## Warne and Muralitharan - a normalised analysis Russell Degnan

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 Australia5 games12w @ 75.42 SR 131.0
v Australia in Sri Lanka8 games47w @ 26.02 SR 54.0
v Bangladesh in Sri Lanka7 games60w @ 10.43 SR 25.6
v Zimbabwe in Sri Lanka7 games61w @ 12.31 SR 44.3

Warne:
v ICC World XI in Australia1 game6w @ 11.83 SR 31.0
v Pakistan in UAE2 games16w @ 9.62 SR 25.8
v Sri Lanka in Australia4 games11w @ 47.73 SR 114.7
v Sri Lanka in Sri Lanka9 games48w @ 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 Australia6.5 games20w @ 59.03 SR 102.5
v Australia in Sri Lanka6.5 games32w @ 31.14 SR 64.6
v Bangladesh in Sri Lanka6.5 games27w @ 21.52 SR 52.8
v Zimbabwe in Sri Lanka6.5 games31w @ 22.25 SR 80.0

Warne:
v Sri Lanka in Australia6.5 games17w @ 50.55 SR 114.7
v Sri Lanka in Sri Lanka6.5 games21w @ 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   [#]

Warne and Muralitharan - a normalised analysis
Fantastic post, Russ. Very thoughtful as always. Is there a way to compare their *best* performances? I'm thinking of Murali's 1998 Oval versus Warne's ?
Samir Chopra  27th May, 2011 07:53:44

Warne and Muralitharan - a normalised analysis
Samir, the official rankings do that, although they don't report individual games, just a rolling average. It is not easy though, because there is no way to know if a performance was good because the player was good, or if the conditions were poor, or the opposition bad, or just a player's own team-mates.

I'm interested in estimating win-shares which is common in basketball and other US sports. And I can use my individual game rankings to show a team rating (and therefore a player ranking). But I haven't worked out a good way of accounting for draws in test matches as forcing a draw that would otherwise have been a loss deserves recognition (and vice versa). When I get time though, I'll get back to it.
Russ  28th May, 2011 17:34:12

Warne and Muralitharan - a normalised analysis
I recently delved into this stats match up with the express point of proving to an Englishman who I got into a argument with that Warne was at least the equal to if not superior to Murali.

The best argument I could make was on away records (minus Zim and Ban):

Warne avg 25.5 s/r 57.1
Murali avg 27.7 s/r 61.7

That and Warne surprisingly having a better record than Murali in India.

As you note, what makes this comparison so difficult is crickets ad hoc scheduling.

Muralis home record is amazing, even adjusted by taking out Ban and Zim, avg of 22.2, s/r 56, rpo 2.4.

Cameron  8th June, 2011 18:37:04