Tuesday 30 December 2008

The curse of the duck

Cricket fans love their stats. Even the most casual follower can rattle off the batting averages of their favourite players or tell you how many wickets such-and-such a bowler took in the last test. The most passionate followers can recite each scorecard from this year's Wisden.

The recent news of the great Indian batsman Sachin Tendulkar surpassing West Indian Brian Lara's record number of test runs has given maths-loving cricket geeks another opportunity to pull out their calculators and Excel spreadsheets. I'm openly one of these nuts and did just that.

At the time of writing, Tendulkar had scored 12,027 runs across 247 innings, to overtake Lara's 11,953 from 232 innings. After a little investigation, I found that despite his outstanding average of over 54 runs per innings, Tendulkar's most common score in test cricket is ... zero!

This was quite a shock — the most prolific run-scorer in test cricket has been out for nought (a duck in cricket parlance) 14 times, well ahead of his second most common score — which incidentally is the next lowest you can get: one!

This is completely counter-intuitive, so I took this investigation further. Australian cricketer Sir Donald Bradman is universally regarded as the best batsman ever to have played the game. His average, an astounding 99.94, is so far above every other batsman in the history of the game that he is often acclaimed as not only the best cricketer ever, but the best player ever of any sport. His average is so iconic in Australia that the postcode of the ABC (the Australian version of the BBC) is 9994 in every capital city. If it wasn't for the fact that much more test cricket is played nowadays than in the early 1900s, and for World War II interrupting his career for six years, Bradman would have scored many more than the 6996 runs he did score.

So, guess what Bradman's most common score was?

That's right, zero!

Indeed, looking at every innings by the most prolific batsmen in test history from Tendulkar at number 1 to Bradman at number 34, the most common score is zero — and by quite a long way too. The following figures show the distribution of scores from these top batsmen — on the horizontal axis you see the number of runs and the vertical axis measures the frequency of dismissals at a particular number of runs. The first chart shows every score between 0 and 100, and the second uses five-run wide bins to show scores up to 250. The data only include scores where the batsman was dismissed and so does not include not-out scores.

First graph

Scores plotted against dismissal frequency.
Second graph

Scores in bins of five plotted against dismissal frequency.

 

Model cricket


A closer look at these distributions shows that they very closely fit what is known as an exponential distribution. An exponential distribution has the form

\[ y=\lambda e^{-\lambda x}. \]

In this case y is the probability of being dismissed at score x with λ being constant.
A common trick when looking at distributions involving exponentials is to take logarithms of both sides to get

\[ ln(y) = ln(\lambda ) - \lambda x. \]


The graph of this function, plotting ln(y) against x, is now a straight line with slope -λ. If the statistical data fits the exponential distribution, then the plot of the logarithm of the frequency of dismissals against the score at which dismissal happened should look roughly like a straight line.

Straight line fit

A straight line fitted to the data. The blue dots represent observed data and the black line represents the model.
Straight line fit
A straight line fitted to the data from the second chart above. The blue dots represent observed data and the black line represents the model.
There is a very strong straight line fit in both charts. Using a standard technique called least-squares regression, we can find the straight line that best fits the data. We can determine λ from the coefficient of x in the equation of this line, and in our case this gives λ equal to 0.023.

The mean of an exponential distribution, a sort of average, is 1/λ. In our case this gives a mean of around 43 - the same as we observe in the raw data. One can make the interesting observation that there is no such thing as the "nervous nineties": players do not "choke" and get out in the 90s, nervous before scoring a glorious test century, any more than they get out at any other score. Indeed, you could argue the opposite given the probability troughs at 94, 98 and in the 190s. You can also see that the probability of being dismissed for a duck is higher than you might expect for an exponential distribution.

So what?


Now, so far you might be thinking that all of this is only of passing statistical interest. So what if cricket scores follow an exponential distribution? Well, I'm glad you asked!
Let’s turn for a second to a different distribution, the geometric distribution. You will be familiar with this distribution from a simple 50/50 coin toss. The geometric distribution describes the number of coin tosses you need before a head (or tail) first turns up. The probability of your first head turning up on your kth toss is described as

\[ Prob(first\; \;  head \; \;  on \; \;  kth \; \; toss) = (1-p)^{k-1}p, \]

where p is the probability of a head turning up on each toss, that is, 0.5. The distribution is memory-less, which is one of its key descriptors. No matter what has gone before, even if you have fluked 100 tails in a row, the probability of a head turning up on the 101st throw is still p.

The geometric distribution only works for integer values of k, that is, you can only throw a coin 2, 3, 100 etc times and not 2.5 times. The exponential distribution is the continuous equivalent of this distribution, extending it to work for all numbers, not just integers. Given that cricket batting scores seem to fit a exponential distribution, this means that we can picture cricket batting scores on a geometric distribution with the probability of you being dismissed at score as

\[ Prob(dismissed\; \; at\; \; score\; \; k) = (1-p)^ kp. \]

Can you spot the profound result here?

Remembering that the geometric distribution is memory-less, you can interpret this as saying that no matter what score you are currently on, you have the same chance p of getting out on that score as you do on any other score! Like a coin toss, the probability of you being dismissed on each score does not depend on what has gone before. A model which assumes that there is no memory is known as a constant hazard model.

This seems to go against every cricketing manual I have ever read. Accepted cricketing wisdom says that a batsman is more dangerous when (s)he "has the eye in" and has scored 10 or 20 runs. Our result seems to suggest that, apart from when a batsman is on 0, you have just as much chance of dismissing him or her on the current score as on any other score.

The next question to ask is, what is the probability of dismissing a batsman on the current score (that is, what is p in the above equation)? The mean of a geometric distribution is

\[ mean = \frac{1-p}{p}. \]

Knowing that the mean of the exponential distribution is 1/λ, and transferring this to the geometric distribution, we get

\[ p = \frac{\lambda }{\lambda + 1}. \]

For λ = 0.023 this gives p = 0.022. Therefore, if you were to turn the television on now and find the cricket coverage, the chance that the batsman you are watching gets out on the current score is 2.2%.

 

Scores near zero


The biggest deviation from the geometric distribution is for scores near zero. According to our data, the chance of being dismissed for a duck is 6.9% — around 3 times more than expected for a geometric (or exponential) distribution. But by the time the batsman has scored two or three runs, the geometric distribution starts to fit well. There is a small peak at four runs, perhaps because you can relatively easily get to four before you become comfortable — it only takes one streaky shot to the boundary. Whilst you can get to three with one shot, you are more likely to have played a few shots and so may be comparatively more "set".

Data and geometric distribution
The data and the geometric distribution. The blue dots represent observed data and the black line represents the model.
An analysis of scores near zero has been completed by Brendon J. Brewer from the University of New South Wales in Getting your eye in: A Bayesian analysis of early dismissals in cricket. Brewer indeed found that batsmen are more vulnerable at the beginning of their innings.

By assuming a constant hazard model, Brewer determined the effective average of a batsman before they have scored — that is, assuming a constant hazard model with probability p of dismissal equal to that of their chance of being dismissed for a duck, Brewer determined the mean of this new distribution.

In our data from the best batsmen of all time, dismissal for a duck occurred with a 6.9% chance. The mean of a geometric distribution built around this probability is

\[ \frac{1-0.069}{0.069} = 13.5. \]


This means that even though our batsmen have a mean of about 43, before they've scored they bat like cricketers with a mean of 13.5. Even the best batsmen bat like tail-enders before they get off the mark!

 

Conclusions


What should we take away from this analysis?

The conclusion seems to be that there is a very small window in the beginning of a batsman's innings in which there is a greater chance of dismissal than there ordinarily is. This makes sense — batsmen take some time to acclimatise to the game conditions. But this is a small window — once the batsman has scored about three runs, you have the same chance of dismissal whatever the current score. Interestingly, tiredness does not seem to play a part — the exponential distribution holds well out to 250 runs (quite a few hours of batting).

It should be remembered that this analysis was completed on the top 34 run scorers of all time (5953 innings) and so represents the best ever batsmen. Lesser batsmen are likely to get low scores, so perhaps this window is slightly wider for them. But if we turn to the greatest of the great, Bradman, the window is essentially one run. His effective average before he had scored was a very mediocre nine runs. After he had scored two runs, this effective average had risen to 69. You had to get Bradman out very early!


More information
  • The data was retrieved from cricinfo during the second test between Australia and India on the 19th of October 2008;
  • Not-out scores were removed from the analysis;
  • The exponential distribution does break down a little for scores above 250 as there simply isn't enough data;
  • Yes, Marc has scored a duck in his cricket career.

Further reading

113 comments:

  1. Very interesting analysis (I've Dugg your submission). But I'm not sure if I follow your move from the exponential distribution to the geometric...

    If a batsman's scoring follows an exponential distribution, and his historical average per innings is 1/λ then:

    P(he will score exactly x runs) = λexp(-λx)

    If I understand correctly, your statement that "if you were to turn the television on now and find the cricket coverage, the chance that the batsman you are watching gets out on the current score is 2.2%" doesn't look right. The probability of getting out next ball isn't constant but depends on how many runs they've already made.

    ReplyDelete
  2. Hi Stanley - thanks for the comment, and the Digg!

    You are right, the batsman's scoring does follow an exponential distribution, but the statement re turning the tv is on is correct.

    Imagine a coin tossed over and over again. The first time a head turns up follows an exponential distribution - like our batting dist - when the head turns up, you're out. There is a 50% chance it will turn up on the first toss. Given that 50% of the time a head has already turned up by the time we toss the coin a 2nd time, the probability that we actually toss the coin a 2nd time is 50% and the probability of that coin toss yielding a head is 50%, so overall, the probability of a head turning up on the 2nd toss is 50% times 50% - which is 25%.

    The trick here is to remember that with a coin toss, at each toss, there is a 50% chance of a head turning up NO MATTER what has come before. Even if you have tossed the coin 100 times, the probability of a head on the 101st toss is 50%. It's the same the with batting, although instead of the probability involved being 50%, its around 2%.

    Re moving from the exponential to the geometric dist, the exponential distribution is the continuous equivalent of geometric distribution, extending it to work for all numbers, not just integers. As you can only get out at integer values in cricket, the geometric distribution is the apt dist to use. For a decent data set like we have here, we can interchange the dists.

    Thanks for reading!
    marc

    ReplyDelete
  3. So Mike Hussey's recent run of low scores is not poor form, it's re-affirming his greatness..

    ReplyDelete
  4. I can think of a batsman that bucks the trend - although obviously I understand that he's an outlier. England's Alastair Cook (66 innings, 2 not outs)'s mode score is 60, which he's been out on five times, compared with just one duck. I guess a few other players (like AB DeVilliers, who's never had a duck) will also fall into a category like this. But yeah, they're definitely exceptions. Really good article :).

    ReplyDelete
  5. It is a proficient article that you have shared here about cricket. I got some unique and valuable information from your article. Thankful to you for sharing this article here.Connect with Cricket grounds umpires and scorers

    ReplyDelete
  6. The information you've provided is quite useful. It's incredibly instructional because it provides some of the most useful information. Thank you for sharing that. Buy Cricket Batting Pads Online

    ReplyDelete
  7. Amazing cricket game statistics. Keep this up. If you want to see newest trends in design for bathrooms check out our services.

    ReplyDelete
  8. It is truly a well-researched content and excellent wording. I got so engaged in this material that I couldn’t wait to read. Read more info about cricket clothing online shopping. I am impressed with your work and skill. Thanks.

    ReplyDelete
  9. Very informative post. Nice blog content. Thanks for sharing. HVAC repair

    ReplyDelete
  10. If it wasn't for the fact that much more test cricket is played nowadays than in the early 1900s, and for World War II interrupting his career for six years, Bradman would have scored many more than the 6996 runs he did score. about us

    ReplyDelete
  11. I'm so happy to found this site, I love science and I'm very curious about everything. https://www.inspectionmanaging.com/

    ReplyDelete
  12. It's great to see this awesome information here. anchorirrigation.com/

    ReplyDelete
  13. Impressive analysis! It's such a great content. Thank you for sharing!
    www.excavationdoneright.com/excavation-contractors-louisville-ky

    ReplyDelete
  14. Remembering that the geometric distribution is memory-less, you can interpret this as saying that no matter what score you are currently on. - basement crack repair

    ReplyDelete
  15. The following figures show the distribution of scores from these top batsmen — on the horizontal axis you see the number of runs and the vertical axis measures the frequency of dismissals at a particular number of runs. home contractor

    ReplyDelete
  16. Thank you for always sharing here an informative blog. info

    ReplyDelete
  17. The data only include scores where the batsman was dismissed and so does not include not-out scores. | sunsetter dealer near me

    ReplyDelete
  18. Interesting article thank you for sharing check article here Securities Classaction Directory

    ReplyDelete
  19. The probability of getting out next ball isn't constant but depends on how many runs they've already made.bathroom remodeling companies

    ReplyDelete
  20. Accepted cricketing wisdom says that a batsman is more dangerous when (s)he "has the eye in" and has scored 10 or 20 runs. Roofing company in el paso texas

    ReplyDelete
  21. I like the content of this blog, very informative one. https://www.americanheatingandairga.com/

    ReplyDelete
  22. Tolerating for the time being that you're searching for an exhaustive manual for making a plans channel that devotees, you've come to the best regions. Deals pipes are one of the chief pieces of web progressing, and whenever done definitively, can make tremendous benefits for your business. In this article, we will examine the basics of game plans pipe movement, and give tips and deceives to making areas of strength for a that will change over programs into purchasers!

    Sales Funnel Development FL

    ReplyDelete
  23. Much appreciation to you for sharing these sythesis for a blog rules with making bloggers like us. Keep on sharing. Respects, https://messiahdfou373.substack.com/p/the-ultimate-cheat-sheet-on-viral?sd=pf

    ReplyDelete
  24. This is much appreciated. I want to read more

    ReplyDelete
  25. There is a small peak at four runs, perhaps because you can relatively easily get to four before you become comfortable — it only takes one streaky shot to the boundary. crawl spaces near me san francisco ca

    ReplyDelete
  26. It's wonderful to see such amazing information presented here. I am overjoyed to have found this website. https://www.electricianvictoriabc.com/emergency-electrician

    ReplyDelete

  27. A common trick when looking at distributions involving exponentials is to take logarithms of both sides to get gmb listing

    ReplyDelete
  28. The following figures show the distribution of scores from these top batsmen — on the horizontal axis you see the number of runs and the vertical axis measures the frequency of dismissals at a particular number of runs. basement crack repair

    ReplyDelete
  29. Remembering that the geometric distribution is memory-less, you can interpret this as saying that no matter what score you are currently on. exterior painting services

    ReplyDelete
  30. Nice! You can also see that the probability of being dismissed for a duck is higher than you might expect for an exponential distribution.

    ReplyDelete
  31. Pretty great post. I just stumbled upon your blog and wanted to say that I’ve truly loved browsing your blog posts.
    moodle nottingham
    moodle maisonneuve

    ReplyDelete
  32. Fantastic blog i have never ever read this type of amazing information. travis bickle jacket

    ReplyDelete
  33. I never thought this much math could be applied into Cricket of all things, it really goes to show how diehard some fans can be because I'm sure the common fan wouldn't go that far over some calculations related to the game. Thanks a lot for sharing this! please be sure to check out the best appliance repair company in Lubbock, TX.

    ReplyDelete
  34. Thanks for this great information you shared. northalpestcontrol.com/

    ReplyDelete
  35. Such an awesome post. Thanks for sharing! more

    ReplyDelete
  36. Glad to visit this site. Great work! debonnaireconstruction.com/

    ReplyDelete

  37. For λ = 0.023 this gives p = 0.022. Therefore, if you were to turn the television on now and find the cricket coverage, the chance that the batsman you are watching gets out on the current score is 2.2%.



    Kurt | drywall contractor

    ReplyDelete
  38. Thank you for sharing this very informative blog here. resolutions-av.com/

    ReplyDelete
  39. I'm Srilankan and I was named after this legend
    https://www.nswtreeloppers.com.au/

    ReplyDelete
  40. Hey! this is so informative. Thanks Awesome

    ReplyDelete
  41. There is a small peak at four runs, perhaps because https://www.drywalldc can relatively easily get to four before you become comfortable.

    ReplyDelete
  42. Yey! this is so informative. Thanks www.watersoftenergurus.com

    ReplyDelete
  43. Sports fans really look into the stats! call us

    ReplyDelete
  44. I don't know why I took this very seriously. hahaha! I had so much fun reading it!
    norelco beard trimmer

    ReplyDelete
  45. This is very informative. And to be honest, this is so fun to read about. Many thanks.
    Tampa best SEO company

    ReplyDelete
  46. This is great info for a beginner like me. southamptonfencingpros.com

    ReplyDelete
  47. So far you have a good content! Thank you 3cre-commercial-real-estate.business.site/

    ReplyDelete
  48. Glad I was able to check this article! Science contents really interest me. contact us

    ReplyDelete
  49. At this point why not just admit this is an excuse to avoid the wives? eastbournetreesurgeons.co.uk

    ReplyDelete
  50. Wow! Thank you from dime method. I love your writing voice because it's engaging and approachable.

    ReplyDelete
  51. Pop culture and Science are two of my favorite things! call us

    ReplyDelete
  52. By assuming a constant hazard model, Brewer and Pasadena Concrete Company determined the effective average of a batsman before they have scored.

    ReplyDelete
  53. Lorem Dela CruzJune 22, 2023 9:53 pm

    You are an awesome writer. I am grateful for this content. If you are looking for house painter near me in West Ashley, SC.

    ReplyDelete
  54. Just read the whole article and found it really interesting! www.shopedc.com

    ReplyDelete
  55. This finding challenges the assumption that the highest-scoring players would also have a correspondingly higher frequency of scoring runs. The charts provided in the investigation display the distribution of scores for the top batsmen, showing the frequency of dismissals at different run levels. superiordraincleaning.com/

    ReplyDelete
  56. Cricket statistics, however, should be viewed as a complement to the overall cricketing experience, as they capture only a part of the game's essence. The thrill of watching a live match, the ebb and flow of emotions, and the camaraderie among fans are equally important aspects that make cricket a beloved sport.

    ReplyDelete
  57. This is so informative! I love it. Thanks Check it out

    ReplyDelete
  58. Based on the search results, it seems that there is no specific term or topic called "cycling and kite core". However, there are some relevant results related to Core kites store and cycling. There are results about a kite fitness gym, kite skiing or snow-cycling, and kiteboarding as a watersport combined with cycling as a way of transportation. Is there a specific question or topic you want me to focus on related to kites and cycling? I will do my best to help if you can provide more specific information.

    ReplyDelete
  59. Even though players like Sachin Tendulkar and Sir Donald Bradman are renowned for their remarkable achievements and high averages, they have also experienced their fair share of failures in the form of ducks. Cricket is a sport that demands consistent focus and skill, and even the best players can have moments of vulnerability. superiordraincleaning.com/

    ReplyDelete
  60. Cricket fans are a passionate bunch, and they love to talk about the game. One of the things that fans love to talk about is statistics. Cricket is a game of numbers, and there are stats for everything from batting averages to bowling averages to fielding percentages.

    ReplyDelete
  61. Thank you for this site. I love your writing voice because it's engaging and approachable. All the best from our vinyl fence installation company Sioux City

    ReplyDelete
  62. You have a very nice output! Thanks https://scottkeeverseo.com/

    ReplyDelete
  63. Focusing on professional skills enables people to get better at what they do. Cheers from wood fence installation in Texas.

    ReplyDelete
  64. Wow, that was a comprehensive analysis of cricket batting scores and their distribution. It's fascinating to see how statistical models, such as the exponential and geometric distributions, can be used to understand and interpret the patterns in cricket scores. www.excavatingcincinnati.com

    ReplyDelete
  65. I also agree with your statement that the most passionate followers can recite each scorecard from this year's Wisden. Wisden is the bible of cricket, and it's a must-read for any serious cricket fan. The scorecards in Wisden are a great way to track the progress of a match, and they can also be a great way to learn about the history of cricket.

    ReplyDelete
  66. Cheers from our vinyl pools company at Amarillo, Texas.

    ReplyDelete
  67. Yey! this is so informative. Thanks click

    ReplyDelete
  68. I'm so happy with the content! Thanks https://www.unmannedsas.com/

    ReplyDelete
  69. How can i connect Science in the Bible? I'm very curious about this two.

    ReplyDelete
  70. Absolutely fascinating analysis! I'm amazed at how even the titans like Tendulkar and Bradman aren't immune to the "duck curse." Your use of statistical models to break down the probability of a batsman getting dismissed at various scores is enlightening. It challenges conventional wisdom about batsmen being "settled" after scoring a few runs and offers a fresh perspective on the game. It’s compelling to think that even the greats bat like tail-enders until they're off the mark! stenciled concrete mornington

    ReplyDelete
  71. Wow, that's some deep dive into cricket stats! It's fascinating that even the greats like Tendulkar and Bradman are most commonly out for a duck. Makes the game feel a bit more unpredictable and exciting! Click here

    ReplyDelete
  72. Fascinating read! Never thought that batting scores would fit an exponential distribution so well. Makes me rethink the whole "settled batsman" concept. Great analysis! gutter repair near me

    ReplyDelete
  73. Fascinating analysis on how cricket scores follow an exponential distribution! The concept that batsmen have the same chance of dismissal regardless of their current score really goes against conventional wisdom. It's especially intriguing to learn that even legends like Tendulkar and Bradman had zero as their most common score. Thanks for shedding new light on the "curse of the duck" and the nuances of cricket statistics! concrete driveway near me

    ReplyDelete
  74. Fascinating read! Surprising to see how stats challenge common cricket wisdom about when a batsman is most likely to get out. gutter repair northern beaches

    ReplyDelete
  75. You have a nice output! Thanks unmannedsas.com/

    ReplyDelete
  76. This is completely counter-intuitive, so I took this investigation further and .remove wall texture. Australian cricketer Sir Donald Bradman is universally regarded as the best batsman ever to have played the game

    ReplyDelete
  77. Thank you for creating such incredible content. click

    ReplyDelete
  78. It's fascinating to see how cricket's greatest batsmen, including Sachin Tendulkar and Sir Donald Bradman, have zero as their most common score. The statistical quirks of the sport never cease to amaze! business brokerage hurricane ut

    ReplyDelete
  79. In cricket we have a lot of memories related to the curse of a duck and so many legendary great players faced it. You can visit us to find more amazing services that helps the people to find the perfect solutions.

    ReplyDelete
  80. Wow, this is so good! Thank you Poseidon Fishing Charters

    ReplyDelete
  81. Wow, it's crazy to think that even cricket legends like Tendulkar and Bradman had their fair share of ducks! pest control cottonwood heights ut

    ReplyDelete
  82. There is a small peak at four runs, possibly because reaching four is comparatively easy for https://www.drywallmarietta before becoming comfortable - one streaky shot to the boundary can do the trick.

    ReplyDelete
  83. I adore this post. Cheers from our best medicare IMO

    ReplyDelete
  84. As someone who's watched countless cricket matches, I've always heard commentators talk about the "nervous nineties" and how batsmen are more likely to get out just before reaching a century. It's intriguing to see this analysis challenging that notion, especially for the top-tier batsmen. The idea that even the best batsmen essentially "bat like tail-enders" before getting off the mark is quite a revelation and certainly adds a new dimension to understanding the game.

    ReplyDelete
  85. I adore this post and site is amazing. You are making a difference. Kindest regards from our Roof Contractor in Wentzville.

    ReplyDelete
  86. The revelation that both Tendulkar and Bradman's most common score is zero is truly surprising, challenging conventional cricket wisdom. The analysis also sheds light on the brief vulnerability at the start of a batsman's innings, emphasizing the importance of acclimatization to game conditions.

    ReplyDelete
  87. I appreciate your practical tips. I'm going to start using them right away. | https://enjoymexico.net/

    ReplyDelete
  88. You absolutely nailed it. It was so satisfying. Cheers from our Cape Girardeau Remodeling Contractor Cape Girardeau at https://www.capegirardeauremodeling.com/

    ReplyDelete
  89. I completely agree with this article! Resin driveways and pavement provide a number of advantages over traditional alternatives. EdinburghPaving

    ReplyDelete
  90. I think I also experience the same when I'm on my highscool auto repair gilbert az

    ReplyDelete
  91. Vaping Fryd wholesale devices work by heating the e-liquid, turning it into vapor. Users inhale this vapor, which often contains nicotine, flavorings, and other chemicals.

    ReplyDelete
  92. This is amazing. Kudos and learn more from our buffalohealthadvisors.com

    ReplyDelete
  93. Whether you're a skeptic seeking to unravel the truth behind the legend or a believer intrigued by the supernatural, join us as we embark on a chilling journey to decipher The Curse of the Duck—an enigma that continues to captivate the curious minds and spark whispers in the dark.
    bankruptcy lawyers near me now

    ReplyDelete
  94. I found out my cousin plays this game.
    https://www.compare1.com.au/

    ReplyDelete
  95. Haha, that's a fascinating cricket stat! Who would've thought that the most common score for the greatest batsmen is zero? Cricket never ceases to amaze with its quirks. ac installation phoenix

    ReplyDelete
  96. It's fascinating how cricket stats can reveal surprising insights! 🏏 Who would've thought that even legends like Sachin Tendulkar and Don Bradman had zero as their most common score? Cricket truly is full of intriguing facts and figures. stump grinding englewood co

    ReplyDelete
  97. Cricket statistics can often reveal fascinating quirks in the game. It's intriguing to learn that some of the greatest batsmen in the sport, including Sachin Tendulkar and Sir Donald Bradman, have had zero (duck) as their most common score. The unpredictability of cricket is part of what makes it so captivating for fans and enthusiasts alike. 🏏📊 #CricketStats #Duck #SachinTendulkar #SirDonBradman bathroom remodeling cleveland tx

    ReplyDelete
  98. Fascinating insights into the world of cricket stats! It's astonishing to see how even legendary batsmen like Sachin Tendulkar and Sir Donald Bradman had zero as their most common score. Cricket's unpredictability always keeps us intrigued, and this analysis adds another layer to the game's rich history. 🏏📈 #CricketStats #ZeroScore #SachinTendulkar #SirDonBradman ginseng benefits

    ReplyDelete
  99. Cricket's allure lies in its intricate statistics, and this exploration of zero scores among cricket legends is both surprising and thought-provoking. It's a testament to the unpredictability of the game and the exceptional resilience of players like Tendulkar and Bradman. Cricket truly is a sport full of intriguing stories and records! 🏏📊 #CricketLegends #ZeroScores #CricketStatistics uti treatment at home

    ReplyDelete
  100. Cricket statistics never cease to amaze! 🏏 It's fascinating to see that even legendary batsmen like Tendulkar and Bradman had zero as their most common score. Goes to show that cricket is full of surprises and quirks. Thanks for sharing this intriguing insight into the world of cricket stats! roof repair miami fl

    ReplyDelete
  101. Thanks for every thing you did in our life I proudly say that I lived in his era.
    https://www.ausluxuryhire.com.au/

    ReplyDelete
  102. Science has a lengthy history of being taught and popularized. I believe a library or an online/Google search will yield a lot of leads.
    Business Listings

    ReplyDelete
  103. Skateboarding Flow Bindings: where creativity meets concrete.

    ReplyDelete
  104. I read about the curse-of-duck in cricket and it is good to read about it here again. You are good to share the detail and we can find more ideas about this game of gentleman. While searching for the dam construction ideas I came here to see these amazing ideas you shared.

    ReplyDelete
  105. septic main line replacement 3 cleanings in Atlanta are like a tune-up for your home's waste management – necessary and beneficial.

    ReplyDelete