The MCG is perhaps the best barometer of crowds because it has both the best data, and is almost impossible to sell out, even when being renovated. There is actually less of interest here than you may think, but it is worth collating occasionally to see.

Start with two graphs. Figures are derived from the MCG, news reports and Austadiums. Not all sources are consistent, but the figures are close enough for this purpose. The first three seasons of the Big Bash are estimates on the Austadium site, but probably within a thousand or so.

• Test crowds are basically constant within the bounds of opposition. This season was down, as Sri Lanka is a weak draw-card, but next season will be up, as the Ashes adds 25-30,000 to the base average.
• One-day crowds are either trending down, or made up of two relatively flat lines, with the introduction of international T20 causing a drop of 5-10,000 per game. The combined aggregate attendance of international limited overs cricket is basically the same as it was before IT20: about 100,000
• One anomaly is the drop in support for English limited-overs cricket. 2006-07 had a unusually large ODI crowd (79,000) but the 2010-11 T20I was consistent with the average for other teams (58,000)
• The International T20 match has shown a significant drop in attendance, from 80,000+ against India in 2007-08, four years of ~60,000 and down to 40,000 this season. If any figure stands out, it is that one. Next year will be interesting.
• Domestic T20 has increased the number of games year on year without a significant drop in average (~24,000 at the MCG, 13,000 at Etihad). That has propelled the aggregate attendance to the top of any format, indicating significant pent-up demand for more local games.
• Conversely, the average BBL attendance dropped this season despite this being an under-whelming January of cricket. This doesn't match what happened in 2009-10 which saw a big increase in average attendance, followed by a big drop when England was in Australia.
• 2009-11 is better discussed in relation to show-piece games (Vic-NSW was followed by 43k) and performance related, consistent with the economic literature on domestic crowds. The season just gone is less clear: outside the two derby games, the Melbourne crowds were weaker than expected, particularly before Christmas, even with both teams doing well.
• It is very difficult to make any conclusions, good or bad, about BBL crowds or trends.
• The next two years will be interesting for attendance, but not necessarily representative either. There is a clear shift away from international limited-overs cricket to domestic cricket; but international attendance is strongly correlated with opposition, so both formats ought to recover with England and India in town.

A final thought: the aggregate attendance of all formats has jumped from around 250,000 to 400,000 in line with an increase in high-profile matches (with apologies to the Shield and ODD Cup) from four to more than a dozen. The average number of people at each event has decreased, but the fan in Victoria has a lot more cricket to go to, and does so. Definitely a good thing.

Update:

I chanced upon another source of daily crowd figures on the MCG site, and by using the wisden almanac, have produced a long-range graph of crowds in Melbourne over 30 years. The key take-away is that Boxing Day has become ever more important, and ODIs have steadily declined, starting in the mid-90s. Note that I didn't include the average for the non-Boxing Day test of 1989-90, for which the 5-day aggregate attendance was 68,865; though it was less than 19,000; figures missing: ODIs: 1990-91 (2), 1984-85 (1) and 1980-81.

The nadir of test match crowds was an almost washed-out match against South Africa (1993-94) although the worst years were behind. Note that ODI aggregates vary wildly from variations in the number of matches played by Australia. Nevertheless, the long-term trend for ODI crowds looks bleak.

Cricket - Analysis 14th February, 2013 21:47:29   [#] [2 comments] 

A special BBL final related graphic on BBL and Test match attendances. The only city in Australia this year to record fewer patrons to the BBL than test cricket: Adelaide. And that was a Strikers semi-final away from being toppled too.

Attendance at test cricket was approximated for several days, but will be correct to a couple of thousand, given the sparse stands. Total attendance 490k in 34 matches for the BBL, ~400k for test cricket over 26 days.

Cricket - Analysis 19th January, 2013 18:47:05   [#] [0 comments] 

A very short statistic today, in honour of Australia's top-3, who've recently made a habit of running each other out. A graph of run-runs (runs minus boundaries) per run-out, by decade and team for the top-order (positions 1-7).^* Notice Australia are getting run-out at the highest rate since WW2:

On another note, New Zealand can ill-afford to be consistently the worst running team in test cricket.

^* Excluding innings with no boundaries recorded, which is the easiest way to discount scorecards where it is not recorded.

Cricket - Analysis 4th January, 2013 11:20:23   [#] [2 comments] 

As a short refutation of the on-going nonsense that the last decade has seen a massive increase in injuries, and bowlers of the past were somehow immune, I present this graph:

This shows the percentage of innings by location that had multiple short overs in test matches - a sign that a bowler was injured. Note that Australian rates are both higher than England, peaked in the 1980s, and have been roughly similar since the 1960s - when the schedule settled in. England has exhibited similar rates since the 1970s.

It isn't clear what changed from the 1950s, although the newspapers of the time record frequent injuries. Professionalism and a reduction in the rate of playing through injuries - even if just to finish the over - is a likely cause.

The biggest change comes from the rest of the world, where injuries peaked in the 1990s. Workload is the likely reason - although the graph is per innings played, it will correlate closely to ODI matches (and therefore total playing time). There is probably no better way to show this than a team-by-team comparison. Note both the massive increase in injuries in the Indian team, and the fluctuations of Pakistan and the West Indies, as their playing schedules changed.

Cricket - Analysis 18th December, 2012 10:20:38   [#] [0 comments] 

Responding to Ponting's use of a nightwatchman in Perth, Steve James made an interesting pointless that their value mostly derives from not having to start again the following day. Which raises the interesting question of how large a problem starting is. It is well established that batsmen start very badly - on nought - and then gradually improve up until the seventies, with an odd but not unexpected jump after passing 100. Compared with starting from an overnight score, and using the top 5 as comparison - the figures for the top order are broadly similar - we can see nearly identical graphs right through the first 100 runs after restarting, notwithstanding some random variation.

Except one aspect, which can be seen by zooming in on the first twenty scored. Batsman on a duck are significantly more likely to get out. Yet there would appear to be no good reason for this, except anxiety, as other than on nought batsman set themselves much the same?

By calculating the difference between the average once a batsman passes 20 - around 43 - with the runs lost by being dismissed early we obtain a difference of 6.2 runs for a batsman beginning his innings and 5.2 for one starting again the next morning. This apparent advantage is offset by a loss of 0.7 runs for a number 8 or 9 batsman, but nevertheless ought to gain some advantage for the following batsman. That it apparently doesn't is the why this will be a series, not just one post.

And to further muddy the waters on the first question. The probability of being dismissed on an overnight score shows no such bias for nought with batsmen on one run just as vulnerable. Although again, there are strange patterns of vulnerability when starting from a low score or a middling one that don't appear random.

That is two mysteries then. Why do batsmen play themselves in an identical manner when regardless of time spent at the crease the night before, except for the first run. And why are there large variations in dismissal rates at various points after an overnight score?

Cricket - Analysis 13th December, 2012 23:02:13   [#] [0 comments] 

There is something almost fun about the way the ICC ratings reset every August. For a system designed to be simple the random wanderings of discarded results cause endless sniping and confusion. Further compounded by their T20 ratings that use such a paucity of data with teams so evenly matched, that any number of odd results turn up. In a previous post on this topic, I looked at some of the operational quirks inherent to the ratings.

In this one I want to demonstrate the mathematical flaws that cause those quirks. Lest that seem petty, it is worth noting that the ICC commissioned a (secret) report that determined that the ratings were fit for purpose when deciding qualification for major events. What I want to demonstrate here is that although it is actually quite hard to make a rating system flawed enough to produce really odd results, the ICC ratings are absolutely not fit for purpose, should they be used for qualification. Leaving aside the more general point, that things like qualification ought to be decided on the field, not via the questionable calculations of statistics nerds.

Problem 1: Linear predictions

It is worth recapping how the ratings are calculated, before deconstructing the problems with that approach. The ICC description over-complicates the formula, which can be simplified into two parts:

• The win points: the percentage of games won, regardless of opposition.
• The opposition bonus: which for teams separated by less than 40 points, is the opposition rating minus 50, and otherwise a team's own rating minus 90 (for the higher placed team) or a team's own rating minus 10 (for the lower).

Each year a team accumulates points according to that formula, divided by the number of games. Series results count as an extra game, so they don't affect the basic formula. As with all ratings systems, old results are diminished with time, but we'll get to that.

Using the standard formula, if a team has an accurate rating, then their expected win percentage against another side can be calculated from the ratings difference. this is a linear formula. Two sides rated 100 will score 50 opposition points and therefore need to win 50% of games to maintain stability. A side ranked 20 points higher will expect to win 70% of games; one 40 points higher: 90% of games. At which point the system breaks down. Any ratings difference greater than 50 would predict more than a 100% win rate. This being impossible, and therefore likely to cause ratings to decline even when a side wins every game, the ICC ratings have a second clause that projects an entirely arbitrary win expectation of 90% for games played outside those otherwise narrow bounds.

The root of these difficulties lies in the linear projection from ratings difference to expected wins. It ought to be obvious that as the ratings difference increases, the probability of the weaker team win will diminish to zero, but not cross that barrier. The ICC ratings (blue line) are too variable for evenly matched teams, and compress the ratings of sides around the 90% win mark, eventually flat-lining when it ought to be a slow curve. An examination of the distribution of margins shows that they are basically normal around the expectation, and therefore win probability is better calculated with a cumulative normal function, based on ratings difference (the red line) - or for simplicity a curved or segmented linear approximation.

A ratings formula that used this property would be stable for all teams included in the ratings. The ICC ratings are, by contrast, not stable with respect to predictions.

Problem 2: Infinite and Zero Bounds

Once the ratings difference crosses 40, the expected win percentage for the better team is capped at 90%. This has two effects: firstly, it makes it impossible to accurately rate a team within this no-mans land of mediocrity (or greatness). There is no difference in expectation between a side rated 50 behind and one rated 100 behind, so there is no way to know if a side should move up or down from their rated position given a string of results with sub-10% win percentage. Where teams have more evenly spaced ratings - such as the T20 table - it is theoretically possible to adjust a team in relation to its immediate rivals, but in test cricket, where Bangladesh are well below a 10% win percentage, their rating is mathematically meaningless.

Secondly, the up-shot of expecting a 90% win percentage when a team is actually winning greater than 90% of games, is that the higher team's rating will increase indefinitely; and vice-versa, the lower ranked team wil be driven to zero. It would be less, but the ratings are artificially bound at zero; this is itself a problem when rating associates because the weakest (zero-bound) associate will almost certainly be more than (a cumulative) 100 point rating difference below the major test teams, meaning the 100 centring is probably too low.

Problem 3: Oscillations caused by adjustments

The effect of infinite bounds and linear predictions causes makes the system highly unstable for the lower-ranked test teams and associate nations. But it is not the cause of more recent random results. That is related to the method used for removing old results.

To understand this, consider the simplified case of a two team system playing one game/series per year. Imagine that prior to year 1, the first team wins exactly 90% of all games played between the two sides. Over time, their ratings will converge to 120 (for the stronger side) an 80 (for the weaker), a difference of 40. Now suppose that, in year 1, and every year after, the two sides are equal, winning 50% of games played. To accurately represent this change, the ratings ought to converge to 100, although it is a matter of preference how quickly this occurs.

The ratings do this by giving the stronger team fewer points because of the opposition bonus, which drags them down below the 100 mark. That is, the higher rated team gets (80-50) opposition points and 50 win points, equal to 80. And the lower rated team gets (120-50) opposition points and 50 win points, equal to 120.

The ICC reduce the power of old results by halving the points value after 1-2 years, and removing results after 3-4 years, calculated each August. This causes some significant problems. Four methods of diminishing old results are presented below to demonstrate the problem.

Method 1: 50% averaging Averaging the most recent year with the rating at the start of the year. Weirdly enough this works perfectly adequately. Because the latest game mirrors the change required, both teams move directly to 100, and then stay there. (blue line).

Method 2: with removal Alternatively, a simple method that reflects the ICC approach is to average the points accumulated over only the previous two years, removing results older than that. What happens here (red line) is that in the first year, the results average out 120,80 and 80,120, which gives the correct result. However in the second year, where both teams accumulate 100 points, the removed result (120) pushes the higher rated tea down to 90 (80,100), before oscillating back to 105 (100,110), and continuing for several years.

Recalling that the ICC effectively uses a year to year points calculation, the prospect of it oscillating is real. Though to be fair, it is not quite that pronounced.

Method 3: 33% averaging Even though 50% averaging is perfectly reasonable, most people would consider that it gives too much prominance to recent results, effectively only the previous year. An alternative is shown here (blue line) that uses 2/3 of the rating at the start of the year, and 1/3 the previous year. It converges more slowly on the 100 point mark, taking 4 years to complete the move (107,102,101,100).

Method 4: ICC averaging The ICC takes a more complex, and needless to say broken aproach to its averaging. Over the three year period calculated each August, it applies 50% weighting to the results from the first two recorded years and the full weighting from the most recent. This produces a very odd result. In years 1 and 2, the results average out to 100 (120,120,80x2) and (120,80,100x2). But in year 3, when the last of the good results are removed, the team drops below 100 to 95, despite never playing at that level (80,100,100x2). That induces an oscillation that is still distingushable until fully nine years after the change in playing strength.

This is exactly what we see in the recent rating change. Australia get a fourth year bounce oscillating up from the knock-on effect of their rating drop in 2009. India, and more particularly, South Africa receive little kicks from the same period, while England receive a small bounce for the Ashes the following year. None of which has any relation to recent results. It is nothing but artifacts of old changes, insufficiently balanced out.

Problem 4: Over-sensitivity

The final issue, which is particularly important in relation to qualifying, is that, as the averaging shows, while the ratings include results from as long as three years ago, they are so sensitive, the previous 12 months of results are the over-whelming contributor to the results. The oscillation, while potentially important, only appears on the graph because the ratings are being held stable.

Thus, a team with a particularly difficult or easy tour in the leadup to the qualifying cut-off will have or lose a significant advantage. Recalling that the ICC makes no allowance for home advantage the order of tours, and the exact (as yet unknown) date for qualifying might have a significant impact on who makes the ICC's major tournaments. Add in an element of randomness via mathematical nonsense and there is absolutely no way they should be used for the purpose being proposed. The fact that a study was conducted that has supposedly concluded the opposite ought to raise some serious questions about the quality of their independent advice.

There are very good, very simple ratings systems available. The IRB have a very sensible approach^*, and include all their members - of whom the ongoing absence from the ICC ratings ought to be an embarassment. But even they are not so unwise as to use the ratings for global qualifying. At some point, putting faith in ratings that are broadly untrusted and produce odd results will cause the ICC more headaches than they are worth.

^* Actually the IRB also use a linear projection, but introduced a different quirk, capping rating changes for wins against team's more than 10 points apart. This too is an unnecessary flaw, as it holds teams within the orbit of those they regularly play, suppressing New Zealand's rating, and keeping Italy, Scotland (and maybe now Argentina) from dropping as far as they sometimes might. it is partially mitigated by rugby's (slightly) more open policy towards playing weaker sides.

Cricket - Analysis 26th July, 2012 02:51:16   [#] [0 comments] 

Test matches are on thing, but series are where it is at. This is a list of the best rating, accumulated quality ratings ignoring games rated below zero. Obviously it favours five test series, but then, so do our memories.

Series			M.	W.	L.	T.	Quality
Australia	West Indies	1951/52	5	4	1	0	7530.84
The most under-rates series and oddly the rated best. The absence of a quality pace bowler let the West Indies down, but the 4-1 scoreline between two great sides isn't representative of the tightness of the contest, decided by just 4 wickets.
Australia	West Indies	1960/61	5	2	1	1	7433.38
The closest of series, between a weaker Australian side than the early 1950s, but a stronger West Indies one; but for a single run and 3 wickets the West Indies would have won 3-1.
England	Australia	1981	6	3	1	0	6973.04
A ridiculously close series, all Australia's until Botham took over at Headingley, and even then they ought to have won two of the remaining three matches.
England	Australia	2005	5	2	1	0	6705.62
But for Warne England would have walked this, with McGrath for longer Australia would have done the same. The swings in fortune were immense, keeping everyone on the edge of their seats, meaning England's tight victories were tense but from well in front.
South Africa	England	1956/57	5	2	2	0	6072.71
Who said the 1950s were boring. A great comeback from South Africa, having collapsed from winnable positions in the first two tests, and been denied by inaction in the third.
Australia	England	1928/29	5	1	4	0	5483.65
England walked this, but the infusion of youth meant Australia were stronger by the finish, and only 12 runs and 3 wickets from a series victory.
South Africa	England	1909/10	5	3	2	0	5267.58
Aubrey Faulker may be the most under-rated cricketer of all time. He was majestic here, outscoring Hobbs with the bat, and taking 29 wickets with the ball.
Australia	England	1907/08	5	4	1	0	5250.67
The first two tests in this series were as tight as any before a strong Australia eased to victory. England were 2 wickets and 50 runs from victory, and 1 wicket from a white-wash.
Australia	India	1977/78	5	3	2	0	5172.06
Technically over-rated because Australia was without their WSC players, but Australia's three victories were all on a knife-edge.
England	Australia	1902	5	1	2	0	4949.98
A damp summer punctuated by collapses. The first two tests were wash-outs, the last two amongst the closest ever played.
England	South Africa	1955	5	3	2	0	4875.68
South Africa fought back in this series against a very strong English side before succumbing to Laker and Lock in the last.
Australia	England	1950/51	5	4	1	0	4776.42
As above, strong sides, close games, and a perhaps unlucky England losing by a lot less than the margin suggests.
Australia	West Indies	1992/93	5	1	2	0	4772.15
Won by a single run, the side accustomed to winning got the better of a draw in Brisbane, and scraped home in Adelaide. The handover would wait another two years.
Australia	South Africa	1952/53	5	2	2	0	4630.24
Close, but not tight games, with South Africa over-coming statistical inferiority to draw.
Australia	England	1998/99	5	3	1	0	4622.74
Australia were waning as Taylor's era closed. Only Slater's blistering hundred in Sydney kept this series from being tied.
West Indies	England	1967/68	5	0	1	0	4542.93
Bizarre series: two wickets from a loss in the first test, two wickets from winnings after following on in the second, and one wicket from victory in the fifth, the West Indies lost 1-0 after declaring twice in the fourth.
Australia	England	1954/55	5	1	3	0	4538.75
Australian collapses let England win three games, but this was a tight series between two good sides.
West Indies	Pakistan	1987/88	3	1	1	0	4523.44
the highest averaging series per game. The best two sides of the 80s toe to toe, paired with another drawn series in Pakistan.
West Indies	South Africa	2000/01	5	1	2	0	4421.05
South Africa clearly superior, yet they won twice by less than a hundred runs as Walsh held the fort.
South Africa	Australia	2005/06	3	0	3	0	4339.95
Australia always had the better of this series, but, as with the whole summer, a few key moments decided every game.
The best series from the four unrepresented sides:
South Africa	New Zealand	1961/62	5	2	2	0	4006.3
A forgotten series, neither side strong, but close games throughout.
Sri Lanka	Australia	2003/04	3	0	3	0	3767.56
Three times Australia conceded a lead, sometimes massive, three times they clawed their way back with Warne to the fore.
Pakistan	Zimbabwe	1993/94	3	2	0	0	2160.21
So close for Zimbabwe, years later Pakistan would be the site of their greatest triumph, but the two Ws were formidable opponents.
Pakistan	Bangladesh	2003	3	3	0	0	1337.58
Not terribly close, except by Bangladeshi standards. Well placed several times, they always fell short.

Cricket - Analysis 20th July, 2011 23:56:05   [#] [0 comments] 

This is by no means meant to be definitive. By calculating the rankings of the two competing sides, and minusing 10 times the calculated run margin, or, if a draw, the distance to victory of both sides, I have created a basic measure of game quality. It doesn't account for dead tests, series context, or other intangibles, nor does it correct for slight ratings inflation as weaker sides have been added. It also strongly favours great sides, particularly Australia who are fairly consistent on that front, meaning some great games between mediocre sides have missed out. That said, the list is interesting, and occasionally surprising.

Match						Test No.	Quality
South Africa	Australia	1996/97	2	Port Elizabeth	Australia by 2 wickets	1360	1925.4
Amazing comeback from Australia, led by series winning knock from Mark Waugh
Australia	Pakistan	2009/10	2	Sydney	Australia by 36 runs	1945	1926.0
Questionable comeback as Pakistan crumble in low chase.
India	Australia	1986/87	1	Madras	Match Tied	1052	1928.3
The second tied test, epic high scoring game as India chased 347
England	Australia	1882	1	The Oval	Australia by 7 runs	9	1930.0
The game that birthed the Ashes as Spofforth takes 14
Australia	India	1977/78	1	Brisbane	Australia by 16 runs	809	1937.2
Under-rated WSC years match as Thomson holds back Gavaskar
Australia	England	1884/85	3	Sydney	Australia by 6 runs	19	1940.0
Flowers and Read bring England close in an under-rated fixture
England	West Indies	1980	1	Trent Bridge	West Indies by 2 wickets	880	1945.9
Despite 5 wickets from Willis, Haynes and Roberts sneak home
West Indies	England	1973/74	5	Queen's Park Oval	England by 26 runs	738	1950.3
Boycott and Grieg draw the series in a fluctuating game.
England	Australia	1981	3	Headingley	England by 18 runs	905	1969.7
A truly great comeback but played between two average sides.
Australia	West Indies	1960/61	5	Melbourne	Australia by 2 wickets	506	1972.5
The final chapter in an epic series as Australia blocked out the Windies spinners to win
Pakistan	England	2005/06	1	Multan	Pakistan by 22 runs	1770	1973.3
A great comeback, started by Butt and Inzaman, finished by Shoaib and Kaneria
Australia	West Indies	1960/61	4	Adelaide	Match Drawn	504	1973.4
Mackay and Kline survive the final session to draw
Australia	West Indies	1951/52	1	Brisbane	Australia by 3 wickets	340	1979.2
The most under-rated series, as Australia just squeeze past Ramadhin and Valentine
Sri Lanka	South Africa	2006	2	Colombo	Sri Lanka by 1 wicket	1812	1979.2
Sri Lanka survive a late collapse as Murali takes 12
England	Australia	1902	5	The Oval	England by 1 wicket	74	1985.1
Jessop's ton allows Hirst and Rhodes to close a brilliant comeback.
South Africa	Pakistan	1997/98	2	Durban	Pakistan by 29 runs	1403	1985.7
Pollock sparks a collapse, but Mushtaq Ahmed holds off the long South African tail.
England	West Indies	1969	3	Headingley	England by 30 runs	655	1987.9
A West Indies comeback falls just short after a middle-order collapse
Australia	West Indies	1968/69	4	Adelaide	Match Drawn	645	1993.8
Australia runout half their side chasing a last day target, before surviving the last few overs to draw
England	Australia	1961	4	Old Trafford	Australia by 54 runs	510	1994.2
Lawry leads a comeback capped by Benaud as England collapse on the final day
India	England	1972/73	2	Eden Gardens	Inda by 28 runs	706	2008.6
Despite Grieg's efforts, England lose a low-scoring affair
West Indies	Australia	1998/99	3	Bridgetown	West Indies by 1 wicket	1453	2013.6
Extraordinary 153 not out by Lara to overcome McGrath and Gillespie
England	Pakistan	1971	3	Headingley	England by 25 runs	689	2016.9
Lever sparks late collapse in see-sawing game
West Indies	Pakistan	1987/88	3	Bridgetown	West Indies by 2 wickets	1097	2024.1
Amazing series ends with Winston Benjamin an unlikely batting hero
West Indies	England	1967/68	5	Georgetown	Match Drawn	636	2032.5
Cowdrey and Knott hold off Gibbs and Sobers all day to draw.
West Indies	Pakistan	1987/88	2	Queen's Park Oval	Match Drawn	1096	2036.6
An amazing match, concluded with both sides in sight of victory
South Africa	Australia	2005/06	3	Wanderers	Australia by 2 wickets	1795	2045.9
Martyn and Hussey mean South Africa fall short again
Australia	England	1894/95	1	Sydney	England by 10 runs	42	2055.6
The first side to win following on as Peel sparks extraordinary collapse
India	Pakistan	1998/99	1	Chennai	Pakistan by 12 runs	1442	2060.7
Tendulkar gets India to brink before lamentable collapse of 4/4
Australia	England	1954/55	2	Sydney	England by 38 runs	392	2073.2
Harvey's 92 not enough as Tyson takes 10 to complete comeback
England	Australia	1997	6	The Oval	England by 19 runs	1377	2074.7
Tuffnell and Caddick prevent Australia chasing low target in dead match
Australia	England	1982/83	4	Melbourne	England by 3 runs	943	2095.2
Thomson and Border fall just short in a game that stayed close the whole way
Australia	Pakistan	2002/03	1	Colombo	Australia by 41 runs	1615	2100.2
Shoaib's spell offers Pakistan hope but they fall just short
England	Australia	2005	3	Old Trafford	Match Drawn	1760	2109.4
Ponting holds back England for just long enough as last pair hold on
Australia	England	1998/99	4	Melbourne	England by 12 runs	1436	2116.2
Australia collapses alarmingly to Headley in evening finish
Sri Lanka	Australia	2003/04	2	Kandy	Australia by 27 runs	1688	2136.1
Gilchrist and Martyn start comeback in Warne/Murali showdown
Sri Lanka	South Africa	2000	2	Kandy	South Africa by 7 runs	1505	2137.4
Sri Lanka lose 4/8 after Ranatunga's dismissal to fail just short in low chase
England	West Indies	1963	2	Lord's	Match Drawn	544	2168.9
Cowdrey comes out with broken arm to see off Griffith and Hall in epic game
Australia	England	1928/29	4	Adelaide	England by 12 runs	179	2170.6
Dual tons from Hammond enough as young Bradman's runout by Hobbs leaves his side short in dead rubber
Pakistan	Australia	1994/95	1	Karachi	Pakistan by 1 wicket	1268	2177.3
Warne beats Inzaman and Healy for byes as largest last wicket chase is achieved
England	Australia	1902	4	Old Trafford	Australia by 3 runs	73	2182.4
Trumble's 10 enough to beat Lockwood's 11 as English collapse leaves them just short
India	Australia	2010/11	1	Mohali	India by 1 wicket	1972	2199.9
Laxman guides his team home in most recent epic game
South Africa	England	1956/57	4	Wanderers	South Africa by 17 runs	437	2207.6
Tayfield takes 9 in 4th innings to hold off English comeback
Australia	England	1924/25	3	Adelaide	Australia by 11 runs	160	2226.1
England almost pull off massive chase but fall just short
Australia	England	1950/51	2	Melbourne	Australia by 28 runs	328	2245.4
Low scoring game meant England continued their long losing streak
Australia	South Africa	1993/94	2	Sydney	South Africa by 5 runs	1243	2274.2
de Villiers bowls South Africa to famous victory as Australia fall just short two years running
India	Australia	2004/05	4	Wankhede	India by 13 runs	1720	2319.4
Crazy low scoring game on difficult pitch. A dead rubber but no less exciting for it.
Australia	West Indies	1992/93	4	Adelaide	West Indies by 1 run	1210	2345.3
My personal favourite, the dominant team of the past 15 years holds off the dominant team of the next 15 on epic fourth day
Australia	West Indies	1960/61	1	Brisbane	Match tied	498	2436.6
The first tied test, Davison and Benaud almost pull off unlikely chase in last session before runouts decide it
Australia	West Indies	1951/52	4	Melbourne	Australia by 1 wicket	345	2465.6
Series winning, 38 run, 10th wicket partnership from Ring and Johnston against Ramadhin and Valentine.
England	Australia	2005	2	Edgbaston	England by 2 runs	1758	2544.3
Warne and Flintoff combine to produce amazing game, finished by Harmison, Lee and Kasprowicz
And, the best games from the three unrepresented sides:
New Zealand	West Indies	1979/80	1	Dunedin	New Zealand by 1 wicket	873	1876.5
Hadlee overcomes the mighty West Indies in an ill-tempered game
Pakistan	Zimbabwe	1993/94	2	Rawalpindi	Pakistan by 52 runs	1240	1474.6
Wasim and Waqar take 9/52 to overcome a gallant Zimbabwe
Pakistan	Bangladesh	2003	3	Multan	Pakistan by 1 wicket	1658	1337.6
Twice Bangladesh has almost taken a proper scalp, twice denied by a great innings, this one by Inzaman

Cricket - Analysis 18th July, 2011 00:43:54   [#] [2 comments] 

While Warne takes his final bows, it is worth addressing an issue that I've meant to get to for some time; the rather vexed one of statistical comparisons between himself and Muralitharan. At face value, Muralitharan is clearly better:

Muralitharan	133 games	800w @ 22.72 SR 55.0
Warne	145 games	708w @ 25.41 SR 57.4

The arguments against that superiority are well rehearsed: Muralitharan had too many wickets against minnows, at home on turning decks; as are the counter-arguments: Warne mostly took wickets against England, New Zealand and South Africa, and failed against India. Others are intangible: the effect of playing with McGrath and Gillespie, rather than Vaas, the psychological effect on batsmen, and the ability to perform at key times.

Here we will ignore the intangibles, and focus on trying to eliminate the more difficult issues. Statistics are not set in stone, but merely a discussion point, so take this how you will; there will be no definitive answer at the end.

As a starting point, we need a baseline for comparison. Because they played on different teams, against different opposition, their records are distorted by who they played, and where they played. Here, for instance, are their home records:

Muralitharan	73 games	493w @ 19.56 SR 50.8
Warne	69 games	319w @ 26.39 SR 60.8

Warne's difficulties toiling on unforgiving Australian pitches make his average worse, whereas despite Sri Lanka's reputation for featherbeds, Murali made best use of spinning conditions. Their comparative record in each other's country shows this too (albeit with a much smaller, and less representative sample)

Muralitharan	5 games	12w @ 75.41 SR 131.0
Warne	9 games	48w @ 20.45 SR 39.6

A straight-forward method of eliminating this problem is to only compare like with like. Thus, we ignore their home records, and their games against each other. That throws up the following:

Muralitharan	55 games	295w @ 25.86 SR 59.0
Warne	65 games	325w @ 25.97 SR 58.3

A hair between the two, and more in keeping with people's perceptions, but equally distorting. Murali played roughly an even amount in each country, ranging from 11 times in India (avg. 45.5), to 4 times in Bangladesh (avg. 19.5). Warne, however, played as many as 22 games in England (avg. 21.95) to just 1 in Zimbabwe (avg. 22.83). A simple method of dealing with this is to normalise the games so that each player plays 1 game in each country:

Muralitharan	8 games	45w @ 24.24 SR 56.0
Warne	8 games	40w @ 27.00 SR 58.2

Which shows at least one interesting thing, namely that Murali would have benefitted from a more even distribution of tours, rather than lots of games in India where is 45.5 average is worse than Warne's 43.1. But such a figure is a step too far, because now Warne's three games against Zimbabwe and Bangladesh are seen as a quarter of his total career. Both figures above are close to meaningless when luck plays such a large part. An alternative method is to normalise to a reciprocal average for games each player played in each country, and normalise to a comparative away average:

Muralitharan	50 games	285w @ 24.98 SR 56.9
Warne	50 games	240w @ 27.73 SR 60.3

Again, Murali comes out a little in front, but there is still the small matter of excluding half of each player's career. To do this we need to calculate the advantage each player had for playing at home. We'll compare their home and away records against all teams (where they played teams both home and away) and create a comparative average for each (as above).

Muralitharan @ Home	94 games	632w @ 19.60 SR 50.9
Muralitharan @ Away	94 games	492w @ 27.38 SR 60.8
Home Factor		Avg: 0.72 SR 0.84

Warne @ Home	64 games	286w @ 27.89 SR 64.7
Warne @ Away	64 games	318w @ 25.49 SR 57.2
Home Factor		Avg: 1.09 SR 1.13

Notice the variation in averages from above achieved just by modifying the weights a little. There really is very little to distinguish between a player who averages 25 in some circumstances and 27 in slightly different circumstances.

We can then use this factor to create comparative home averages based on an even distribution of opponents, as above. Because Warne only played major nations at home we are looking only at England, India, New Zealand, Pakistan, South Africa and West Indies. Without the factor added, their home records are as follows:

Muralitharan	54 games	466w @ 21.07 SR 58.4
Warne	54 games	250w @ 26.60 SR 61.0

With the factor applied to create a home average normalised to away results this comes to the following:

Muralitharan	54 games	334w @ 29.44 SR 69.8
Warne	54 games	274w @ 24.31 SR 53.9

Excluding Bangladesh and Zimbabwe has a deterious effect on Murali's adjusted home average, but it is also true that the sheer number of wickets he took at home when the best option with the ball drags his figures down, whereas Warne benefited from not bowling as much in (adjusted) pace friendly conditions. What is also true though is that whereas Warne averaged 62.6 at home to India (mostly in his forgettable debut series), Murali averaged only 24.72. Adjusted, those figures become 57.2 and 34.5, more in line with their near identical averages in India.

Combining the comparative adjusted averages produces the following:

Muralitharan	104 games	618w @ 27.39 SR 70.2
Warne	104 games	514w @ 25.91 SR 57.9

That leaves a number of series where no direct comparison can be made.

Muralitharan
v Australia in Australia	5 games	12w @ 75.42 SR 131.0
v Australia in Sri Lanka	8 games	47w @ 26.02 SR 54.0
v Bangladesh in Sri Lanka	7 games	60w @ 10.43 SR 25.6
v Zimbabwe in Sri Lanka	7 games	61w @ 12.31 SR 44.3

Warne:
v ICC World XI in Australia	1 game	6w @ 11.83 SR 31.0
v Pakistan in UAE	2 games	16w @ 9.62 SR 25.8
v Sri Lanka in Australia	4 games	11w @ 47.73 SR 114.7
v Sri Lanka in Sri Lanka	9 games	48w @ 20.45 SR 39.6

The ICC World XI "Test" and Pakistan series in the UAE are near impossible to reconcile as they were once-offs. Unfortunate for Warne who dominated both, but not really relevant to the discussion here. The others represent almost a quarter of Murali's output and both his best and worst performances. We can reconcile them to our existing total by normalising the teams played and locations.

Locations can use the existing factors (1.09 for Australia, 0.72 for Sri Lanka). To normalise the batting we need the average runs scored by the key 6 nations (Eng,Ind,WI,Pak,NZ,RSA) in away series in those same places over the course of each bowler's career. That average comes to 31.95 for Murali and 31.44 for Warne. We then calculate the average for our oppositions in those same places, to get an opposition factor (Bangladesh: 0.68, Zimbabwe: 0.77, Ausralia: 1.17, Sri Lanka: 0.86). Multiplying out the wickets taken by the factors and normalising to 6.5 games per circumstance (close enough to the average) gives:

Muralitharan
v Australia in Australia	6.5 games	20w @ 59.03 SR 102.5
v Australia in Sri Lanka	6.5 games	32w @ 31.14 SR 64.6
v Bangladesh in Sri Lanka	6.5 games	27w @ 21.52 SR 52.8
v Zimbabwe in Sri Lanka	6.5 games	31w @ 22.25 SR 80.0

Warne:
v Sri Lanka in Australia	6.5 games	17w @ 50.55 SR 114.7
v Sri Lanka in Sri Lanka	6.5 games	21w @ 33.12 SR 64.19

Because they've been normalised to the existing away average, we can add these to the existing total to get an approximate idea of a cross-player normalised career average:

Muralitharan	130 games	728w @ 27.98 SR 70.6
Warne	117 games	552w @ 26.94 SR 60.1

Muralitharan's (and Sri Lanka's) significantly weaker performances away from home account for the difference, but there is something unsettling about a set of numbers that implies that Murali's home average of 21.07 against decent opposition is really worth 29.44 off Sri Lankan turners. Nevertheless, the numbers clearly indicate the relative worth of averages, which are not only very sensitive to a handful of results, but on the luck of opposition match-ups and home conditions.

Muralitharan is far and away the more prolific wicket taker, toiling away for his side. Unlike Warne, he took considerably more wickets in the first innings than Warne who had the support to focus his energies on last day efforts. But it is also fair to say that there is little to statistically separate the two bowlers once conditions and opposition are accounted for. Taking 250 wickets in Australian conditions at less than 27 is phenomenal for a spin bowler. Both are greats. Warne is the better all-round cricketer, for his tactical nous, batting, fielding and ability to seize the moment, as numerous recent articles have highlighted. Murali took full advantage of favourable conditions to lead his country from make-weight to serious competitor.

Cricket - Analysis 21st May, 2011 21:44:38   [#] [3 comments] 

Always keen to prove themselves correct, Hawkeye recently released some of the data over the controversial Tendulkar LBW referral. What is missing are the raw numbers, and even the raw images, which would allow us to produce an accurate reconstruction. But we can work with what we do have, with appropriate caveats, to discuss a few pertinent matters in this case.

Reconstructing Hawkeye

I have taken the images from the PDF and imported into a graphics program to make measurements. The pixel at the left-most point of the ball in each mage has then been taken to get a distance for sideways movement. Although the camera angle foreshortens the distance, the ball seems to cover slightly less ground as it moves closer to the stumps. By taking a linear measurement, therefore, I am making the ball slightly (very slightly, maybe 2 pixels) less likely to hit the stumps.

One thing to note is that the edge defintion is often blurred. What I don't know is whether hakweye has substantially clearer images to take their measurements from. By taking the negative of consecutive images, the ball would be much clearer than in a colour image where it blends with the pitch, but on this evidence it is hard to see how the measurements could be improved by more than half a pixel.

Projecting the pre-bounce line down, and the post-bounce line up registers the bounce at pixel 239. There are then seven points to calculate the projection from at 243,254,264,275,285,295 and 305. In the following frame of the video the ball actually hits the pads and falls to the off-side, giving the impression that Tendulkar was hit more centrally than he probably was. Because we are projecting a curve, anything fewer than three points makes the projection impossible - you'd need to assume a linear projection which may or may not be accurate. The data given indicates a frame-rate of around 150 fps over the 3m between pitching and impact. That however would be problematic for fast bowlers pitching and hitting the batsmen inside 2m. Hawkeye claims to be using technology that can operate at "up to 500 fps" however. Since that would be too much data to analyse quickly, we'll have to assume that they are either a) not showing all the data they analysed in their PDF, or b) only analysing enough data to make a projection (which would be sensible). Giving them the benefit of the doubt that they do the latter, we'll move on.

From the x-coordinates taken above we can see the ball moves 10 or 11 pixels leftwards at each frame, averaging 10.33. From the overhead hawkeye projection and the side-on shots we can calculate the distance the ball travels per frame, the total distance the ball travels from bounce to impact, and impact to the stumps as follows:

Calculated Parameters
Impact -> Stumps	1857mm
Bounce -> Impact	3032mm
Distance per Frame	424mm
Bounce -> Stumps Frames	11.54
Sideways movement per frame	14.9mm
Sideways Impact Point	+0.33mm outside leg stump

By calculating the number of frames from bounce to stumps (11.83), we can calculate the total sideways movement for a linear projection 14.9mm and add it to the bounce point to find where the left-hand edge passed the stumps pixel 358.23. Because the right hand of the stumps lies at 358 it appears Hawkeye is approximately correct, and the ball does miss the stumps, albeit by (in real terms) 0.33mm. Hawkeye claims more than this, but never actually says how much more. The lesson from that: small changes in the measurement value can have impact the end result by several millimetres.

Error and the UDRS

The difficulty with this projection is that it ignores error. The measuring error at a 1 pixel level (and as noted, that is probably generous given the blur in some shots) is 1.44mm. The standard deviation of the sideways movement measurements is 0.52 pixels or 0.74mm. Across the 5.13 frames of projection, that makes the total error ± 3.82mm just on the projection (there are also measurement errors for the bounce, each frame measurement, and the edge of the stumps).

Taking the projection error alone, and given the projected point where the ball passed the stumps, the probability that the ball actually missed the stumps was a meagre 53%. Still in Tendulkar's favour, but (you'd think) not remotely enough to over-turn a decision. Given the closeness of the projection, in order to know with 90% certainty that the ball actually was missing the stumps Hawkeye would need to be some 15 times more accurate than the data they have presented. They probably aren't, given the 2.5m exists as a clumsy attempt to deal with the poor accuracy of projections over that distance. While in pure probability terms the right decision was (probably) arrived at, this almost certainly over-stepped the bounds of a remit to correct "obvious" mistakes.

Cricket - Analysis 13th April, 2011 13:08:35   [#] [6 comments] 

[<-- previous]    [next -->]