## An English Cricketing Carol Russell Degnan

Almost a decade ago, as Australia reeled from back-to-back Ashes losses, I put together a piece that put Australia's historical batting performance in context. The conclusion, that while those losses were below recent peaks, they were consistent with Australia's historical performance and what you'd expect to see given a largely random availability of elite talent within their talent pool.

As England reel, not from back-to-back Ashes losses, but an historically poor batting performance from the top-order that is not Joe Root, it is worth re-examining those statistics from the other side. They show that, while England is not performing wildly below expectations, there are underlying issues that are making it increasingly difficult for England to compete with Australia regularly.

It is odd, in one way, to look at England's Test performance, because the underlying definition of "Test cricket" is "how good is a team, relative to England". England are the base case, the stable comparative, always armed with some capable seamers, technically correct batters and one or two all-rounders who are neither, but win the odd game. They have had good and bad sides of late, but they haven't tended to reach the highs or lows of other teams.

The ghost of cricketing past

Historically, by which I mean, across the entire history of Test cricket, England and Australia have been well matched, with Australia having a slight edge. That said, the periods that England have been dominant have got shorter and less frequent over many decades. The graph below looks at this through the lens of my ratings, highlighting in blue where one team would be rated high enough to win both home and away, and tracking a decadal average gap relative to home advantage (100 rating points or 50 runs) between the teams in green.

A trend line would show Australia getting more dominant, but that would be driven somewhat by the relative performances of England at the turn of the 20th century and Australia at the turn of the 21st. Across a decade Australia has averaged more than home advantage on only four occasions: immediately after World War I, the age of Bradman, the age of McGrath and Warne, and the last five years. England have not done so since 1886-1895 but they got close in Australia's slump from 1978-1987. About 36% of the time the two teams have been evenly matched, such that each would be expected to win at home, and lose away. You could reasonably conclude from this graph though, that England have, largely been a reasonable side, but sometimes inferior to a great side.

That perception that England have been a consistent side is largely borne out in the batting statistics. Here I have taken the three year average of each position in the order, to eliminate the vagaries of selection changes, and the immediacy of who they play.

In the post-war period England have consistently averaged slightly above 35 with their top-six. That average was a little higher in the 1950s and 1960s, and has had a little bit of variability, especially with the team from 2009-2011. The last four years have been below that historical average, but the markedly poor outcome in 2021 includes only one year of data, and a regression back to the mean is likely. England though, are a team that has always had a solid and consistent top-6, with perhaps fewer names hitting the heights above 50 than other nations.

Not having looked at the bowling, and it is the bowling that wins games, this only loosely translates to results, but those results - being slightly worse than Australia across a long period - are consistent with the same graph for Australia.

In this case, a higher level of variability, marked by an average typically above 40 for most of the past 30 years. It is worth noting here too, that England is a more difficult place to bat, generally, than other parts of the world, and that is likely to impact England's batting averages. This was particularly true last year, when they played the three top sides in Test cricket. For the most part I'll be comparing the trajectory of change, not the absolute values of averages.

The ghost of cricketing present

It's here I'd like to talk about player production. It is easy to focus on the Test side and lose site of the broader context, but think of a cricketing nation from the base: hundreds of thousands of players, normally distributed in terms of talent, the worst playing for some hack village side, the best couple of hundred playing first-class cricket, and the best six batting for their country. That tiny tip of the distribution is the selection quandary, but it is the big broad base that defines who will be available for selection.

In the graph below (from 1945 to 1972) you can see the probability that in any particular year, that position in the top-6 averaged that amount. Averages over 50 were quite rare with around 15% of players for both Australia and England; the median average was around 40, and then it drops off. Some small percentage of years, a position would average less than 20, but with relatively few Tests each year, that could happen, as performance itself will be somewhat randomly distributed.

There are three other things worth noting from this graph. The first is the idea of a "replacement player". That is, if you picked the next best player out of County Cricket, what would the average in the Test side: the seventh best player, in other words. In practice, the seventh best player in the nation is probably about as good as the sixth best. The normal curve of talent distribution gets fatter as you go along, and while any individual may underperform in any one year, their true talent is going to be roughly where this line ought to cross the 100% mark if you projected the first 50% up. Assumign this is about the 80th percentile, for Australia, across all post-war players, that historical replacement player will average about 33. For England about 30, and for New Zealand, about 23.

The second thing to notice about this graph is that England close the gap to Australia. Fewer players averaging over 50 than anyone other than New Zealand but more players averaging 35 than anyone other than Australia, and closing that gap to them. There is an ongoing question in English cricket about the number of County sides, and this graph supports why that is, in my opinion, misplaced.

Consider the career arc of an average Test cricketer. They come out of school at 18, struggle to find a place at first-class level for several years until 22 to 24, reach their prime and the Test side around 27 years old, get dropped around 30 years old, then play a few years at first-class level, passing on their experience to the next generation.

In order for a player to push for Test selection in their late 20s they need to stay in the system in their early 20s. That means having professional contracts and support in a period when they probably aren't good enough for first-class cricket. Having more counties helps this, because it provides opportunities to keep talent around, particularly late bloomers. Greg Chappell had a theory, based on the trajectory of transcendent talents, that if a player was not showing by age 24 they should move out for someone else. The impact of this approach was to dillute the quality of the Shield competition (particularly the second XIs) and lose players before they reached their peaks. England's greater ability to find replacement level players who can average 35 is a testament to the larger system, and their ability to ensure that an 18 year old potential Test players are able to find opportunities within their first class system.

By contrast, Australia's tendency to pick undercooked 22 year olds in the hope they learn on the job does not always help the Test side. In more specialised positions, like spinners, there just aren't enough spots across the six Shield sides to provide a learning environment for young players, with Test spinners picked more in hope than anticipation. Introducing substitutes for the third innings would help get around this issue, but it remains a pipe dream.

The final thing to take from this graph is the proportion of players at each average for each nation, and the probability each team has of finding them. Australia and New Zealand have a reasonably consistent gap across the entire spectrum of averages, where Australia is roughly 2.5-3 times as likely to have a player in their side with that average than their smaller neighbour. That doesn't rule New Zealand out from getting a great collection of talent in any particular year. But it does mean, as a rule of thumb, that Australia will generally have a player averaging 50+ and a couple average 40+, while New Zealand are more likely to have one averaging 45+, and a couple averaging 35+. This is borne out in their historical averages, noting a gradual improvement over time.

The ghost of cricketing future

If we switch our focus to the last 25 years you see a quite different prduction function from the post-war period. Most obviously, there has been a general improvement in batting average across the world, with the notable exceptions of the West Indies (alarmingly!), and England.

Large parts of this period were poor for England results-wise, so much as Australia has been ahistorically strong, it could be argued England have been ahistorically mediocre. But they have shifted from being on par with Australia in the post-war period, to well behind, and it is reasonable to suspect there are greater headwinds than the vagaries of player development.

At the turn of the 20th century Australia looked to England as the paragon of quality cricket. They were a superior side, even when best amateurs didn't tour, but Australia was capable of producing great cricketers, and won plenty of games. England had a healthy demographic advantage though, and it showed, with almost 9 times as many people as their antipodean colony.

Australia has grown markedly faster (percentage-wise) than England across the last 100 years however. By 1960, that population ratio had dropped to 4.5. In cricketing terms, with Australia's broader cricketing popularity that crossed class barriers, 1960 also appears to be the inflection point, when Australia were consistently producing batters to match England. And while England had a period of relative superiority across the 1970s and 1980s, that merely masked that they were slowly falling behind.

As of 2020, England's population remains 2.3 times as large as Australia's, but adjusting for the relative popularity of cricket, Australia's production function is almost double England's. In other words, for every Joe Root England has in their side, Australia will have two (Smith and Labuschagne), for every Anderson, a Cummins and Hazlewood. Whereas Australia's replacement player averages around 36 across the last 25 years, England's averages 30.

While England will continue to look to the Ashes as their rivalry series, the modelling suggests that majority of the time, England will be competitive at home and flogged away. In fact, while the finances will say otherwise, the more interesting series is less likely to be the Ashes than that against Australia's smaller neighbour.

While England's population remains 10 times that of New Zealand, the latter is a much more efficient producer of cricketers, versus their population. There are fewer competing sports, and the smaller base of players has made recognition easier. When New Zealand entered Test cricket in the 1930s the production gap was around 3.5, but it is down to only 1.5 now, and their current side is one of the best in the world, and with some recent debuts playing well, expected to stay there for a while yet.

There are other reasons to suspect that England's future production will be worse than even this relative decline though. England's class gap has deteriorated over the past 15 years following the shift from Free-to-Air television. Cricket was always an upper-middle-class sport, but no amount of targeted advertising can make up for day-in-day-out cricket coverage over a summer, and it takes a lot of coaching to make up for young cricketers being able to emulate the players they see on television.

The ECB does not operate a census, unlike Australia, New Zealand and every associate nation, so we need to draw on alternate, and less consistent measurements for participation. Sport England has only been tracking participation since 2015, but this still showed a 20% drop to 2019, before a World Cup bump (of 15%) and a Coronavirus drop (of closer to 40%).

Where English cricket lands in the coming years in terms of participation remains to be seen. There is, at least, some acknowledgement that the current numbers are not adequately drawing on the resources of the nation. The next generation (those currently aged between 20 and 25) grew up with the 2005-2011 English team that was the best of any English side over the past 50 years.

But if that generation fizzles out over the next five years; if the opportunities that come with a successful team to build a larger base of participation for future success were squandered; then the post-Anderson/Root/Stokes team will be depressing viewing for English fans.

Which is not to say that England will not have good or even great teams in the future; New Zealand are the World Test Champions after all. But unless they can boost participation, which is a 20-year goal, not a short-term option, then it is increasingly likely that England will perform closer to New Zealand's test record in Australia (won 3, drawn 11, lost 20) and England's since 2000 (won 4, drawn 2, lost 22) than their record from 1970 to 2000 (won 13, drawn 14, lost 21) which will make series victories infrequent at best.

Cricket - Articles 2nd January, 2022 13:09:55   [#] [0 comments]

## A bad format, associates or not Russell Degnan

The long lamented and dreaded ten-team World Cup has finally started and the arguments over the format are unlikely to cease until the trophy has been lifted if not after.

Strangely, within the general public, the argument over whether Associates should be included has been largely won. That doesn't mean the ICC will change the format, but the change from a decade ago when a smaller World Cup was the majority position amongst journalists to now reflects a growing realisation that the game depends on its smaller (actually, mid-sized) nations.

The question for this World Cup will be not whether it lacks something without the Associate teams, but whether a ten-team World Cup is what the ICC promised: the most competitive and exciting format, harking back to 1992; or just a money-making exercise by guaranteeing India nine matches.

Bertus de Jong has been a consistent voice for reason on the problems with a ten-team league-format World Cup and highlighted several on twitter around the narrative that such a long group stage brings.

My position has always been that there is no "right number" rationale for twelve, fourteen or sixteen teams over ten, eight or six. Obviously, fewer teams will have smaller gaps in performance between best and worst - though not necessarily more competitive matches. Equally obviously, large groups where a team can lose many games and still qualify, or be knocked out with matches still to play will have more dead-rubbers than knock-outs. To some extent the "correct" size of a World Cup is the one that allows all the members a reasonable opportunity to participate.

Almost ten years ago, when the ten-team tournament was first mooted, I wrote about how large a World Cup should be noting that cricket was far removed from the roughly six-to-one ration of Association Football and Rugby Union.

I also highlighted five myths that had been inflicted on the debate at that time:

1. That more teams led to a longer World Cup when that is derived from the format;
2. That low odds of victory for teams with lower ranks against the top teams is normal in sport;
3. That cricket doesn't have sufficient depth for a large World Cup;
4. That a larger World Cup has more pointless matches; and
5. That the only purpose of a World Cup is to anoint a winner: that many teams participate to reach the next stage, or just to get there.

The third and fourth points are particularly important because they speak to the quality of the viewing experience. A few months afterwards, not satisfied with a hand-waving explanation I put forward an analytical method to look at formats. Put simply, the excitement inherent to a match is related to the change in probable outcomes.

There are beautiful match graphs for baseball that look at probabilities within a game. They show the probability of victory as a game progresses, and it is easy to see the difference between the very exciting (such as the Red Sox-Indians game shown) where the probability of each team winning shifts violently, and the not (Giants-Athletic) where it remains the same throughout.

We can assess the likely excitement of a World Cup match against a similar formula. In this case, the expected change in the probability of each team qualifying for the next stage of the World Cup.

Start with a simple example: in a knockout between evenly matched teams the probability of progressing for both starts at 50% and ends at either 0% or 100%. The change in probability adds to 1.00

A tournament where the expected change in probability was always 1.00 would be non-stop excitement. However it is also impossible. Between non-evenly matched teams the expected change in probability drops substantially.

In group matches the expected change drops further. An evenly matched four-team group has slightly less than half the excitement per game of a knockout at around 0.46. A calculation of the 2014 FIFA World Cup where teams are not equal produced an average expected change of around 0.35.

The perfect tournament would maximise the expected change in probability within other constraints - making sure each team plays a few games, getting enough content for television and so forth. The Cricket World Cup had a TV deal requiring at least 48 matches which rules out a simple 16-team with four groups of 4 and knockouts. But since 2003 it has had formats with at least this number of matches.

By simulating each round of previous World Cups we can assess them against how exciting they ought to have been. For the most part, since the small cups from 1975-1987: pretty fucking bad. Note that the key column to look at here is the simulated result, remembering that it should be as close to 1.00 as possible.

(Note that super-6 and super-8 games were not replayed. I have not adjusted for any additional interest factor from the first round matches because it is not clear how to do so).

1999 was the best World Cup format of recent times. Not surprising then that it is well remembered amongst everyone who wasn't an English journalist. 2007 was unlucky: the first round was actually exciting, but the second round was very long and it lacked take-off as the 8-team round-robin drifted over many weeks. Recent cups have also been poor by this measure, but the 10-team World Cup will be the worst ever for interest. And it is not close. We might get lucky with multiple contenders at the pointy-end but don't bet on it and it will be a loooong journey.

The best formats offer incentives to all teams. The recently axed World Cricket League tournaments with 6 teams, 2-up, 2-down were inherently exciting because the margin between qualification and relegation was thin. Teams expected change in probability was an average of 0.18 on both measures, giving a combined 0.36 per match.

It is for this reason that I landed on my preferred 20-team format that sends first place to a quarter-final and second and third to a repechage. First place in the group would be strongly incentivised as the winner can both skip the round of 16 and play an easier quarter-final opponent. So much so that the probability of overall victory is roughly double than for coming second or third place. More importantly, the depth of associate cricket is such that all five teams in the group would have a reasonable change of qualification in at least third place, removing the just-hear-for-the-scenery nature of most associate participation to date.

Based on rankings after the qualification tournament for 2019 a 20-team would have looked like this:

By running a similar simulation on both that format and a 32-team World Cup we can assess them against the formats to date. a 32-team World Cup would be a bridge too far - and yet still be better than a 10-team one! But a 20-team competition with a repechage and eleven knockout matches has sufficient uncertainty that it would be the best since the 8-team format last used in 1987.

Would a better format make up for lost revenue when India doesn't slog through 9 games over two months? Perhaps not, but it is not as far off as might be expected. A calculation of revenue based on Indian TV ratings indicated that the loss would be as small as 10%. And because it is based on a more reliable revenue stream than interest in one team, it would retain value even if India flame out early.

Given the flow-on benefits to participating teams in terms of sponsorship and recognition, a larger World Cup should be a no-brainer. But, here we are, almost 10 years after it was first announced, a 10-team World Cup.
Bring coffee, you'll need it.

Cricket - Articles 1st June, 2019 22:41:34   [#] [0 comments]

## The WSC Transition Russell Degnan

Bradman and Packer: The deal that changed cricket - Dan Brettig

Of the various revolutions to convulse cricket since its inception, the Packer one has garnered the most attention, and courtesy of several decades of Nine commentators, the most praise.

In its own way though, it was the least impactful on the nature of cricket. The International revolution, when Australia first defeated England in 1877 then, more importantly, followed up with tours and further victories in England was part of a continuum of touring sides dating to William Clarke's All England Eleven. But the Australian Eleven was a box-office draw like no other, and set the shape of international Test Match tours that continues almost unabated to this day.

The Board of Control takeover, from 1905-1912, that saw tours shift from the hands of Player's Elevens to national boards, concomitant with the founding of the ICC was less revolutionary, with almost no impact on the general public, but had enormous influence on the nature of cricket administration and player payments that eventually led to World Series Cricket 70 years later. More recently, the advent of domestic T20 has had more significant impacts on the shape of cricket than any event since the advent of the International game.

The ructions caused by World Series Cricket were significant, but short lived. The "peace treaty" was signed in 1979, but the public face of cricket, particularly in Australia was changed forever.

Most histories focus on those public changes: the white balls, coloured clothes and changed emphasis to ODI cricket. Dan Brettig's new book focuses on the private changes, and most importantly, the role of Australian cricket's most important figure: Donald Bradman. In doing so, it makes the Packer revolution look less like a revolution, and more like an extended transition from amateur to professional cricket board.

International cricket boards exist for three purposes: to administer the game, to act as a monopoly employer of cricket talent, and to sell a product. The Board of Control takeover was a victory for the first of these tasks at the expense of the latter. In the Board's eyes, the player led tours were reaping undue rewards from a product they had no right to control. It was a victory for establishment amateurism and sporting purity.

Bradman came into international cricket 16 years after the Board takeover in the dying days of players having control of their income. League cricket - with more in common with today's T20 leagues than County cricket - could still lure Sydney Barnes and Learie Constantine with reasonable salaries; and some of the older Australian test players had played with those of the earlier era of player control. Some, like Victor Richardson, had markedly different approaches on and off the field to Bradman who, despite an early run-in with the Board, was philosophically and politically inclined to the establishment. As a member (and for most of that period, Chairman) of the Board for 35 years he did more than any other to entrench a Board approach that focused on the administration of cricket at the expense of labour.

The graph above provides an inflation adjusted (to 2012) summary of cricketing salaries from 1893 to 2018, taken from Trove news articles and Brettig's research for the WSC/PBL era. The Players era pre-1912 provided variable but healthy incomes from tours to England (and therefore higher when home receipts are considered) that exceeded what cricketers would earn from the game until the Packer revolution.

Not that tours were unprofitable (at least to England) in the ACB-era. Players could expect around 50,000 in today's money for their six months on tour. It was the home salaries that lagged, and even a late increase (undercut by rising inflation) prior to World Series Cricket did little to bridge the gap between what they earnt, and what Packer was willing to pay.

Brettig picks up the story in 1979. Both Packer and the ACB were haemorrhaging money trying to compete for local interest, the ACB for lack of star players and control of their game, and Packer for lack of cost control. The untold story, until now, of Bradman and Packer agreeing to treat for a resolution puts these into perspective. Packer had no need to retain either the players nor overall control of cricket; his interests lay in selling the product and in Bradman he found an unlikely ally.

The stability of player incomes over almost 50 years was underpinned by the inherent conservatism of the Board. Its membership was driven by continuity. A certain amount of income was received from ticket sales, an amount allocated to associations and player expenses. Bradman didn't believe in full professionalism, but he did believe in attractive cricket and his later writings showed plenty of willingness to embrace innovation in the game. Unlike most of the board, paralysed by fury and disbelief, Bradman was pragmatic and readily acceded to Packer having not only the TV rights, but the marketing of the game via PBL in exchange for certainty and control.

The deal was a fleecing of the ACB, but it made sense for a Board entrenched in the amateur era. As Brettig describes the post-WSC period, it took almost a decade and a South African rebel for the ACB to realise that they were seeing a fraction of the money coming in to cricket. For players on the ACB books, renumeration was well above the pre-WSC era, but remained well below what it could have been.

There was a further issue with PBL having marketing control of the game, and that was their focus on ODI cricket as the core product of Nine's summer. Test matches and ODIs were interspersed throughout the 1980s and early 1990s with the tri-series competition given higher standing and better promotion. Lynton Taylor as Chairman of PBL marketing had no problems telling the ACB that Test cricket was dying. Average crowds declined through the 1980s as Australia struggled, and beyond before reaching a nadir in the early 1990s when the MCG was hosting as many days of ODIs as Test matches with three times the average crowds.

A change had been sweeping through the Australian Cricket Board though. Empowered by younger business oriented members in Malcolm Gray and Graham Halbish, the retirement of Colin Egar and Bradman (officially), and the success in hosting the 1992 World Cup the board took back control of selling their product.

The "revolution" in the management of Australian cricket, that started in 1977 with WSC, became a Board transition that didn't end until 1994 (if not later when it achieved independence from the State Associations). Whereas the Bradman-era Board was unwilling to treat with Packer, then blindsided by his ability and willingness to outbid them for players, the Board from the mid-90s on has been more frequently accused of being for players and product over administration. The players, empowered by the Board's growing income, unionised and ensured their contracts soon jumped far above the y-axis of graph shown above.

The rhythm of cricket changed too. Test cricket returned to the centre, and not unremarkably, soon recovered both crowds and prestige. The ODI tri-series carnival that drip fed cricket into lounge-rooms nightly for the entire summer went into a terminal decline, was progressively shortened, and finally replaced by domestic T20 cricket.

This book provides an important glimpse into these changes, the personalities involved and the downsides to Nine/PBL's control of many aspects of cricket in an era otherwise tinged with nostalgia and a belief that everything changed, when in some important aspects nothing changed at all, and in others the change was fundamental, but much more drawn out than supposed.

Cricket - Articles 4th March, 2019 00:39:38   [#] [0 comments]

## ICC competition reform with Tim Cutler, Associate Cricket Podcast Russell Degnan

The ICC's major reforms to associate playing competitions have been released and former Cricket Hong Kong CEO Tim Cutler (@timcutler) joins Andrew Nixon (@andrewnixon79) joins Russell Degnan (@idlesummers) to discuss that and various other issues. The World T20 sub-regional tournaments contineu and we look back at the Asia East (0:20) and Africa Southern tournaments (4:30) which had a few surprises and almost a major upset, and China and South Korea joined the growing list of teams with official women's T20 matches (8:20). We cover the ICC's new league structures in some detail looking at changes to 50 over, 4 day and 20 over cricket (9:20). The tail end of World Cricket League division three was in play as we recorded and we discuss some of the outcomes of that tournament (27:20) as well as the change in ICC streaming policy. We then turn to match fixing which has been a prominent issue in the past month with associate cricket continuing to encounter significant risks of corruption (42:30). There is news regarding the UAE T20x, the Asian Games, Kinrara Oval in Malaysia and the ICC women's development squad (54:00), and we conclude with previews the World T20 East-Asia Pacific group B and ACC West Zone tournaments (1:06:50).

Direct Download Running Time 69min. Music from Martin Solveig, "Big in Japan"

The associate cricket podcast is an attempt to expand coverage of associate tournaments by obtaining local knowledge of the relevant nations. If you have or intend to go to a tournament at associate level - mens womens, ICC, unaffiliated - then please get in touch in the comments or by email.

Cricket - Associate - Podcast 20th November, 2018 21:19:30   [#] [0 comments]

## Fixing the ICC ratings Russell Degnan

In my post on the fundamental sameness of ratings I implied some criticism of the ICC ratings. Many choices about how to construct a ratings system are (for the most part) either a design choice - home advantage doesn't matter with a large sample and even schedule - or relate to what is trying to be achieved. The decay rate will be different if a rating is supposed to reflect the last 2 months versus the previous two years.

The ICC ratings go to a championship trophy and should therefore reflect the previous 12 months, but with scheduling so uneven that is near impossible, and different choices have been made to provide a relatively simple system.

As discussed in a previous post however, the ICC ratings have some genuine problems. The choice to cap the implied probability at 90% means that for a large number of matches the ratings are a poor reflection of the quality of the sides. Similarly, the choice of decay that reduces then drops previous results causes other issues when the quality of opposition has already been accounted for.

Both of these issues are relatively easy to fix, and this post discusses the benefits of doing so, particularly in a new world where nations with wildly different abilities must both be included in the ratings - as opposed to the full member oriented system where all teams were broadly at the same level.

Changing the implied probability

As noted, the basic issue with the ICC ratings' implied probability is that once teams are more than 40 ranking points apart the ratings assume that the stronger side will win 90% of matches. This pushes the ratings apart - particularly when one side is significantly weaker than their opponents. It also means that the points on offer for wins over strong sides are lower for bad sides than good ones - which limits the ability of the ratings to adapt to changes in ability.

As the graph above shows (the blue ICC lines), once the gap between teams gets above 40 points, their points gained relative to their current rating remain same. The value of a win therefore declines as the probability of them winning decreases. At its most extreme, when sides are rated more than 180 points apart, a strong side will get more points for losing a match than the weaker team will get for winnings it.

The solution is to adjust the points on offer in proportion to the ratings gap of the two teams, as per the red lines in the graph which eventually settle on the stronger side receiving no additional points (ie. their current rating) for a win - an implied probability of 100% - and the weaker team half the ratings gap plus 80 in the unlikely event they win.

The formulas would therefore be as follows:

Ratings gapICC FormulaProposed Formula
Stronger teamWeaker teamStronger teamWeaker team
0-40Win: OppRat + 50
Loss: OppRat - 50
Win: OppRat + 50
Loss: OppRat - 50
Win: OppRat + 50
Loss: OppRat - 50
Win: OppRat + 50
Loss: OppRat - 50
40-90Win: OwnRat + 10
Loss: OwnRat - 90
Win: OwnRat + 10
Loss: OwnRat - 90
Win: 0.1 * OppRat + 0.9 * OwnRat + 14
Loss: 0.6 * OppRat + 0.4 * OwnRat - 66
Win: 0.6 * OppRat + 0.4 * OwnRat + 66
Loss: 0.1 * OppRat + 0.9 * OwnRat - 14
90-180Win: OwnRat + 10
Loss: OwnRat - 90
Win: OwnRat + 10
Loss: OwnRat - 90
Win: 0.05 * OppRat + 0.95 * OwnRat + 9
Loss: 0.55 * OppRat + 0.45 * OwnRat - 71
Win: 0.55 * OppRat + 0.45 * OwnRat + 71
Loss: 0.05 * OppRat + 0.95 * OwnRat - 9
180 plusWin: OwnRat + 10
Loss: OwnRat - 90
Win: OwnRat + 10
Loss: OwnRat - 90
Win: OwnRat
Loss: 0.5 * OppRat + 0.5 * OwnRat - 80
Win: 0.5 * OppRat + 0.5 * OwnRat + 80
Loss: OwnRat

They look more complicated than they are. The existing ICC ratings use either a team's own rating or the opposition. The combination allows the much more gradual increase in points shown above (optimally the area between 0 and 40 would also be curved, but I have chosen to leave it as is).

The changed implied probability shows the benefits of this approach:

Whereas previously teams were either closely matched or a 90% chance of victory, now their approximate chance of victory can be determined across a full range of ratings gaps.

This change would only make subtle changes to the ratings. Bangladesh's improvement a few years ago would have given them a more rapid (and noticeable) boost, reflecting their actual ability rather than their long period of tepid performances. The odd associate upset would have been better reflected in their ratings - when they are included. But as these results are rare, the broader outline of the ratings would be the same. The more important change is to the decay rate.

Changing the decay rate

As a matter of basic maths, if points were to accumulate indefinitely then new matches will have a decreasing effect on the ratings. The ICC works around this in the simplest way - by reducing the previous two years by 50% and excluding anything before that. But it has an unfortunate side effect: each exclusion date, ratings jump, sometimes substantially, and often, in strange directions.

The effect of this change can be seen in a simple example. Here a team plays (and wins or loses matches) at different levels over the course of several years. The true rating of the team in each year (and which, nominally the ratings should reflect) is as follows: 100, 80, 100, 120, 120, 120, 100. The graph shows this shift (at the start of the year) and the impact of the ICC decay formula (at the end of each year).

Notice that, because the previous year is reduced to 50% in preparation for a new year, the rating shifts away from the true rating at the end of the second and third years as old results are re-weighted up relative to the past year. The ICC rating eventually meets the true rating only if the team has maintained the same rating for two years, otherwise it is often substantially far from correct.

The oddity with the simple choice of decay is that it is also unnecessary. The "natural" way to ensure old results do not impact the rating without unseemly jumps is to merely divide both the points accumulated and the number of matches by an amount. In the graph above this was 3, effectively reducing the impact of old results by a third each year (and by a ninth the following year).

The proposed system never quite matches the yellow line - though arguably nor should it - but it is consistently closer than the ICC and gradually gets closer the longer a team stays at the same level (in the third year of ratings at 120 it reaches 119).

More importantly, there are no jumps. As both points and weights are declined by the same amount, a team stays on the same rating until they play. Which is exactly how it should be.

Cricket - Analysis 23rd October, 2018 23:33:04   [#] [0 comments]

## The fundamental sameness of ratings Russell Degnan

Two things generally hold for any half-way reputable ratings system:

1. Some observers will criticise a particular ranking because they've forgotten a set of results occurred.
2. The basic result will look the same as everybody elses. The good teams will be good, the bad teams will be bad and there will be a big blob in the middle.

It is hard to fuck up a ratings system.

People do. But since in its most basic format, a league table is a ratings system, and a league table will usually give a decent approximation of the best and worst teams, it is quite hard to do worse.

It is worth considering its constituent elements though, for anyone planning to construct one, to outline the basic issues of design, and problems in scheduling structures that bring them undone (or need to be corrected for). To do this I'll look at five systems: a basic league table (which as noted, is a form of rating), the ICC system for cricket, the IRB system for rugby, Elo (which is widely used, but I'll focus on football) and my own cricket ratings.

Margin of victory

Your standard results-based backward-looking rating system (there may be others but they aren't widely used) bring together a set of results and project the quality (and possibly future performance) of teams based on games played. There are two basic two options for the result: the result; or the margin of victory.

A league table and the ICC use just the result. The IRB has a little each way by providing a bonus for a larger margin of victory, while the Elo soccer rating and my own cricket ratings use the margin of victory. The benefit of using the margin is that it provides more information, particularly in sports where the result is relatively predictable but it might reasonably be considered that there is a Pythagorean relationship between the points differential and eventual wins.

One thing I have considered but not implemented was to account for Test draws by examining "distance to victory". Hence a drawn match with one side 100 runs in arrears and the other needing 2 wickets would have a margin of 100 - 2 wickets (nominally 50 runs in my ratings). A non-linear relationship for wickets is another margin option to consider. Note that the added accuracy of these changes is marginal at best.

Strength of opposition

Here lies the first leap forward from a basic league table: the measuring of schedules. In many leagues this is not strictly necessary as the schedules are relatively even. In cricket it is nonsense to forgo it.

Accounting for opposition means having an implied probability of victory. That is: if an average team (50% probability of winning against an average team) is expected to win less than half of the matches against their schedule, then the points awarded are increased to make up the deficit. All ratings have an implied probability of victory, but the results vary.

My ratings are margin based - though there are adjustments for wins/draws - and use a "normal" implied probability around a standard deviation of 180 runs. Basic Elo ratings are based on three results (win/loss/draw) and therefore use a different function. Both of these are smooth curves, as per the image.

The ICC and IRB use linear models. The downside to linear models is that eventually teams hit a limit of 0% or 100% probability of victory, in which case their rating cannot increase (or decrease) in proportion to their ability versus their peers. For the IRB, this caps the maximum rating difference at 10 points (100% likely to win) - bonuses have got New Zealand up this limit, but the only way is down.

The ICC does something quite strange - on which more details can be found in this older post - which is to cut the implied probability at 90%. Teams above this threshold can theoretically keep increasing their rating to infinity, and vice versa (which is why a number of teams have been marooned around zero. There are ways this could be fixed, but will be the subject of a later post.

Strength at home

Adjustments to the implied probability are often made for home advantage. This is not strictly necessary as the difference is marginal, but if a schedule is sufficiently unbalanced it can be necessary.

A league table (needless to say) doesn't do so, and nor does the ICC. The other systems being examined do and the implied increase in probability given a ratings gap is shown above. Note that the IRB is linear as it merely shifts the system by 3 points. For Elo and my own ratings the greatest increase in probability is in the centre (around 50%) as that is where the variability is highest. A 1% probability of victory doesn't tend to shift regardless of home advantage.

Some systems extend this further by having a "home" and "away" rating that allows variation in the quality of home field advantage. The upside to this is that some teams are substantially better at home (teams at altitude for example) or poor away (isolated teams needing to travel) and this allows that to be accounted for. The downside is that it halves the amount of data - which for cricket is already sparse - unless some combination of recent home and away results is made. The standard method of adjusting for home advantage as if it is always the same isn't perfect but no rating system is. There are always trade-offs and the biggest is yet to come.

Recency of results

The fundamental difference between most systems is the speed and method by which they exclude results. Prediction models generally show that the more data put in the more closely the predictions run, which would imply that recent results should decay very slowly. However, no team stays the same, personnel changes, improves and declines, there is an element of form (perhaps indistinguishable with luck) and injuries will subtract and then add to quality just as the rating adjusts. There is no right answer.

Seasons offer a simple method, and a league table that resets to zero is as good a method as any if you don't want to predict results during the season. Conversely, it is a complex and unknown question how to adjust ratings from the previous season. FiveThirtyEight's Elo models converge to the mean, producing strange zig-zags for persistently strong sides. Leaving the rating as the previous season is not any better though. The most promising method if seasonal boundaries are fixed is to substantially lower the weight of old results, such that new results drive fast change, then get embedded in.

My ratings had a series of more complex issues to solve, and therefore decay in strange ways. Firstly, historically some teams played relatively infrequently - South Africa in the 1960s being the canonical example - which meant that when their ability moved, a differential system (as used by Elo or the IRB) would shift the teams with well-known ratings just as much as the team with few results. The first change was to add a weighted shift for number of results.

Secondly, the sparseness of matches and clumped schedule where teams would play the same side five times in a row means that there times when a rating needed to either shift rapidly or return to a spot after one bad (or good) tour. The solution was to keep a "form" variable that would add to the change if the direction of change was aligned. The "decay" of my ratings is therefore not a straight line, but an area: the top-line being relatively slow, and the bottom relatively quick, but converging after a couple of years.

As noted previously, the ICC ratings make strange and unnecessary choices regarding their result recency and every year the shift in ratings when no games have been played makes that clear. That aside though, the choice of decay is driven largely by the number of matches being played (and therefore the amount of data) and a personal preference for monitoring form. There is no correct answer, as even if the aim was to predict future results, there is unlikely to be a high level of consistency from one year to the next between models.

Baselining

The final element to ratings is actually the most complex element of all. For many leagues, where continuity is taken for granted, a baseline only matters as a point of historical interest. For others, such as the Elo chess ratings, where the volume of participants entering and leaving is high, there can be an impact on inflation, but not relative ability.

Cricket, and to an extent football, have their issues with baselining though, and it is worth considering them. Firstly, the introduction of new participants into a small closed system (like full member cricket) means adding a team at a level below the others that may (at some future point) be level with them. I rebaselined my ratings to 1000 for each of the first ten full members (using first-class ratings for Ireland and Afghanistan), and took their first rating as the lowest current member.

This is definitely wrong, as seen by the sharp drop in the rating of Bangladesh on entry to Test Cricket. The alternative is to run a new entry forward until they settle and then add them. But because of the accelerated decay detailed above, the wait for Bangladesh to find their level was short.

The second issue is more complex, and more likely to matter in other sports. In cricket, most teams don't play each other. To a degree even the full members don't play each other, but the standard rating system works by transivity: A > B and B > C means A > C. As long as a subset of teams play a random number of teams in the overall set of teams a rating system will work.

But this doesn't always happen. In cricket the full members play, and the associate members play (also split into tiers and regions), and on rare occasions there is a small set of matches between subsets of each of those sets.

Thus while the relative strength of each column of teams within a "league" is set, there are rarely enough games between teams in other leagues to be able to baseline the leagues against each other. In the diagram above each tier could be shifted up or down relative to the others, as only one or two teams is playing in each. Recently (and finally) the ICC extended their rating system to all Women's T20 International teams. it is a welcome change but some teams (such as Argentina) have not played outside their region for some years, while others (such as PNG) play a handful of matches outside their region every few years. If EAP was to improve, then PNG (as their only representative) will gain points internationally, then lose them to their regional rivals. The imbalance will change, but slowly, as PNG shuffle points back and forwards like fetching water from a well.

Football suffers a similar issue with relatively few inter-regional tournaments (like the World Cup) internationally or (the Champions League) domestically. Any ranking system that combines different subsets should be approached warily, though a correction is nearly impossible to provide.

The solution, probably, is to provide a regional subset adjustment system, whereby teams are weighted by their games within each subset and the whole subset shifted as the ranking of any member in the set changes. This would maintain the relative distance between all teams using the information we know - the relative rank of each team in their subset and the relative results of a representative team in the subset against a representative of another subset - and adjust the information we don't - the relative rank of each team in the whole set. Unfortunately, in Test cricket, the total number of matches between Test and Associate subsets is two and the Associate subset wasn't too well known anyway.

For the ICC, the benefits of a global ranking system will outweigh the complaints from the small handful of people following cricket in the Associates closely enough to notice oddities in the rankings. And if you do want to complain, remember, ratings systems make a lot of choices, and in most cases it isn't clear which are better - though I obviously have my opinion.

And anyway, they are all much the same. It is hard to fuck up a ratings system.

Cricket - Analysis 14th October, 2018 22:16:14   [#] [0 comments]

## Americas WT20 Qualifier Review, Associate Cricket Podcast Russell Degnan

As we switch from northern to southern summers there are tournaments across the world, and Andrew Nixon (@andrewnixon79) joins Russell Degnan (@idlesummers) to cover them all. Hong Kong gave India a scare in the Asia Cup (0:20), USA and Canada qualified for the next stage of the Americas WT20 qualifier (6:20), there were improved associate performances in the Africa T20 Cup (9:30) and we look at the East Asian Cup (13:00), and Stan Nagaiah Trophy (15:40). There is ICC news on the olympics and associate status (16:20) and a preview of the Asia (East) WT20 qualifiers and Hong Kong tour of PNG (23:00).

Direct Download Running Time 29min. Music from Martin Solveig, "Big in Japan"

The associate cricket podcast is an attempt to expand coverage of associate tournaments by obtaining local knowledge of the relevant nations. If you have or intend to go to a tournament at associate level - mens womens, ICC, unaffiliated - then please get in touch in the comments or by email.

Cricket - Associate - Podcast 1st October, 2018 21:46:18   [#] [0 comments]

## Women's World T20 Qualifier Review; Associate Cricket Podcast Russell Degnan

Andrew Nixon (@andrewnixon79) joins Russell Degnan (@idlesummers) for a big episode covering a wide range of men's and women's tournaments over the past two months. The Women's World T20 Championship Qualifier (0:20) and further mens World T20 qualifiers from Africa, East-Asia and Europe were played with more teams progressing to the regional qualifiers (5:30). Hong Kong came through the ODI Asian Cup qualifiers in a fascinating tournament (18:10) and the South American Championships returned with Brazil winning the women's event and Mexico the men's (24:10). There was also an African Women's tournament in Botswana (29:10), U/19 qualifiers in Africa and Europe (37:20) and numerous bilateral series (40:50). There is news from USA and Kenya (44:30), and we preview the Americas Group A World T20 qualifier amongst other tournaments (51:10).

Direct Download Running Time 55min. Music from Martin Solveig, "Big in Japan"

The associate cricket podcast is an attempt to expand coverage of associate tournaments by obtaining local knowledge of the relevant nations. If you have or intend to go to a tournament at associate level - mens womens, ICC, unaffiliated - then please get in touch in the comments or by email.

Cricket - Associate - Podcast 15th September, 2018 00:21:47   [#] [0 comments]