PhD Candidate | Department of Statistics | University of Auckland
I am current a PhD candidate in the Department of Statistics at the University of Auckland where I spend my time investigating statistical models that can be utlised in the field of sports analytics. My current research involves the development and implementation of various machine learning algorithms that can be applied to the sport of cricket, primarily to estimate and predict the past, present and future abilities of professional cricketers, as well as to predict the likely outcome of upcoming matches.
I also provide statistical and data consulting services to those looking for help with data modelling, data analysis and other data-related questions. I have advised clients who work in a range of fields including IT, market research, clinical trials and sports analytics, and I’m always up for a new challenge.
Feel free to take a look at my past and present research below, or get in touch if you have any questions regarding statistics, data, cricket or otherwise.
- Sports analytics
- Bayesian inference
- Machine learning
- Computational statistics
Doctor of Philosophy (2017 - present)
Since mid-2017, I have been studying towards a Doctor of Philosophy under the supervision of Dr Brendon Brewer. Following on from my Masters, my research has involved developing a range of statistical models that can be applied to the analysis of sporting data, with a particular focus on cricket. As with any sport or profession, we shouldn’t expect a player to perform with some constant ability throughout their entire career. Instead, we are likely to observe both short and long-term variations and fluctuations in ability due to the likes of age, experience, fitness and general improvements or deteriorations in technique.
Therefore, I have derived a range of models that use machine learning algorithms to better estimate and predict the past, present and future batting and bowling abilities of professional cricketers. When estimating current player ability, the models account for a range of external factors, including recent form, strength of opposition and venue of past performances (e.g. home or away). These estimates have been proven to provide more accurate predictions of player peformance compared with traditional cricketing metrics, such as batting and bowling averages. Additionally, the models have the benefit of maintaining an intuitive cricketing interpretation, unlike other popular ranking metrics, such as the official ICC rankings. Given two proposed playing XIs, we can use the estimated player abilities to provide a percentage prediction of each team winning a match.
See below for an overview of my current Test batting and bowling rankings, including an interactive application that allows users to visualise the batting and bowling career trajectories of international cricketers.
Master of Science (2016 - 2017)
In 2017 I completed my Masters degree under the supervision of Dr Brendon Brewer. My research looked to tell a more meaningful story behind a cricket player’s batting average. Using Bayesian statistical techniques, I explored more in-depth methods of quantifying a cricketer’s batting ability than the simple batting average. More specifically, I built statistical models which estimate how well a batsman is playing at any given point in their innings, allowing us to quantify the cricketing concept of a batsman ‘getting their eye in’. The primary focus was on Test match cricket, with wider applications to 4-day first-class cricket. Using these models, I also explored the plausibility of popular cricketing superstitions from a statistical point of view, such as the commentator’s favourite, the ‘nervous 90s’.
ABSTRACT: Cricketing knowledge tells us batting is more difficult early in a player’s innings, but gets easier as a player becomes familiar with the local conditions. Using Bayesian inference and nested sampling techniques, a model is developed to predict the Test match batting abilities of international cricketers. The model allows for the quantification of players’ initial and equilibrium batting abilities, and the rate of transition between the two. Implementing the model using a hierarchical structure provides more general inference concerning a selected group of international opening batsmen from New Zealand. More complex models are then developed, which are used to identify the presence of any score-based variation in batting ability among a group of modern-day, world-class batsmen. Additionally, the models are used to explore the plausibility of popular cricketing superstitions, such as the ‘nervous 90s’. Evidence is found to support the existence of score-based variation in batting ability, however there is little support to confirm a widespread presence of the ‘nervous 90s’ affecting player batting ability. Practical implications of the findings are discussed in the context of specific match scenarios.
Click here to read thesis titled “The nervous 90s: a Bayesian analysis of batting in Test cricket”.
Bachelor of Science (Honours) (2015)
ABSTRACT: At a glance, data is more meaningful when presented in graphical form. This project explored innovative methods of automating the display of catch data for large-scale conservation projects. High priority was given to developing methods that allow users to interact with their data, affording them some control over the graphics that are produced. Two interactive applications were developed that allow conservation volunteers to select the data they want to view and how to view it. After a day in the field, volunteers are able to use these applications to see their day’s work summarised on a map or graphic. These graphics highlight the positive impact their efforts are having on the local environment, keeping volunteers motivated and engaged in their work. Various methods of improving the automation of these graphics are outlined, as well as other practical uses of these statistical applications.
Click here to read dissertation titled “Graphical applications for large-scale conservation projects”.
Top 100 Test batsmen
Players must have participated in a Test match since 2019 and must have batted in a minimum of 15 Test innings to be ranked.
Last updated 10th December 2020.
|Rank||Player||Country||Innings||Runs||Career average||Predicted average||ICC rating (#)|
|1||Steve Smith||AUS||131||7227||62.8||58.1||911 (1)|
|2||Marnus Labuschagne||AUS||23||1459||63.4||56.0||827 (4)|
|3||Kane Williamson||NZ||141||6727||52.6||54.3||886 (2=)|
|4||Babar Azam||PAK||53||2045||45.4||53.4||797 (5)|
|5||Virat Kohli||IND||145||7240||53.6||51.2||886 (2=)|
|6||David Warner||AUS||155||7244||48.9||48.0||793 (6)|
|7||Angelo Mathews||SL||154||5981||45.3||47.6||658 (17)|
|8||Rohit Sharma||IND||53||2141||46.5||46.6||674 (16)|
|9||Mayank Agarwal||IND||17||974||57.3||46.2||714 (12)|
|10||Joe Root||ENG||177||7823||48.0||45.7||738 (9)|
|11||Ross Taylor||NZ||179||7276||46.1||44.7||676 (15)|
|12||Cheteshwar Pujara||IND||128||5840||48.7||43.4||766 (7)|
|13||Azhar Ali||PAK||152||6129||42.9||42.7||627 (23)|
|14||Ajinkya Rahane||IND||109||4203||42.9||41.7||726 (11)|
|15||Tom Latham||NZ||93||3812||42.8||41.0||733 (10)|
|16||Mushfiqur Rahim||BAN||130||4413||36.8||40.5||654 (18)|
|17||Ben Stokes||ENG||122||4428||37.8||39.5||760 (8)|
|18||Dinesh Chandimal||SL||103||3877||40.8||39.4||563 (39)|
|19||Rishabh Pant||IND||22||814||38.8||38.2||555 (43)|
|20||Travis Head||AUS||28||1091||42.0||38.2||643 (19)|
|21||Shakib Al Hasan||BAN||105||3862||39.4||38.2||576 (37)|
|22||BJ Watling||NZ||110||3658||38.5||38.1||615 (25)|
|23||Tamim Iqbal||BAN||115||4405||38.6||38.0||597 (31)|
|24||Kusal Mendis||SL||85||2995||37.0||37.7||628 (22)|
|25||Usman Khawaja||AUS||77||2887||40.7||37.7||584 (34)|
|26||Asad Shafiq||PAK||128||4660||38.2||37.5||608 (26)|
|27||Dimuth Karunaratne||SL||128||4524||36.8||37.1||680 (14)|
|28||Dominic Sibley||ENG||19||686||38.1||36.6||567 (38)|
|29||Faf du Plessis||SA||112||3901||39.8||36.3||586 (33)|
|30||Henry Nicholls||NZ||51||1754||39.0||36.1||635 (21)|
|31||Ravindra Jadeja||IND||71||1869||35.3||35.8||551 (45)|
|32||Dean Elgar||SA||110||3888||38.5||35.4||624 (24)|
|33||Brendan Taylor||ZIM||62||2055||35.4||35.2||599 (30)|
|34||Joe Burns||AUS||36||1379||38.3||35.1||491 (59)|
|35||Quinton de Kock||SA||80||2934||39.1||35.0||706 (13)|
|36||Craig Ervine||ZIM||36||1208||35.5||35.0||549 (46)|
|37||Sean Williams||ZIM||24||770||33.5||35.0||480 (66)|
|38||Jermaine Blackwood||WI||57||1700||32.1||34.6||559 (41)|
|39||Mominul Haque||BAN||74||2860||40.9||34.4||556 (42)|
|40||Soumya Sarkar||BAN||74||2860||40.9||34.3||421 (77)|
|41||KL Rahul||IND||60||2006||34.6||34.1||504 (54)|
|42||Jos Buttler||ENG||82||2543||33.9||34.1||637 (20)|
|43||Colin de Grandhomme||NZ||36||1185||37.0||34.0||583 (35)|
|44||Matthew Wade||AUS||55||1440||31.3||34.0||488 (60)|
|46||Sikandar Raza||ZIM||30||1037||34.6||33.6||487 (61)|
|47||Dhananjaya de Silva||SL||57||1863||35.2||33.4||561 (40)|
|48||Darren Bravo||WI||100||3527||37.1||33.3||431 (75)|
|49||Jason Holder||WI||77||2045||32.0||32.7||552 (44)|
|51||Shan Masood||PAK||43||1368||31.8||32.3||600 (29)|
|52||Rory Burns||ENG||38||1233||32.4||32.2||597 (31)|
|53||Hanuma Vihari||IND||16||552||36.8||31.6||529 (49)|
|55||Niroshan Dickwella||SL||66||1921||31.0||31.3||578 (36)|
|57||Ollie Pope||ENG||20||645||37.9||31.2||531 (48)|
|58||Haris Sohail||PAK||23||819||37.2||30.8||480 (66)|
|59||Tim Paine||AUS||50||1330||31.7||30.6||516 (52)|
|60||Joe Denly||ENG||28||827||29.5||29.6||520 (51)|
|62||Roston Chase||WI||66||1869||30.1||29.5||484 (64)|
|63||Kusal Perera||SL||33||934||31.1||29.0||481 (65)|
|65||Temba Bavuma||SA||67||1845||30.8||27.9||485 (63)|
|66||Shane Dowrich||WI||62||1570||29.1||27.6||521 (50)|
|67||Jonny Bairstow||ENG||123||4030||34.7||27.5||486 (62)|
|68||Wriddhiman Saha||IND||50||1238||30.2||27.4||388 (83)|
|69||Shimron Hetmyer||WI||30||838||27.9||27.4||500 (56)|
|70||Liton Das||BAN||34||859||26.0||26.6||450 (70)|
|71||Chris Woakes||ENG||60||1321||27.5||26.5||404 (79)|
|72||Cameron Bancroft||AUS||18||446||26.2||26.2||368 (90)|
|73||Sam Curran||ENG||31||728||27.0||26.2||440 (74)|
|74||Kraigg Brathwaite||WI||120||3703||32.8||25.8||504 (54)|
|75||Aiden Markram||SA||37||1424||38.5||25.6||608 (26)|
|76||Mitchell Santner||NZ||29||741||25.6||25.6||377 (84)|
|77||Regis Chakabva||ZIM||34||806||25.2||24.8||337 (94)|
|79||Imam ul-Haq||PAK||21||485||25.5||24.3||367 (91)|
|80||Jeet Raval||NZ||39||1143||30.1||24.2||451 (69)|
|81||Mitchell Marsh||AUS||55||1260||25.2||23.8||371 (89)|
|82||Ravichandran Ashwin||IND||98||2389||28.1||23.6||372 (88)|
|83||Mitchell Starc||AUS||85||1515||22.3||22.7||375 (86)|
|84||Shai Hope||WI||64||1603||26.3||22.7||449 (71)|
|85||Lahiru Thirimanne||SL||68||1404||22.6||22.7||329 (96)|
|86||John Campbell||WI||20||410||24.1||22.5||396 (82)|
|87||Moeen Ali||ENG||104||2782||29.0||21.9||358 (92)|
|89||Theunis de Bruyn||SA||23||428||19.5||20.8||317 (99)|
|92||Marcus Harris||AUS||17||385||24.1||20.2||323 (98)|
|100||Imrul Kayes||BAN||76||1797||24.3||17.5||333 (95)|
Top 50 Test bowlers
Players must have participated in a Test match since 2019 and must have taken a minimum of 30 Test wickets to be ranked.
Last updated 1st December 2020.
|Rank||Player||Country||Wickets||Career average||Adjusted career average||Predicted adjusted average||ICC rating (#)|
|1||JJ Bumrah||IND||68||20.3||23.0||24.3||779 (9)|
|2||PJ Cummins||AUS||143||21.8||24.3||25.1||904 (1)|
|3||I Sharma||IND||291||32.4||32.7||25.7||729 (17)|
|4||N Wagner||NZ||206||26.6||27.6||25.8||843 (3)|
|5||K Rabada||SA||197||22.9||25.0||26.8||802 (6)|
|6||JM Anderson||ENG||538||25.4||26.5||27.2||781 (8)|
|7||TG Southee||NZ||284||29.0||30.3||27.6||821 (4)|
|8||JR Hazlewood||AUS||195||26.2||28.1||28.0||769 (11)|
|9||JL Pattinson||AUS||81||26.2||26.9||28.4||333 (43)|
|10||SCJ Broad||ENG||513||27.5||29.9||28.5||845 (2)|
|11||Mohammed Shami||IND||180||27.4||29.4||28.6||749 (13)|
|12||R Ashwin||IND||365||25.4||27.7||29.5||756 (12)|
|13||Mohammad Abbas||PAK||80||21.7||25.3||29.6||749 (13)|
|14||TA Boult||NZ||267||27.6||28.7||29.7||770 (10)|
|15||MA Starc||AUS||244||27.0||29.1||29.8||797 (7)|
|16||BA Stokes||ENG||158||31.4||31.6||30.1||587 (24)|
|17||C de Grandhomme||NZ||47||31.6||30.7||31.1||476 (32)|
|18||Shakib Al Hasan||BAN||193||31.1||30.7||31.2||NA|
|19||KM Jarvis||ZIM||46||29.4||33.8||31.4||347 (41)|
|20||KAJ Roach||WI||196||28.2||29.1||31.8||744 (15)|
|21||Yasir Shah||PAK||224||30.7||30.9||32.2||609 (23)|
|22||RA Jadeja||IND||213||24.6||27.6||32.3||722 (18)|
|23||UT Yadav||IND||144||30.5||32.7||32.4||650 (21)|
|24||CR Woakes||ENG||112||29.3||30.0||32.9||666 (19)|
|25||MJ Leach||ENG||34||29.0||29.6||33.0||372 (40)|
|26||MA Wood||ENG||50||32.4||34.5||33.8||406 (37)|
|27||NM Lyon||AUS||390||31.6||32.7||33.8||742 (16)|
|28||ST Gabriel||WI||139||31.2||32.4||34.0||663 (20)|
|29||Hasan Ali||PAK||31||28.9||31.2||34.3||NA (NA)|
|30||Taijul Islam||BAN||114||33.2||33.8||34.6||585 (25)|
|31||Shaheen Shah Afridi||PAK||35||31.3||29.4||34.7||459 (33)|
|32||KA Maharaj||SA||110||33.2||33.9||35.5||548 (27)|
|33||Mehedi Hasan Miraz||BAN||87||33.1||34.0||35.8||570 (26)|
|34||JO Holder||WI||111||27.5||27.6||36.0||810 (5)|
|35||MR Marsh||AUS||42||38.6||36.4||36.1||310 (51)|
|36||RL Chase||WI||69||41.1||38.3||36.8||505 (31)|
|38||MM Ali||ENG||181||36.6||37.2||38.5||516 (28)|
|39||RAS Lakmal||SL||151||37.4||36.8||38.5||620 (22)|
|40||SM Curran||ENG||41||32.1||35.0||39.3||403 (38)|
|41||MDK Perera||SL||156||35.3||34.7||40.2||512 (30)|
|43||L Embuldeniya||SL||30||39.8||39.1||42.6||318 (49)|
|44||CBRLS Kumara||SL||67||36.6||37.8||43.0||514 (29)|
|45||JC Archer||ENG||38||31.1||36.5||44.2||383 (39)|
|46||MJ Santner||NZ||39||44.7||40.9||44.3||262 (58)|
|47||MJ Henry||NZ||30||50.2||46.0||46.0||249 (59)|
|48||Sikandar Raza||ZIM||32||41.8||41.8||46.1||323 (46)|
|49||AD Mathews||SL||33||52.9||45.4||47.4||130 (81)|
*incomplete data is available for players who made their Test debut prior to 2008.
The batting and bowling rankings are obtained from the models developed as part of my Masters and PhD degrees at the University of Auckland. More detail about these models can be found in the papers I have published, which can be found in the Publications section below.
When estimating a player’s current batting ability the model accounts for recent form, venue of matches played in (i.e. home, away or neutral) and whether the player was batting in their team’s first or second innings of the match. Additionally, the model accounts for the “getting your eye in” process for each individual player. The data support the general belief that players tend to score more runs when batting in their team’s first innings of a match, at a home venue.
The “predicted average” is the the number of runs we expect the player to score in their next Test innings, assuming their next innings is played at a neutral venue and it is unknown whether they are batting in their team’s first or second innings of the match. The official International Cricket Council (ICC) ratings (and world ranking #) are also provided for comparison. The ranking of players is generally similar between the two methods, although there are a couple of notable differences.
Firstly, our model rewards players who are able to overcome the “getting your eye in” process and remain on a not out score, while the ICC ratings simply provide not out innings with a “bonus” that we susepct is too low. For example, Rohit Sharma has a number of 50+ not out scores, suggesting he frequently overcomes the difficult “getting your eye in” process, but for various reasons, has not had the opportunities to convert these not out innings into big scores.
Secondly, the ICC ratings tend to place more emphasis on recent innings compared with our models. Our general findings suggest that there is little evidence to suggest that recent form is a significant predictor of current batting ability for the majority of players. Instead, we believe a player’s underlying ability tends to change slowly over time, rather than erratically between innings as a direct result of recent performances. It is unclear whether the ICC ratings attempt to provide predictive accuracy of ability, or instead tries to formalise expert judgement about who is in and out of form. These two goals may not be entirely compatible.
Thirdly, the ICC apply a rating decay system, whereby players who have not batted in a recent match, see their rating slowly
decline. While well intentioned to reflect the best current batsmen in the world, the decay system is inherently biased as it tends to affect smaller nations disproportionately, who are generally afforded fewer opportunities to play Test cricket.
Finally, while both methods provide a general indication of batting ability, by measuring underlying batting ability in units of a batting average, rather than arbitrary “rating points”, we are able to maintain an intuitive cricketing interpretation when comparing players. Instead of concluding “Steve Smith is 99 rating points better than Kane Williamson”, we can make more meaningful probabilistic statements, such as “we expect Steve Smith to outscore Kane Williamson by 10 runs in their next respective innings”, or “we expect Steve Smith has a 59.9% chance of outscoring Kane Williamson in their next respective innings”. In both statements we are assuming a neutral venue and it is unknown whether they are batting in their team’s first or second innings of the match. Of course, we can update these estimates to include match-specific information, if we know the venue of the next match and whether the player is batting in their team’s first or second innings of the match.
Like the batting rankings, the model used to predict current player bowling ability accounts for recent form, venue of matches played in (i.e. home, away or neutral) and whether the player was bowling in their team’s first or second innings of the match.The bowling model also adjusts for the historic strength of opposition batsmen they have bowled to.
In order to make this adjustment, a new metric, “adjusted bowling average”, has been derived, representing a player’s career bowling average if they had bowled to the “average” Test match batsman their entire career. Introducing this metric allows for a fairer comparison of bowling performances, as the relative strengths of batsmen bowled to is accounted for. The derivation of this metric can be found in my PhD thesis in the Publications section below (as of 18th December 2020).
The “predicted adjusted average” is the the number of runs we expect the player to concede before taking their next wicket, assuming they are bowling to the “average” Test match batsmen and the match is being played at a neutral venue. The official International Cricket Council (ICC) ratings (and world ranking #) are also provided for comparison.
Visualising player ability
Here you can find an application that allows users to visualise how these model estimate changes in player batting and bowling ability, on two scales:
1. Long-term changes in batting and bowling ability that occur between innings, over a playing career, providing an estimate of a player’s career trajectory to date, as well as a prediction for their current and future ability. These estimates are what are used to compute our batting and bowling rankings rankings.
2. Short-term changes in batting ability that occur during an innings due to the “getting your eye in” process.
Stevenson, O. G., & Brewer, B. J. Finding your feet: a Gaussian process model for estimating the abilities of batsmen in Test cricket. Submitted to Journal of the Royal Statistical Society: Series C (Applied Statistics). Preprint.
Stevenson, O. G., & Brewer, B. J. (2018). Modelling career trajectories of cricket players using Gaussian processes. In R. Argiento, D. Durante, & S. Wade (Eds.), Bayesian Statistics and New Generations: Proceedings of the 2018 Bayesian Young Statisticians Meeting (pp. 165-173). Springer, Cham. Preprint.
Stevenson, O. G., & Brewer, B. J. (2017). Bayesian survival analysis of batsmen in Test cricket. Journal of Quantitative Analysis in Sports, 13(1), 25-36. Preprint.
Stevenson, O. G. (2017). The Nervous 90s: A Bayesian Analysis of Batting in Test Cricket. Masters thesis, University of Auckland. Online version.
Blog & News
The models I have been developing to measure how player batting ability varies and fluctuate over the course of a playing career, were recently featured in the July 2019 edition of the New Zealand eScience Infrastructure (NeSI) newsletter.read more
The research I undertook as part of my Masters degree was recently featured on the University of Auckland’s, Department of Statistics webpage.read more
University of Auckland | Department of Statistics | Room 303S.376