## Bowleds, LBW's, and a little quiz

Whenever people study umpiring bias, they almost always look at LBW's. There's not a lot else you can do from looking at scorecards — other dismissal types are much more clear-cut.

A paper by Trevor Ringrose in 2006 ('Neutral umpires and leg before wicket decisions in test cricket', J. R. Stat. Soc. A 169, 903) considered LBW rates by country and the presence of neutral umpires, and found that the neutral umpires made no difference to the home-side bias of LBW decisions that affects some sides.

That paper's too technical for me to be bothered wading through this evening, so instead I'll talk about what Charles Davis did in The Best of the Best. For each team X, he calculated the difference between X's LBW percentage (that is, number of LBW's divided by number of wickets) and their opponent's LBW percentage, first for X's home Tests, then for X's away Tests. Find the difference of those two values and you get the home-side bias in LBW decisions for team X.

Pakistan is the major side that apparently gets favoured the most by home umpiring, clearly ahead of Australia. But Davis points out that in addition to having lots of LBW's go their way, Pakistani bowlers (I'm sure we know which ones) in the 1990's also got a very high number of bowled wickets. Correcting for this, the apparent umpiring bias in Pakistan becomes comparable to that in other countries. It just seems worse because they hit the pads so often.

So, following thinking along these lines, I took all bowlers with at least 100 Test wickets since World War II and plotted their LBW to caught ratio (i.e., number of LBW's divided by number of wickets caught) against bowled to LBW ratio. There's no fancy regressions to the mean or anything, these are raw numbers.

There's a bit of a trend there, but plenty of scatter. Ian Johnson (109 wickets) has one of the highest bowled to caught ratios (just over 0.7) but an LBW to caught of less than 0.2.

The two W's are fairly easy to spot — they're the ones fairly close together with LBW to caught ratios above 0.6, and bowled to caught ratios above 0.5. So they indeed got plenty of bowled and plenty of LBW's. But there are several bowlers with lots of LBW's and not many bowleds.

Now for that little quiz. Waqar has the highest LBW to caught ratio at 0.68. Wasim is third at 0.62. Who's second? He's the other data point quite high on that scatterplot, with a bowled to caught of 0.29.

You've put up that "Monster with two arms pointing up" icon as your profile picture! I'm amazed at your obsession with it.

I saw another Wordpress blog recently with the monsters, and decided that I should adopt my light blue arms up guy.

It's not the best monster, but the Internet would be a better place if everyone had a monster avatar.

No monster but...

I'm wondering if second place is Murali??

If not, is it a spinner or MP bowler?

Cheers.

Not Murali. It's a medium-fast or fast-medium swing bowler.

What I find interesting, is that there seems to be practically no correlation between bowled and lbw dismissals at all.

The low bowled/caught ratio is the giveaway to the quiz. Someone who never had the pace to get through a player's defence. So... Terry Alderman, who oddly enough, would have rarely got lbws playing on his home ground. But I guess he made up for that in his trips to England.

Terry Alderman it is.

While he had a much better record in England than in Australia, his wicket-types are fairly similar in the two countries.

Aus: 34 caught, 9 bowled, 25 LBW
Eng: 41 caught, 12 bowled, 30 LBW