LBWTF

So, I got given out LBW for a duck no the 2nd ball of the innings last Saturday. In my last game for the cricketing Stallions. I don't often enjoy getting out LBW, but there was a few things about this one that really stuck in my craw. Firstly, the bowler was left arm over the wicket. This should make it hard to get an LBW as:

• The ball must pitch on the line of at least leg stump, and
• Be still hitting the wickets

which is not an easy task starting with that angle. As a result I've always thought that if you are a decent way down the track you should be pretty much immune to LBWs for left arm over, unless:

• The ball is very full, and/or
• There is significant movement back in

This ball was neither full (I was hit adjacent to my left knee), nor did it (to the best of my recollection) deviate especially much. However, the umpire was adament that not only did the ball pitch in line, but it also hit me in front of middle and off, and moveover that it was "plumb".

I was still dirty about it the following day, so I thought I would do some analysis. Were my beliefs flawed?

I want to start by saying that the umpire:

• Only has a split second to consider a number of factors
• Only rarely has to consider height a factor on Wellington pitches, albeit many balls did bounce over the stumps on this deck.
• May have a different view of my underlying assumptions.

This has been written completely without malice and as an academic exercise.

I started with basic assumptions about the pitch; dimensions from the graphic below which came from Wikipedia.

I also noted from this article that:

• The wicket is 23cm wide
• The stumps protrude to 71.1cm above the ground

For the point of impact I used the following:

• For across the pitch, stated impact was in front of middle and off. I reckoned this to be 1/3rd of the way from the edge of off stump, i.e. 7.67cm from the edge of off stump
• Up the pitch is a little harder to estimate. I take guard with my back foot usually 30-50cm in front of the crease, putting my front foot about 1 metre out from the crease. I was hit on the front pad of my front foot. While I was certainly not playing the ball on the back foot, I hardly got a stride in either. I've used 1 metre from the crease for my calculations, and I think that is a fair estimate.

So, assuming a totally straight trajectory and impact on Middle and off, where could the ball have been bowled from?

I used FreeCad to create the above diagram; the files I made are downloable here. To explain:

• The Red box is the 'vitrual mat' which goes between both sets of stumps.
• The Blue box is the distance from the point of impact to the popping crease
• The Black lines indicate the range a ball could have been delivered from, hit the impact point and gone on to hit the stumps

The answer is that a straight ball could have been delivered from anywhere from up to 41.28cm outside of leg stump at the bowlers end, hit the batsman at the stated position and then go on to cip the edge of off stump.

OK, so how about the pitching in line with leg stump? First, some more observations:

• As mentioned previously, I was hit adjacent to my knee. The measured height of this is 54cm.
• Given this height, it is safe to conclude that this was not what is generally regarded as a Full Length Ball, i.e. within 4m of the batsman. It is more reasonable to conclude that it was a Good Length Ball, bouncing between 4-7m from the batman.

The fathest out ball still hitting off stump crosses the leg stump line 4.54m from the batsman, so it is in this zone.

However, the height causes other issues:

• If the ball was fuller, the implication is that it has gained height quickly (and will therefore continue to do so). Given impact 54cm up, the top of the 71.1cm of the stumps could easily be missed.
• If the ball was shorter, meaning height would not be such an issue for LBW, this then narrows our possible delivery point.

Investigating that second point further, if the ball had pitched on leg stump at the end of the Good length, i.e. 7m from the batsman, it would have:

• had to have been bowled from not more than 11.2cm outside of leg stump to still go through the impact point. 
• hits the wickets 2.81cm from the outside edge of off stump

Still do-able, but quite tight indeed given that this is the release point of the ball, and that parts of the bowler's body could generally be expected to be closer to the stumps as part of the action.

In conclusion, it is possible to be correctly adjudged LBW to a:

• non deviating, 
• good length ball 
• from a left arm bowler 
• even if you are hit on the front pad well down the wicket

However, the bowler MUST deliver from very close in to the stumps, and even then the window that needs to be hit is very small.