of the tournament they still had the bird firmly entrenched. Another semi-final and another different result await them. The Sri Lankan bird had "eternal bridesmaid" in big blue letters on it. In 200 minutes of faultless cricket they managed to send the bird off flying.

A much-loved team, at home and away, two great gentlemen cricketers playing their last game in this format, Sri Lanka's success was very well received and appreciated. As already mentioned, they were the fifth team to win the title, in five different World T20s. The match was won in the first four and last four overs of the Indian innings: 34 runs, two wickets and one four in eight overs bowled by Nuwan Kulasekara, Angelo Mathews, Sachithra Senanayake and Lasith Malinga tells the story.

It is sad that Yuvraj Singh is being blamed by all and sundry. He might have played poorly, but the others were not much better. How can one batsman get the blame when the well-set Virat Kohli and the master finisher MS Dhoni could not do anything? Give credit to the bowlers and stop at that. In the last 27 balls; the following is the story.

Kohli: 10 balls - 8 runs
Yuvraj: 10 balls - 5 runs
Dhoni: 7 balls - 4 runs

I hope that Australia or South Africa or New Zealand win the next World T20 to round-off a perfect half-dozen. I will also extend my coverage of a format that is an analyst's delight.

To download/view the complete list of the 398 T20-I matches, please CLICK HERE. My take is that many of the questions can be answered if you download this file and view the contents.

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

Comments have now been closed for this article

  • MilPand on April 20, 2014, 9:38 GMT

    India played 42 overs instead of 50. So 327 is scaled down using match best fit curves to 296 which means India had to chase 297 for victory. My calculations are off by 1 run which means either some of the constants I used are different from ICC version or my implementation is wrong.

    But the match stopped after 41.3 overs. Par score at that stage is 293 which means winning score is 294. India scored only 277 runs at that stage (more than NZ's 271) but lost because "NZ would have gone harder if they knew from the start they would only have 42".

    I get a 16 run loss (293-277) but official version is 'New Zealand won by 15 runs (D/L method)'.

  • MilPand on April 20, 2014, 9:19 GMT

    The D/L exponential equation is : Z(u,w) = Z0(w) [ 1-exp{-b(w)u } ]

    where Z is the score in u overs where w wickets have been taken. Par value for Z is 245 for a 50 over match.

    We begin by calculating Z for lost overs.

    Par Z for 16.4 overs & 2 wkts = 119. Par Z for 08.4 overs & 2 wkts = 72.97

    Effective resources lost 46.03 which means resources used is 198.97 out of 245.

    271 actually scored in 42 overs. Nearly 199 resources used out of 245. Using both we determine 50 over equivalent as 327. Note that D/L equations do not require NZ score after 33.2 overs just the wickets lost at that stage because the model uses balls remaining and wickets remaining. Actual final score and G50 value of 245 are used to find the best fit for that match.

    Revised Z with match values for 16.4 overs & 2 wkts = 137.36 Revised Z with match values for 08.4 overs & 2 wkts = 80.5

    Res lost = 56.86 or Res used = 327-56.86 = 270.98

    The tiny difference with 271 will also be used to determine India's target.

  • MilPand on April 20, 2014, 9:18 GMT

    SLSup: Glad to note that you find DL the best fit for most situations instead of Notworth. You dislike it and in my opinion it is a beautiful method. Whatever I dislike about the ODI version is trivial as compared to the parts I like. I have not used any T20 example because I don't know of any model that accounts for the scoring pattern of this format.

    Regarding your point about scoring more than the opposing team let us review ODI 3458 between NZ and Ind. After 33.2 overs, NZ lost 2 wkts. NZ batted for 8.4 overs out of remaining 16.4 as the match was reduced to 42 overs. NZ scored 271 eventually. Extract from match commentary:

    Michael: "So NZ and India get the same number of overs? No D/L Formula for this? Surely NZ would have gone harder if they knew from the start they would only have 42?" No Michael, New Zealand's total at the end of 42 overs will be scaled up by the D/L method.

    Will provide some details not of significant interest but attimes such additional information helps.

  • SLSup on April 18, 2014, 14:56 GMT

    Response to MilPand & Anantha: It is not unreasonable to say DL is "deemed the best fit for most situation" compared to others and that it is "not possible to tweak" a method in situations that are more questionable/objectionable than others. Fair enough. I like Anantha's thought on the two of you working on something together, albeit as a "theoretical" exercise. : ) Your readers are REAL and when a method becomes LAW it is because the game's governing body DEEMED FIT to go with one over the other. It doesn't have to mean they settled on the best. WE KNOW WHAT THE PROBLEMS ARE WITH DL. And ALL THINGS EXIST AS THOUGHTS FIRST. Everything around you was once a thought. THOUGHTS, even if are only "theoretical" is relevant and useful. ICC need not validate a system to establish it's practical worth. Your time spent on developing a new method will be time well spent THAN the time spent doing other things when you know there HAS to be a better way!
    When we can find time to devote some extended time.

  • SLSup on April 18, 2014, 3:22 GMT

    MilPand: Unlike Natwar who thought this public forum his personal inbox, I thank you for your time and appreciate your opinion - even though it is contrarian to my views! Aha! G50 is a generic concept that is admittedly flawed per D & L themselves. But it is ESSENTIAL to DL Method. There is no arguing the method is consistent in its application but (as Anantha noted) a method that his brillance wholeheartedly diagrees with in SOME aspects is flawed at some level. Your intelligence cannot miss that! DL moves away from the primary objective of scoring more than the opposing team to setting targets that ARE speculative and objectionable. Its objectionable BECAUSE it is arbitrary. CONSISTENT in application, Yes, yet through means that were/are contentious and arbitrary. To your point that DL Method is excellent - any thing can be shown to excel based on point-of-reference. Hence, your comparison between methods. I dislike DL. A wicket is a greater interruption at times than rain.
    My apologies. However the apologies must come from Cricinfo. Despite my telling them many times, they keep on publishing the comments on my articles and if I am lucky, they would revoke the publication so that I could re-publish. Else I would not even know.
    My opinion of D/L is in between yours and Milind's. There have times I have agreed with it whole-heartedly. There have been times when I felt it was completely wrong. However I have more problems in T20s rather than ODIs because the wickets are nowhere as important in T20s as in ODIs. Instead of just tweaking the ODI model, they should have got a new one for T20s, from scratch. I am sure that, if Milind and I put our mind on it, we could develop such a system from scratch. The problem is it would end up as a perfect theoretical exercise.

  • MilPand on April 17, 2014, 12:31 GMT

    In Feb 2012, I commented about D/L & VJD here - http://www.espncricinfo.com/blogs/content/story/620850.html . Back then I was not sure about the variables used in Professional edition but these are in public domain now. Online documentation has not been updated though. Read http://en.wikipedia.org/wiki/Duckworth%E2%80%93Lewis_method to understand that there are 2 versions of D/L, standard and professional. It states 'in the Professional Edition Team 2's target score is simply increased in proportion to the increase in total resources when R2>R1, and there is no G50'. In fact G50 is very much a part of the professional edition.

    Without understanding the nuances, it is easy to question the base value of 245. It should be noted that it goes along with several other constants and has been deemed the best fit for most situations by two very wise and honourable gentlemen. So we can't tweak it slightly to fix it only for the few occasions where we disagree with the end results.

  • MilPand on April 17, 2014, 12:29 GMT

    If India had scored 119/0, this 50 over value would become 286 because 119 is higher than par score of 92. Worst case scenario of 119/9 would translate to 125 because 119 is much lower than the par score of 234.

    Both systems ignore all that happened prior to 119 in 29. Both models attempt to derive an equivalent score based on actual overs. Neither system aims to speculate what would happen if the match continued. Both are applying the same set of equations fairly to summarise the match situation. D/L uses all three known values of runs scored, balls played and wickets lost which also means that it is not that simple. Simple it may not be, excellent it is.

  • MilPand on April 17, 2014, 12:25 GMT

    D/L does not assume to "know" variables it cannot possibly account for. In fact it is very similar to the system that uses 200 in 50 @4 an over.

    India scored 119/3 after 29 in ODI # 3387. We will use this example to find out a 50 over equivalent score. (SL had a target of 178 from 26 overs but that is irrelevant in this example). This run-rate method, which does not differentiate between 119/0 and 119/9, uses a linear equation y = mx where m is the run rate of 4.10 and x is the number of overs which is 50. Thus we get 205 as the equivalent 50 over score.

    D/L uses an exponentional equation iteratively for best fit where both wickets and runrate are taken into account along with number of interruptions and the precise score at each point. It uses a G50 constant of 245, some other values and one exponential equation to determine a 'par score' of 118 for India. India scored 119 fairly close to 118. So we get a 50 over equivalent of 246 instead of 245 (our G50 constant).

  • SLSup on April 15, 2014, 16:01 GMT

    Reaction to Anantha's response on DL Method: Glad you WHOLEHEARTEDLY disagree with SOME aspects of DL. Now I don't have to spend the rest of my life wondering what happened! I think the DL intent is pure but the method IS flawed because it assumes to "know" variables it cannot possibly account for. NZ with interruption got to 270 + while without interruptions they could have gotten out for 220 without completing all 50 overs. Whose to kow? - not Duckworth & Lewis! Projections are just that, projections. There is a reason I engage in comparisons and not predictions/projections. Wonder if anyone's ever carried out an extensive pro's & cons on DL Method.
    There was a far better D/L equivalent created by Jayadevan. However it got lost somewhere. Probably BCCI did not put their considerable weight behind the system.
    Reaction to Charith99: Weeks before World T20 Mahela/Sanga had said this would be their final WT20. Just as 2015 WC will be there last. MANY other players have done so in the past. It was Sanath's public utterences as Chairman of Selectors that was a disgrace. SLC was mad they lost upper-hand when players offered to play w/out money.

  • Charith99 on April 15, 2014, 10:42 GMT

    as a big fan of your articles even from the it figures days i know for a fact that you never idolize sachin like many other indians. i do admire sachin a lot and i think he has being a wonderful icon for cricket in general.however never making a controversial comment and never criticizing anyone should not be considered as a good thing because the current state in indian cricket can not be that rosy and wonderfull.Regarding mahela and sanga's outburst it could not have come at a better time, eventhough we won the cup the whole of sri lanka knew that the win was achieved by the players without any help from the pathetic administration.win or lose sl fans have never thrown stones at players or their houses because we know our players have played for us with or without their salaries.sanga and mahela have guided youngsters even better off the field.i do not mind even if this comment is not published but i wanted you to know the truth of the situation from one of your loyal fans.