Sunday 21 July 2013

Skill and Luck in Cricket.

The cricket season is now in full swing, even if the Ashes is virtually a done deal, so I thought I'd trawl the web and crunch a few cricketing numbers. As a sport, cricket is much more akin to baseball than it is to an invasive team sport such as football. Therefore, whereas team statistics is the more rewarding starting point for the latter, cricket lends itself more to individual player analysis.

Evaluating player talent in football is complicated not only by the support given by teammates to statistical headline grabbers, such as goal scorers. But the lack of a rigid playing format also means that a soccer player can shoot from any position on the pitch, whereas a bowler is restricted to repeatedly hurling the ball down a consistent length of pitch. Therefore a bowler's figures are the product of a controlled, repeatable trial, but a goals scorer may be benefiting from taking his shots from varying field positions.

Cricket is much more about simply taking wickets. Batsmen finding scoring difficult at one end of the pitch may be tempted to take more risks at the other and present wickets to the lesser bowler in the process. However, is would be hard to argue that the best bowlers aren't also prolific wicket takers. So I'm going to dip my toe into cricket stats and look at wicket taking rates for test bowlers and particularly the likely spread in talent across this stat.

The method follows a familiar pattern, the average wicket taking rate for a group of bowlers is taken and then the spread of this rate within the group is compared to that expected from random chance. The more smeared out reality is from the hypothetical, entirely luck driven expectation, then the greater the spread of real, actual talent is likely to be within that group.

Perhaps unsurprising to anyone who has picked up a cricket bat, bowling and specifically in this case the rate of wicket taking is a talent. And a spread still exists at the highest echelons of the game. Such is the amount of cricket played in the modern era and the vast number of "trials" the top bowlers have taken part in, a top player's raw rate requires very little regression towards the mean to improve our estimation of his likely true ability.

Dale Steyn is the overall leader in the rate of wicket taking in test cricket with over 300 wickets from over 13,000 deliveries and very few test players change positions from their raw percentages, even when sample size is allowed for. Glenn McGrath has a marginally inferior strike rate to England's Darren Gough, but he manages to creep ahead into 9th overall once sample size and regression towards the mean is applied. A rare Aussie victory over England this summer.

Australia in happier cricketing times.
An average, elite test bowler takes a wicket every 60 balls and before you can begin trust the evidence of your own eyes and begin to believe that the performance you are seeing represents more skill than good or bad fortune, a bowler should be observed to bowl something in the region of 222 overs of test cricket. So a player who bowls poorly or well on debut hasn't been given anywhere near the opportunity to demonstrate his likely test career path.

If we repeat the exercise for one day  international cricket, again we see a spread of wicket taking rates that differ significantly from a random spread based around the group mean that indicates the presence of repeatable, human talent. Although in this case slightly less so than in test cricket. Wicket taking on the part of bowlers and wicket retention for the batsmen are less important in these day long run chases, so it is understandable that less skill and more luck is involved in taking wickets in a late order slog.

In the curtailed form of cricket an elite bowler strikes on average once every 38 balls, so despite the greater element of chance, this overall enhanced strike rate means that a bowler will most likely demonstrate his talent over and above his good or bad fortune after about 180 overs. Still a substantial number of matches given the limits on the number of overs a bowler may bowl in a single one day international.

Regressed Bowling Strike Rates in Test and One Day Cricket.

Player. Reg. Strike Rate. Balls/Wicket. Test Cricket. Players. Reg. Strike Rate. Balls/Wicket.
One Dayers.
D Steyn (SA) 42.3 B Lee (A). 30.0
Waquar Younis (P). 44.4 Waquar Younis (P). 31.0
M Marshall (WI). 47.5 Saqlain Mushtaq (P) 31.1
A Donald (SA). 47.8 A Donald (SA). 32.1
F S Trueman (E). 50.1 S Malinga (SL). 32.1
Sir R Hadlee (NZ). 51.3 Shoaib Akhtar (P). 32.1
J Garner (WI). 51.5 M Johnson (A). 32.3
M Holding (WI). 51.6 S Broad (E). 33.2
G McGrath (A). 52.2 M Ntini (SA). 33.2
D Gough (E). 52.3 A Agarkar (I). 33.4
D Lillee (A). 52.5 N Bracken (A). 33.8
J Thomson (A). 53.4 A Flintoff (E) 34.0

If we finally compare the talent required to effect certain dismissals across the two formats of cricket, test match play invariably allows for the talent to shine through. The top leg before wicket takers have the time and less pressure to prevent runs in test cricket to demonstrate their art fully. A list of the top lbw wicket takers in one day matches is more likely to contain a lucky player than one with a deadly, inswinging yorker. Likewise, when it comes to hitting the stumps or inducing a stumping, talent is more diffused than in the short game.

However, one category of dismissal appears to show a greater spread of talent in odi's than in test cricket. Namely, wickets by way of catches. The days of odi's being contested by the same team as turned out in the test arena is long gone. Boycott opening for England in a 60 over match is unthinkable, nowadays. Specialist fielders/batsmen are now common place. The talent spread may be catching bowlers who were fortunate to play with excellent catching teammates. So ultimately individual cricket stats, as with football also owe some level of input from the players surrounding you.

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