Do you recognize this situation?
You are a decent pace bowler; you open the bowling for your club, or perhaps come on first change. Today your team is playing against quality opposition, proper batsmen who don’t give their wicket away too easily, although rumor has it that they have a fairly long tail. Bowling well and working hard, you eventually pick up three wickets for twenty-three runs off eight overs (8 – 0 – 23 – 3) and the oppo are 103 for 6 off 24 overs. So you are feeling quite pleased with yourself as you take a well-earned blow down on the fine-leg boundary.
But what’s this?
Sensing that the opposition batting lacks depth, the captain brings himself and his best mate on at the fall of the seventh wicket, and they proceed to clean up the tail-enders, with skipper skittling 9, 10 and 11 in four overs and finishing up with better figures than you at with 4 – 0 – 19 – 3.
“No fair”, you find yourself thinking, as you trudge disconsolately back to the pavilion, watching the team’s coterie of brown-noses slapping the captain on the back.
Well, fear not, change is at hand, Professor Hermanus H. Lemmer of the Department of Statistics, at the University of Johannesburg feels your pain.
Supposing we could find a way to attach a weight to the wickets taken depending on where the batsman was in the batting order? If we could do that a bowler would get more statistical credit for taking out Hashim Amla than Monty Panesar, and that can only be a good thing, (sorry Monty).
Professor Lemmer has done just that by producing a weighting for every position in every form of cricket – multi-day, 50 over and Twenty/20.
Here for example is the scale for 50 over games
Yes, I’m afraid it still adds up to 11, you won’t be able to claim points for non-existent batsmen.
So for clarification Lemmer’s statistical analysis has shown that number 7 batsmen score on average 0.98/11ths of all runs scored in 50 over games, number 11 batsmen (i.e. people like me) have scored just 0.19/11ths. So this scale gives a bowler seven times as much credit for taking out a number 3 or 4 batsman than a rabbit at 11.
So how to put this table to practical use? Lemmer has designed the Combines Bowling Rate (CBR*) as a new measure of bowling performance, CBR* is calculated with the following formula.
CBR* = 3R/(W*+O+W*xR/B)
Where R = runs conceded
W*= sum of weights of the batsmen out
O = overs bowled
B = balls bowled
So let’s apply the traditional AVE system and Lemmer’s CBR* methodology to our mythical situation and see what happens.
The Average (AVE) for you (Mr. Excellent Bowler) is 23/3 = 7.66
Whereas Mr. Meally-Mouthed skipper gets an average of 19/3 = 6.33
Now imagine you had taken out batsmen 1, 3 and 5, so calculating CBR* using the formula above, the outcome for Mr. Excellent is now 4.92 – looks better already doesn’t it? And the CBR* for the Skipper, (who took out 9, 10, and 11 remember) is now 9.5.
As with AVE the lower the figure for CBR* the better, so now justice has been seen to be done. Despite the fact that Skip picked up the same number of wickets in only half the overs bowled, your figures are convincingly better because you took out the quality batsmen.
Some bowlers will come out of this very well, when Professor Lemmer applied his CBR* rankings to the first Twenty/20 World Cup, Jimmy Anderson’s ranking improved from 28th to 22nd due to the high number of lower order batsmen he gets out, whereas Umar Gul slipped from 2nd to 5th for the opposite reason.
All we need now is someone to design an iPhone app to calculate CBR* and good bowlers everywhere will be happy.
Mark, thank you for writing about my measures. You have clearly illustrated how unrealistic the traditional bowling average can be. Just be careful to write the formula as CBR* = 3R/(W*+O+W*xR/B). I may mention that CBR* is used for limited overs matches only. For unlimited overs matches (like test matches) I have defined the dynamic bowling rate DBR* with a different formula and also a different set of wicket weights.
Thanks Professor Lemmer, I have adjusted the formula. The concept of this blog is to make sense of academic research and present it in a way that is of use to the jobbing Level 2 coach (such as myself) or club cricketer who perhaps doesn’t have time to trawl through academic papers. That’s why I have focussed on one-day cricket up till now, because that’s primarily what my intended readership deals in.
However I will return to the ‘Cricket-Moneyball’ theme shortly, and I will include research on multi-day cricket in my future posts.
Somebody needs to write a popular-science type book on this whole subject of Cricket Moneyball, and as the Godfather of the field I think that should be you, Professor.
Thanks again, for taking the time to respond.