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.


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] 

The performance outcome cliff of early professionalism
Russell Degnan

The last decade has seen professional contracts expand across both associate and women's cricket. The opportunities have improved player skills, and undoubtedly history will be kind to the first generation of professional players wherever that has occurred. But it also causes a problem. One that has manifested in many of the teams across the world over many years, both at international and first class level.

Namely: if you give a small number of elite players generous contracts to improve performance, the next generation won't be able to displace them until they are in steep decline.

It was a problem, misdiagnosed largely, when Australian first class cricket aged considerably in the early 2000s, with the Kenyan team of the same era, and more latterly, with the English women, and the Irish team, both of whom bemoan the lack of emerging youth.

The phenomenon is best demonstrated with a simulation. In the graph below, five careers overlap, with different starts, peaks and lengths. The blue lines represent the best outcome for a player (continually professionally contracted), the red lines represent a player contracted only if they were in the top two players in the previous year. They receive a 10% performance jump in the first year, and 25% in subsequent years, while contracted. The thick lines are the average of the top two players

In an optimum selection outcome, players A and B would be selected through years 7-12, A making way for C until year 14, B for D until year 16, C for E until year 18, when C returns for D at the end of their short but prolific peak. The selected pair maintaining an average of close to 50 from year 10 until 18.

In the selection outcome with limited contracts, A's declining performance is not matched by an under-developed C until year 14, when they are actually replaced by D. C comes into the side for B a year later, but the lack of experience means the average drops into the low 40s from year 13 to 17. E, similarly, does not emerge from D's shadow until year 19, causing another gap from optimum to selection to form.

The numbers in the simulation are made up - if hopefully in the appropriate ballpark. We don't know what the performance advantage of a professional contract is, and there is still a glaring hole in the research over peak performance years. But the general shape will be correct, and that points to a gap between potential performance and what teams get on the field.

This may not be the problem right now. There may be no players in Ireland with the potential to perform better than the golden generation in situ. But with only eighteen contracts on offer for the entire squad, there are certainly going to be young players that aren't getting the opportunity to reach their peak. Some, many, will drop out altogether, as non-professionals tend to do. Others will have a late career bloom as the simulated C and E did, but not achieve as much as they ought.

This is an under-appreciated aspect of professional development in sport. Across most sports a player will not reach that peak performance until their late-20s. Yet, their future must be decided by their early 20s, because they need to be in the system until they reach the top. Club programmes work through this via a process of drafting and recruiting, second teams and development leagues. They tend to be cut-throat, and not necessarily in a good way.

A centralised representative sport like cricket tends towards promoting only the top performers, letting late developing or second-tier talent drop off. Often this also manifests as the flip-side to letting talent drop: of prematurely promoting youth on potential, in the hope that they will develop faster in an elite environment.

Perversely, premature selection can be a good thing, as limited opportunities are best given to those with the greatest potential. But it will always be inferior to selecting the best option from a group that have all had the chance to reach their peak. The challenge for all teams, is ensuring they find, and more importantly, improve the talent they have available. Repeatedly, we've seen a strategy of giving contracts to the players you need now, and not the players you might need later, result in ageing stars wondering why noone was there to replace them.

Cricket - Analysis 24th August, 2016 12:57:20   [#] [0 comments] 

Automated no-ball detection, proof of concept
Russell Degnan

The first test between Australia and New Zealand may not have hung on the non-dismissal of Voges at the end of the first day, but the 232 runs it cost New Zealand certainly made it a lot harder. Predictably, a noticeably wrong umpiring decision led to a renewed call for third umpire reviews on every delivery, the return of the back-foot no-ball rule, and some less predictable, non-sequiturs about punishment.

But there is an easy solution.

Tennis has, for over 30 years used electronic means to judge service calls, and more recently, detected let calls with motion sensors. These are relayed to the central umpire, and they use that in calling the point. No-balls in cricket are slightly more complex, as they depend on the position of the foot over (not necessarily on) a line, with confounding shadows and the curved surface of the ground preventing the use of light beams that worked (mostly) for tennis.

But there is an easy solution.

With a fixed side-on camera with a clear view of the line (two is preferable), it is incredibly easy to build a system that will detect a landing foot within an area, and decide if it fell in front of, or before the line.

Computer vision techniques, the sort used by path finding robots, have been around for several decades. I learned the basics (in 1998) and those and more advanced techniques have been developed into the free OpenCV library I used for the code outlined below. To give a sense of how ways it would be to implement automated no-ball checking: my code, using not-particularly high-res footage, sans any setup programs, a live stream, or communication device to the umpire (a phone will suffice for that though) took me around 14 hours. But that involved me learning, from scratch, the OpenCV library, installing Java and SBT, and relearning some coding techniques.

There is no excuse for no-balls not to be automated. It is a trivially easy application of computer technology to a glaring issue.

Step 1. The code [downloadable here] uses the VideoCapture to load the video, and the BackgroundSubtractorMOG to detect edges from the non-filled part of the crease.

This image shows white areas where there is movement from the previous sequence of frames; grey areas show where there is a change, but the same colour as before (indicating shadow). You can see the outline of the bowler as he moves through the crease, and the non-striker backing up.

Step 2. Each frame is examined within the space shown below, to look for objects that will land within it

In a real-world application it needs to specify the side of the pitch to view, and be turned on and off for each ball (as hawkeye also would, so the same operator could be used).

Step 3. A relatively simple formula was used to calculate if a foot was within the frame:

  • There must be at least ten rows of pixels (out of 20) with a continuous line longer than 60 pixels (about 8 inches), and less than 120 pixels.
  • A threshold is used to determine the continuity as there are often bits of noise at the edge
  • Two edges are determined for the back foot - a hard edge (more than 10 rows, and a soft edge (more than 3 rows) to account for movement on the foot. That left a 3 pixel margin of error in this instance (around 10mm), but further testing could improve that. This is the blue box in the first image)
  • That line is compared to the crease line, that is configured before hand (the red line in the first image).

Needless to say, on the ball in question, the bowler was unquestionably behind the line (by 9-12 pixels, or 3-4cm).

Assuming a stream from the fixed cameras could be obtained at the ground, a working and fully tested system could be in place in less than a month. Sometimes, there really is an easy solution.

Cricket - Analysis 22nd February, 2016 20:24:00   [#] [0 comments] 

Batting form and the "hot hand"
Russell Degnan

There has been an interesting paper in circulation recently that deals with the idea of a "hot hand", which in cricket terms we`d refer to as "good form". It is primarily interesting because for several decades, the idea of streaks being anything other than random luck has been derided. Attempts to measure it in cricket have been few and far between, but there was little to suggest a batsman was more likely to score runs having just done so - or indeed, that they weren`t largely replicable with a random number generator.

The paper in question upends a key piece of prior research because of a rather simple, but slightly counter-intuitive piece of statistics. The various explanationstend towards the counter-intuitive end of the scale but I`ll try to explain.

The technique being used is very elegant: take an action that occurs roughly 50% of the time and measure the number of successes that follow a previous success. If they are completely independent, the subsequent attempt will continue to have a probability of 50%. If the successes are clustered around other successes, that number ought to be higher.

The quirk, is that because strings of attempts are being measured, the average probability found in those strings will not actually be 50%. This is the counter-intuitive part, but is relatively easily seen on a simple graph:

Here is shown strings of eight attempts broken down into the number of times a measure took place (that is, the previous attempt saw a success). The number of instances of measurements breaks down as a binomial distribution centred on 3.5: 2 of zero (ooooooox and oooooooo) and seven (xxxxxxxx and xxxxxxxo), 14 of one and six, and so on as follows:

AttemptsOpportunities usedInstancesPercentage

The distribution of opportunities to take a measurement is similar, but because it takes more successful attempts to generate higher opportunities, it is shifted slightly across, and centred around 4 (or n/2). The breakdown also demonstrates the key to the problem: if four opportunities are to be had, the attempts will be distributed in such a way that the average success rate is 50%. But the only way to generate 7 opportunities is to have succeeded in each of the first 7 measurements. The percentage will be either 6/7 (83.33%) or 7/7 (100%). And as a consequence, the average of multiple strings of measurements ought to sit not at 50% (the middle of the opportunity distribution), but at the centre of the instances of measurement distribution (plus a term for the two extras) - around 45% for strings of length 8.

All very fascinating, particularly as it implies that previous studies showed a "hot hand" after all. But what does it say about cricket? The short answer is that this is a very elegant way of measuring form: find the median score for a batsman, if they surpass it, then test their subsequent score.

For Tendulkar, who played so many innings that the expected percentage is close to 50, his test "form" saw a 53.1% success rate in innings where he`d surpassed the median (excluding not outs below the median). In ODIs however (counting only matches where he opened) the figure drops to 50.5%.

That is only a single data point, and some batsmen are likely to be more prone to runs of form than others, but it also points to an issue. In ODI cricket, where multi-lateral series exist, a batsman tends to shuffle opposition quite quickly, and therefore face a reasonable variety of bowling strength from match to match. In test cricket, the subsequent innings is less likely to be independent from the first, without being held in identical conditions - the second innings being on a wearing pitch. Apparent runs of form may just be a string of matches against poor opposition.

Conversely, ODI cricket may be less prone to form, being a format that requires a higher amount of risk-taking, and therefore more luck. Hence a discrepancy between test and ODI matches is feasible. Comparing all innings adds in time gaps when a player might fall out of form (and vice versa), and a proper study ought to remove them. The relative sparsity of innings means that when a player is really in form, it would be hard to distinguish between that and luck with any method. Most likely the effect is small - perhaps three or four runs on a batting average, but probably half that.

Hence measuring the effect, if any, of form remains difficult. On selection matters, - the only avenue where form might matter - there is a lot to be said for judging a player on technique, temperament and overall career trajectory and ignoring runs of form. Everything else is largely academic, albeit an interesting question.

Cricket - Analysis 16th October, 2015 00:45:10   [#] [0 comments] 

Short Stat: Stability and performance
Russell Degnan

We know such an approach is a good thing. There is an obvious correlation between that and success, though which is the chicken and which the egg is debatable.

- Rob Smyth - The joy of selection roulette

The need for stability is always the catch-cry of teams struggling, and players fearful of their places. It has been an article of faith that Australia built their dynasty around youth in the 1980s, though even that might need some revision.

The longest period of batting stability for Australia immediately followed the 1989 Ashes, with only the substitution of one Waugh for another in 21 tests. But it was also a period marked by weak opposition, with the only losses being in NZ and to the West Indies (2-1). The 12 tests that followed the enforced retirement of Geoff Marsh, leading up to the 1993 Ashes, was anything but stable, with 6 different openers, 4 different players at first drop and 6 more players in the middle order - 7 of you include Greg Matthews. The results? Only three losses, one in NZ, and a 2-1 loss to the West Indies. Another two top-order changes were made for the first test in 1993; as in 1989, Australia were 4-0 up by the final test.

Perhaps results might have been better with more stability (a series lost by one run has a lot of what-ifs); or perhaps the opposition over-rides whatever difference might exist. It is reasonably unlikely that swapping the 6th best player for the 7th makes a big difference, though ongoing panic such that you select the 13th best, might.

To factor out the opposition, we can compare the expected margin against the actual result, and graph that against the number of changes made. There is a lot of noise:

There is also some indication that making zero changes is better. In the short term, the best side is probably the one you thought was the best side. But making one or two changes is still likely to produce a (very slightly) above-average result - note that 20 ratings points equates to 10 around runs, a fifth that advantage conferred by playing at home. Though this doesn't necessarily solve Smyth's chicken and egg quandary, as a result above expectations may merely represent below average expectations.

It gets more interesting when we look at changes per match over the previous two years. A side in constant flux ought to under-perform relative to expectations, if stability matters.

Actually, we don't see that. There is a lot of noise, and the difference is minimal, but sides making fewer than 1 1/2 changes per match do worse than expected than those making more.

I'd proffer two possible explanations. Firstly, that there is an information problem, in finding the best set of cricketers, and most likely some benefit in trying several out until one shines sufficiently to become more permanent. And secondly, that stable sides are more likely to be older sides - established, successful - and therefore more likely to be declining in performance. That doesn't mean an alternative player will perform better though, particularly in the short term. As the game to game suggests, more often than not, the best players a team has are those who've proven to be the best they have, even when they are losing.

Cricket - Analysis 12th June, 2014 19:35:33   [#] [0 comments] 

Short Stat: Adelaide and batting first
Russell Degnan

Don't. There are exceptions, but the oft-told story of Richie Benaud's that as a captain he was told to "bat; if in doubt, think about it, then bat anyway" hasn't been true for 20 years.

S Rajesh noted as much a couple of weeks ago, but his analysis was based on the results obtained which has issues (amongst them, that Australia automatically bats) while other sides are a little more discerning. We can run a slightly more sophisticated analysis by comparing the expected margin (based on my ratings) against the actual margin and seeing whether the batting or fielding team beats expectations in each match. In short: for the last 20-odd years they have not.

In the 1930s - with uncovered pitches - the advantage in winning the toss and using the (most likely) best conditions was clear: it added as much as 40 runs per game. But that benefit has steadily eroded, and batting first is now a negative proposition, while fielding sides are regularly beating their expected margin. Interestingly, this is happening in both drawn (margin of 0) and result games:

A drawn games means the better side missed its expected victory. And for the better side, fielding first offers the advantage of time. By bowling there is no wasted runs from the need to set a target - such as last season when Australia still needed two wickets at close of play and had 172 runs, but also in 2003 and 2006 when the batting side had a first innings in excess of 500 and still went on to lose courtesy of a poor third innings. Even with the margin as large as it was, given the rain on the last day, England probably wouldn't have managed to beat Australia in Adelaide in 2010, because their bowlers would have been tired (had they enforced the follow-on), or they'd have run out of time.

Similarly, despite having to bat last on a potentially wearing pitch, if the match is heading for late on the fifth day, the need to buffer a margin by 100 or so runs when declaring helps the weaker side avoid a loss. Of the three recent bat-first-and-win games at Adelaide, all three went into the fifth day, despite the losers scoring less than 520 runs in total in the match. Australia and England both batted and lost in that period with more than 680 runs.

In general, a side that wins beats its expected margin, because the expected margin takes into account draws. In games with a result then, you'd expect any advantage from the pitch to accrue to the batting side, because they get the best conditions, and managed to exploit them. But in recent years we've not seen that; the new pitch has offered movement to the bowlers, and the old pitches haven't broken up significantly enough to negate that. There isn't a huge difference (and quite a bit of randomness), but taking into account the time benefits the bat-first approach is no longer valid, and actually unhelpful.

So unhelpful, in fact, that the expected margin for the toss winner was negative in the 1990s and first part of the 2010s, as well as negative for those batting first in the 2000s. By less than a dozen runs, but negative is negative. Any side with ambitions to win in Adelaide should bowl first; new pitch caveats aside, there is little to fear on the fifth day.

Update on Adelaide:

Australia chose to bat; but that is not a surprise. For reference, this graph depicts the number of total runs in the match for teams batting first and second since 1990; wins at the top, losses at the bottom, and draws in the middle.

For teams batting second, more than ~560 almost guarantees at least a draw, although it is possible to win with less (because obviously the opposition can be bowled out for less). Batting first, there has only been one victory with less than 590 (by a single run no less), and three losses with more than 600. The runs required to force a result in Adelaide are substantial.

Moreover, there is always pressure on the side batting first to keep batting well, because all results remain possible, even with very high totals. Whereas, the side batting second can, if they bat well enough, guarantee at least a draw and press for a victory.

Finally, the innings by innings runs per wicket for the top order: 1st: 48.5 2nd: 49.5 3rd: 31.5 4th: 28.9. That calculates to a total value in the top-order of batting first of 11.2 runs (miniscule in context). The Adelaide pitch clearly becomes harder to bat on, almost twice as hard: but it does so too late to gain advantage in the second innings, and too early to prevent a catastrophic third innings resulting in defeat. In Adelaide, it is the third innings that counts, and you are better off bowling when it does.

Cricket - Analysis 4th December, 2013 14:01:14   [#] [0 comments] 

Observations on Cricket Finance
Russell Degnan

What follows is necessarily inexact. Perhaps very inexact. Cricket has many issues that confront it, but by far the biggest is a lack of transparency. The Woolf review, despite the resources available to it was forced to admit much the same:

We believe there is an overall lack of transparency around financial distribution in global cricket, which means certain aspects of the finances of global cricket are not well understood. We have been unable to obtain a full picture of the current financial position of global cricket. For instance, although there are various media estimates in circulation of the impact of tour cancellations (actual or threatened), it is not known with any degree of certainty the financial effect a tour by one Member has on another Member. It is clear that tours by certain Members (such as India) to other Members give a significant revenue boost to the host nation.

There are four points we know with relative certainty however, from which we can begin a deeper investigation. Again, to quote the Woolf review:

  • The level of funds flowing through the ICC and global cricket has been completely transformed in the last ten years, with a significant increase in revenues, principally from growth in income from television rights.
  • For ICC-run events, the additional funds from television rights flow through the ICC to the Members.
  • For other competitions and matches, such as those under the FTP, the income flows directly to the Members.
  • The most notable source and beneficiary of the greater revenue flowing into cricket is India. That nation's love of the game has combined with significant population and GDP growth in recent years, to make India the commercial hub of world cricket. There are unsubstantiated estimates that India generates between 60% and 80% of revenues flowing into global cricket. India also has a significant impact on the ICC's Commercial Revenue, as almost all of the ICC's major commercial partners have significant links with India.

The basic structure of cricket finance runs from TV markets - nominally constituted at a national level - to either the home board of a particular fixture, or the ICC. We therefore need to make three assessments: the size of a local cricket market; the flow of money generated from that market to various bodies; and the distributive flow from the ICC and others.

For most purposes here I'll be talking averages over four years, because this takes into account the cycle of both the FTP (give or take), and the ICC major events. Every cricket board exhibits substantial variation from year to year, depending on who is touring, and the dividends distributed by the ICC.

Cricket Market Size

This is the most inexact of all the estimates, not least because it isn't clear what percentage of the cricket market is actually being drawn on by various members. Empty stands and no push to fill them by sensible scheduling, and fixturing that makes an inefficient use of resources, and no attempt to contextualise the season means most boards make less money than they might.

A previous assessment of TV rights deals across sports in Australia indicated that cricket gets roughly what you'd expect, given its ratings, and total hours of programming. Taking into account sponsorship, merchandise and match-day attendance; then cross-checking against Cricket Australia's annual reports, and adjusting for income earned from overseas, puts the size of the Australian cricket market (or at least, the part of that that pays to watch professional players), at something like an average of AUD$150m (which for current purposes is nearly identical to USD) over the past four years. The most recent TV deal has probably inflated that to nearer AUD$200m . The continuing rapid inflation of sports rights makes this process harder than it might otherwise be.

The simplest model for calculating market size is to multiply GDP (incomes, which includes population) but the level of cricket interest. There are various reasons why it won't correct: the distribution of cricket fans amongst income quartiles (particularly in England and to a lesser extent India where cricket is an upper-class sport); the size of disposable income which will make the sports market in wealthy nations much larger; and the difference between TV income and ground income, with the latter more easily captured in richer, but smaller nations. Nevertheless, I'll look at three methods of assessing cricket market size. Two are quite simple but (relatively) complete, the third complex, but stifled by the lack of annual reports from the most poorly governed members.[1]

Announced Revenue
avg. Last 4 years
(2007 millions)
GDP (millions USD)% Cricket Players% Cricket Articles
Kaufman + Patterson (2005)
Market Estimate
% News Articles
Market Estimate
% Cricket Players
Market Estimate
Regression Method
South Africa6206548.63843152.06%20%384324908640000
New Zealand313994.21696802.39%17%144232628218000
Sri Lanka19.3594088%*57%1693121685
West Indies372194.5501453%*28%70201170120000

* Estimate - by which I mean guessed and/or completely made up
+ Estimates of USA market size are very sensitive to assumptions. The K+P figure was close to zero, but also 8 years ago, and there has been a recent shift towards more cricket articles. Similarly, estimates of the number of players vary from the official figure of ~30,000 to ten times as many. Consider this a low figure; under reasonable assumptions the USA is cricket's fourth biggest market. Though almost none of that goes into US cricket.
# K+P give two figures for England - 8% normally and 17% in summer - I have used the higher one for obvious reasons (estimates outside the season are irrelevant). They don't offer similar figures for Australia, which makes all the figures in this column sensitive to this assumption.

Method 1: Estimate from GDP/news media

One of the more interesting pieces on cricket take-up in various nations is the 2005 piece by Kaufman and Patterson. It is worth reading the paper, but for my purposes its most useful feature is an estimate of cricket popularity by counting articles in the sporting press. The numbers have been relayed into the table above, and used to calculate, by multiplying that out by GDP and a factor that makes the markets I have good data (Australia, England, India and New Zealand) approximately the right size (around 120,000).

Method 2: Estimate from GDP/playing numbers

Playing numbers as a proportion of population ought to be a good measure, but are complicated by the fact that, although have a complete set of figures for associate/affiliate nations, I have none for most test nations. Estimates of the major nations should therefore be taken with very large grains of salt. Nevertheless, it gives some reasonable numbers, and those give a good indication of the size of markets where published annual reports are sparse, or the market is undeveloped for lack of matches.

Method 3: Estimate from Annual Reports

Estimating market size from actual revenues is complicated by the amount of revenue generated by most boards in external markets (either overseas tv rights or sales to spectators), and the lack of reporting on the source of that revenue.

India is perhaps the easiest market to estimate, because the BCCI generates relatively little profit from external sources. Their annual report puts average four year revenue (adjusted for currency) at USD$168m, of which $25m is dividends from the IPL or CLT20. Those two competitions have approximately $240m in revenue. The ICC brings in around $200m in revenue a year, of which India is the source of approximately 60% (by most accounts). Finally we must estimate the amount of revenue earnt by playing India at home, and which therefore goes to the local board. If that is assumed to be around $100m then the Indian market is roughly three times that of Australia and England: around $600-700m. This is less than most estimates, but consistent with their annual reporting.

What we really need to do though is understand where the money comes from, and where it goes.


ICC Distributions are relatively easy to calculate, and the annual report is quite informative. 75% of profits - after events costs, TAPP payments and administration are removed - are paid as dividends to the ten full members, with the remaining 25% going into the development fund, the majority of which is distributed to the 96 associate and affiliate members. Dividends to full members over the last four years were USD$319.9m, with USD$41.4m being distributed to the development fund. That doesn't include prize money, or TAPP funds, from which relevant members took an extra million or so (relatively little, when considered over four years).

Non-full-members are paid according to a scorecard system - judged on 35% the men's ranking, 41% various participation figures, and 24% administrative development. The top-tier receive $300,000 USD, the bottom $5,000 USD, in addition to $100,000 for associates and $10,000 for affiliate members. High Performance Program members receive funds commensurate with the expected costs of transitioning from amateur to semi-professional cricket structures, depending on what events they play and qualify for. The Asian Cricket Council derives significant additional funding (approx $5m) from the Asia Cup, which in turn feeds into their member-base.

Estimating value: a multi-variate regression approach

A significant proportion of income for full members comes from the rights to host certain nations via the FTP - unless you hire Haroon Lorgat, then all bets are off. To estimate the size of these flows I went through every recently published annual report and noted the revenue in USD - converting by the exchange rate of the time - the year, the ICC grant (where noted, or estimated based on the ICC report where not), the number of home matches, and the number of those matches that were played against Australia, England, India or Other (meaning everyone else). A linear regression was then run, which produced some moderately accurate looking numbers:

The top line of figures - in thousands USD - is the important one - the second is the standard deviation which is worth noting only because they are quite large (around $1.2m on each variable). By multiplying out the revenue earned for a day of cricket by the number of days played I've estimated the flow from markets to boards in the following figure (click for pdf version).

This is necessarily representative, which is why I left the figures off. The size of each board logo and market is proportioned to represent the relativity between comparable entities. Where arrows are not clear, remember the money flows from market to board, sometimes via intermediaries (such as the ICC). I have not noted any payments directly from board to board, though the Woolf report implied they might exist. [2] Nor have I accounted for county cricket (which earns perhaps $40-60m) nor other T20 leagues which aren't accounted independently. In the interests of readability, flows less than $1m have been left off, as have most associate members. I can't guarantee I caught everything. [3]


There are a number of points that can be made from this. In no particular order:

The BCCI earns around $4m more than average from home matches, as does England, with Australia on $2.7m. (All give or take $1.2m; the Ashes earns at the top-end of those numbers - i.e.. above $4-6m per day). This makes intuitive sense. It also shows the importance of attendance versus TV in the revenue streams of otherwise smaller markets, and the weakness of the BCCI in creating a home schedule that meets what they might earn. As the annual reports bear out, India earns less from their home internationals than England, which doesn't accord with their perceived financial muscle.

Notwithstanding that the IPL effectively doubles what the BCCI make from their home market, they ultimately end up with only around half the revenue generated locally, despite having a monopoly control over the team that market pays to watch. This is both quite surprising, and an indication of why they are increasingly bullish about increasing their share of global revenue.

Board revenue has increased by $6m a year; that is, the regression estimates base revenue of $29m in 2000, and $89m in 2010. Obviously only three boards actually earned this; the variables are best interpreted as relative amounts. Moreover, the large standard deviation hints at the growing disparity in how much teams have managed to gain from overall revenue increases.

Playing India earns $1.6m for the home team more than Australia or England, and $2m more than any other team. This, in one sentence, explains most of what you need to know about the nexus of finance and the obnoxious chaotic scheduling of the FTP.

South Africa make $450k above the base rate (around $1m per match) from home matches, but New Zealand and the West Indies are making less than that, which means matches against teams outside the big-3 are likely to be losing money. We know this, in relation to why test cricket costs these teams money to play, but add in Pakistan - whose market lies dormant with no tours possible; Sri Lanka, Bangladesh and Zimbabwe, and it is clear the bulk of fixtures are neither profitable nor generating particular interest.

The total size of the non-full member market is around $90m; but it is almost certainly not being tapped. Zimbabwe has no market to speak of at all - less than $0.5m. Their GDP is tiny, their population is small; cricket is a minority sport. You frequently hear commentators remark on the importance of building up existing markets, rather than chasing markets in nations cricket has a small profile in. This is basically nonsense. There are three really big cricket nations, each of which has a GDP in the top-15 in the world. There is limited scope for growth in the big-3. But amongst the rest, because they are already pushing against the point of market saturation; and because their GDP is relatively small - despite their population size in the case of Pakistan and Bangladesh - their potential for growth is weak.

If one attitude weakens cricket's case for globalisation it is the perception - largely because of the bias in the origin of the cricket media - that there is a certain standard to aspire to equal to India, England, Australia and perhaps South Africa. With the possible exception of the USA, and in the longer term, China, no nation will reach that standard in the next 20, or perhaps 40 years, without remarkable (unprecedented) growth. The nations currently in the HPP are too small, or too poor, or both; the G-20 nations that might open up new frontiers have tiny playing bases.

There is, nevertheless, strong encouragement to the idea that cricket could have 20 nations of a standard somewhere between that historically maintained by New Zealand and currently by Bangladesh. With the assumption that, given that, at least a half dozen of those teams will have a transcendent talent (ala Hadlee or Muralitharan) that will allow them to compete with the big-4. A future post may look into this; as some nations will surprise.

If it wasn't obvious, cricket's finances are fundamentally unstable. The wealth available to three boards, and their local competitions means that noone else can afford the market rates for their players. While we haven't seen mass defections, it is increasingly clear that international cricket, as currently structured, cannot support the existing nations, let alone provide the investments needed to promote and grow the game elsewhere. Either a substantially larger proportion of the money moving from market to boards needs to be routed through the ICC (which means them taking ownership and control of tournaments), or a substantially larger proportion of the money must direct itself into competitions that will pay players from all nations, with a reduced emphasis on international cricket.

This would not be historically unusual; it has been the case for West Indies cricketers from the turn of the 20th century in English league cricket, through Constantine and Sobers; and onto the Packer years. There are also various ways both these scenarios could come to pass. Some are outlined in my manifesto on test cricket; others ideas will have to wait for another day. But don't be surprised if the CSA-BCCI spat is a harbinger of things to come. There are too many opportunities for the BCCI to redirect money currently exiting the Indian market back into their own pockets, and too much inequality, for things to stay as they are.

[1] It is interesting the cricket's largest markets come under both the best and worst governed nations but relatively few in the middle. The crisis of governance at ICC level is exacerbated by very different philosophies of action by its board members.
[2] The late Ronald Coase would have found this interesting. There is no good reason why boards couldn't bid for tours, thus maximising both BCCI income and cricket's overall revenue by playing the most desirable fixtures (albeit not those that make the best competition/product). Transaction costs at the ICC are high though, and we are far from man efficient touring structure.
[3] Also, apparently cutting a google map means I get abused by nationalist idiots over J+K. I don't care. Don't bother me over your craziness. It isn't remotely relevant to cricket.

Cricket - Analysis 11th October, 2013 01:52:36   [#] [0 comments] 

Short Stat: On the Back of a Collapse
Russell Degnan

One of the standout aspects of Australia's collapse in Durham was the tentative batting; admittedly it was what begun the collapse - Khawaja and Clarke's half hearted footwork - and not what continued it - Haddin and Watson's playing across the line. But it raises an interesting question over whether players play worse in the midst of a collapse, or much the same. Is there a drop in performance from the psychological pressure, in other words.

I tested this proposition using a technique Chris at Declaration Game used, by comparing the runs scored by the 5th and 6th wickets against the other innings, and matched that against the difference in runs between the fall of the 2nd and 4th wickets (the collapse amount - though most aren't a collapse).

As it turns out, there is no effect. The average scoring for the 5th-6th wickets is 59, which is consistent with one exception across the range of collapse amounts. Not only that, but there is so much randomness in the difference between the two innings, and the previous run-scoring, that even sample sizes over a hundred for low collapse amounts end up with reverse effects from one to the next.

You can see from all the data points that the difference remains resolutely centred at zero for all low amounts. This is actually doubly odd, because it indicates that even where several wickets have fallen for other reasons - a crumbling pitch or new ball - the difference between that and the previous innings was negligible.

Data clumping over shows some of the randomness, and don't be confused by the jump around 30; a different division produces a completely different result.

What both graphs do show though, is that where the previous two wickets have put on 200+ the average of the 5th-6th wickets combined drops to 45. It isn't clear why this is - the bowlers, presumably are tired - but perhaps one or more large preceding partnerships make it harder for an incoming batsman. Something to look at another day.

It does bode badly for Australia though. There is a tendency after a collapse to attribute it to the moment, and assume that next time, more focus and hard-work will arrest the problem. The data suggests that even losing three wickets for not many makes almost no difference to the mind-set. If a team is in the habit of losing 6 or 7 for not many it is because they are poor, and just as likely to lose quick wickets when the previous stands have been productive or dismal.

Cricket - Analysis 14th August, 2013 19:16:20   [#] [1 comment] 

Short stat: 2013 Ashes Probabilities
Russell Degnan

Inspired by Fake Ritzy's ICC rankings based analysis of Australia's Ashes chances, I ran a monte-carlo simulation of the series using my own (25% draw probability, matching the historic English average).

Australia is a roughly 1 in 8 chance of winning, and a 1 in 8 chance of drawing. 3-1 England is the only scoreline returning a positive net return on the betting markets. Australia's most probable winning scoreline, 1-2, is very (very, very) slightly more likely than losing 5-0. Australia wins 5-0 in about 0.04% of series. I think Australia's Indian tour has caused their rating to under-estimate their chances. With a decent team selection there is grounds for no more than mild pessimism, but given Watson is locked in to open, things are very bleak. Very.

Cricket - Analysis 29th June, 2013 01:13:21   [#] [1 comment] 

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