Speed Gun Shenanigans

For many a year now, cricket fans and commentators alike have been obsessed by the magical aura of the speed gun.

Measuring the speed of the ball by a radar is similar to measuring the speed of the moving car. It works by sending a radio wave that is reflected off the cricket ball. The gun gets this echo and then by using the principle of Doppler Shift, calculates the speed of the ball.

The problem with this technology is that it relies on using speed rather than velocity. Velocity is a better measure as it takes into account how far the ball actually travels to get to the batsman, rather than just the speed it is travelling at.

Think of it this way. To walk from your front door to your couch may be 5 metres in a straight line. However, if you deviate via the fridge to get a beer, it may be a 10 metres trip. You still walk at the exact same pace, and you get to the couch, but it takes longer to get there.

Let’s look at why velocity is a better measure than speed.

Mitch Johnson bowls a full toss bowled at 135kph that goes perfectly straight and for the purposes of this exercise, doesn’t lose speed as gravity and wind resistance grab hold. It will reach the batsman’s at the popping crease at head height in 0.471 secs. The ball has travelled 1768cm from the bowlers popping crease to the batsman standing on his popping crease.

Mitch now bowls that same ball at 135kph, but it’s a half track bouncer. It will take 0.48 secs to reach the batsman (again, assuming no loss of speed due to any factor). That’s 1.9% longer that the batsman has to respond, even though the speed gun shows the same speed.

The diagram below reflects half the ball’s journey on the way to the batsman. The total straight line distance popping crease to popping crease is 1768cm (half pitch is 884cm as shown above).

I have even taken the liberty of calculating the release height at 226.4cm. This is based on taking a 179cm (6ft) man, adding 86cm (34 inches) for arm length and removing 40.6cm for the head and neck height. the ball has to travel 1824cm

For that bouncer to reach the batsman in the same 0.471 secs as the full toss, Mitch would have to release the ball at 139.1 kph instead of 135 kph

Both of these examples assume Mitch releases the ball over middle stump and it passes of the batsman’s middle stump.

However, Mitch may release the ball from close to the stumps but send it 3 stumps wide of a left handed batsman’s off stump. That in itself adds another 31 mm to the ball’s journey or another 2% reaction time. A right handed batsman would get more time to react as the ball travels even further.

What if Mitch bowls an inswinger and not a ball that doesn’t travel in a straight line? Again, the distance the ball travels on a curve will be longer, and therefore the batsman will have additional time to react.

So what the hell am I trying to tell you?

Firstly, that speed in isolation is a poor indication of how fast a batsman will perceive a bowler is going at it. I can bowl at 135 kph, but if it’s short, wide and swinging, it could appear to be around 5% slower to the batsman in regards to reaction time. In fact, it would seem to be a Ishant Sharma like 128.2 kph

We need to add the element of distance that the ball has travelled, both in total distance vertically, total distance deviated from the stumps and also an allowance for swing to get an accurate measure.

It means a speed gun reading from a head high full toss is probably very accurate if it doesn’t swing too much.

It means a speed gun reading from a half track bouncer is not reflective of how long the batsman has to respond. In fact, a fairly straight bouncer gives the batsman around an extra 4% longer to respond than a full toss. Add some width and swing, and it could be much more.

So, enjoy your speed gun numbers. However, like the IPL, they don’t mean much

 
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