Law 8 of the Laws of Cricket specifies the size of the stumps as follows.

8.2 Size of stumps
The tops of the stumps shall be 28 in/71.12 cm above the playing surface and shall be dome shaped except for the bail grooves. The portion of a stump above the playing surface shall be cylindrical apart from the domed top, with circular section of diameter not less than 1.38 in/3.50 cm nor more than 1.5 in/3.81 cm. See Appendix D.
8.3 The bails
8.3.1 The bails, when in position on top of the stumps,
- shall not project more than 0.5 in/1.27 cm above them.

Since 2016, the ICC’s DRS rules for LBW specified that if at least half the ball was projected to hit the stumps (i.e. if the centre of the ball passed within the rectangle 9 inch x 28 inch) then such a delivery would be classed as “hitting” (red, in the chart below). If some part of the ball, but less than half was projected to hit the stumps, this would be classed as umpire’s call (orange), and if no part of the ball was projected to hit the stumps, then it would be classed as missing (green).

On height, the hitting zone ended at the top of the stumps. It did not include the bails. The logic behind this exclusion was based on a finding in the MIT review (see Osman Samiuddin’s excellent reporting about that study) that ball-track was less reliable in its estimation of height than it was in its estimation of line.

The estimated position of the ball when it crosses the plane of the stumps (this is traditionally shown as the beehive chart on TV) has an error which is not equal for height and line. In other words, if one drew the zone in which the centre of the ball is estimated to pass, then this zone would be an ellipse with a major vertical axis, and not a circle.

In the executive summary of the MIT review of the technologies in DRS in 2016 , the authors estimated the following. These quotes are from the executive summary of the reviewers report to the ICC. They were shared with me 4 years ago. The report was never published by the ICC (it will probably never be published, either in its full form or in executive summary, and at least some of the reasons for not publishing this report this are probably good). Since the ICC appears to have moved on from the recommendations of that report by updating its DRS rules further, I share the relevant bits from what was quoted to me about four years ago about the error estimates. You may wish to read these more than once, since they are precisely worded conclusions and it is important to understand what they do not say.

"Using 4 or more frames after bounce brings the prediction error within the RMS value of the measured location. Therefore we recommend that the operator informs the third umpire if less than 4 uninterrupted frames after bounce are available for simulation and that the 3rd umpire either ignores the simulation or understand that the error in height can be as high as 23mm and 6mm in width when less than 4 frames are used."
"The maximum error of ball tracking was 8mm or about 1/10th of the diameter of the ball in the width direction. We therefore recommend that the line of umpires call in width is reduced to the middle of the ball hitting the outside of the off or leg stump. In other words if more than 1/2 of the ball is touching the stump then the call is out. If less than half the ball is touching the stump then it is umpire's call.
The above has only been tested and therefore only holds for frame rates of 340 fps. However, since it is defined in terms of number of frames the theory and error margins should be the same for other frame rates. This will be tested soon."

The parts of the report which have been quoted to me do not explicitly say that length (height) and line (width) are not equally accurately predictable. But this has been a persistent point brought up by everyone with whom I’ve discussed ball tracking over the past decade, including Paul Hawkins of Hawkeye, that height is harder to estimate than line. The MIT reviewers determined a relationship between the number of frames of video available after pitching, and the reliability of the estimate of the position of the ball at the plane of the stumps. Notably, they found that when less than 4 frames were available, the average error increased more for height than it did for width. (Note that for the average fast bowler - 120 kph or 33.3 m/s at the batting end - at 48 fps, 4 frames cover ~70 cm, at 120 fps they cover ~28 cm, at 340 fps, they cover ~10 cm. Hence the 40 cm rule in DRS.)

Based on what was quoted to me from the MIT study four years ago, in the worst case, the ball is almost certain to lie within a range x +-8 mm on width, and some figure larger than 8 mm (most probably somewhere between 8-16 mm) on height. Note that these are not figures for average error. They are the figures for the maximum error (i.e. the worst case.).

A “Beehive” of the locations of the cricket ball in Test cricket based on the hawkeye data published by the ICC in the scorecards on its website is classified into “hitting”, “missing” and “umpire’s call”. The size of the ball and the estimated zone of its location based on an approximation of the measured errors is shown as well. The errors used to draw the ellipse for the estimated location of each ball uses +/- 8mm on the minor (horizontal) axis, and +/- 10mm on the major (vertical) axis. The -ve x direction represents the off-side for the right-hander.

The point of all this is that all the evidence points to the fact that the location of ball is more difficult to pinpoint on height than it is on line. The ICC’s decision in 2016 to narrow the umpire’s call zone overall, but restrict the hitting zone to the frame of the stumps and leave the bails (an additional 1.27 cm) was a conservative choice which reflected this fact.

The changes announced this week expand the ‘hitting’ zone to the top of the bails instead of the top of the stumps, and place the ‘umpire’s call’ zone above that. From 2016-2021, the umpire’s call zone (the orange band) had a width of 3.56 cm (or the radius of the cricket ball) on line, and 3.56+1.27 (or 4.83 cm) on height. The hitting zone (red) measured 22.8.6 cm x 71.12 cm. Now the ‘hitting’ area has been increased to 22.86 cm x 72.39 cm - an increase of 1.8%. The band on height is also 3.56 cm now.

Given the distribution of deliveries (in the picture above, deliveries from seamers are shown) from ball tracking, under the rules which existed from 2016-2021, 13% of deliveries (from bowlers of all styles, not exclusively seamers) fell in the ‘hitting’ zone. 13.6% of deliveries will fall in the ‘hitting’ zone under the new rule. Put differently, on average about 237 deliveries are in the ‘hitting’ zone in a Test match. Under the new rule, this will increase to about 249 deliveries per Test match. On average, 12-13 deliveries which were in the umpire’s call zone under the old rules will now be classified as ‘hitting’.

In doing this, the ICC seems to have discarded a key point about ball-tracking which was offered by the reviewers from MIT - that estimates of height are less certain that estimates of width. The new rules presume that estimates of height and width are equally certain.

Essentially, the stumps, for the purpose of DRS, are no longer the actual stumps pitched on the ground. These have been overrun in cricket’s imagination by the modeled stumps in the visualization of the ball-tracking simulation. Years and years of watching that visualization show the ball clipping the bails and have it return “umpire’s call” have poisoned the minds of viewers and ex-players alike. They began to say they were “confused”. And instead of trying to clear up the confusion by trying to understand the mathematics of the matter, they used their powerful voices to campaign for the mathematics to be ignored.

To its credit, the ICC’s Cricket Committee has not buckled entirely. They have retained the ‘Umpires Call’ zone. But they have narrowed it. It is a compromise. In 2016, when they first narrowed the umpire’s call zone by reducing its width to the radius of the cricket ball (as opposed to the diameter of the cricket ball, as it was before 2016), I argued that a bad idea had won, because the umpire’s estimate of whether or not the ball would go on to hit the stumps had been disciplined bureaucratically. At the time, the copy editors at The Cricket Monthly used the fitting title ‘Television Killed The Umpiring Star’ for the story. Right now, the title ‘The Superstars Killed The Mathematical Star’ would be an apposite sequel. A good idea - that the ‘umpire’s call’ zone should be wider for height than it should be for line, since the ball-tracking estimate is less confident about height than it is for line - has lost.

Nevertheless, given that the basic structure of the review and the Umpire’s Call zone has been retained, the application of DRS for LBWs remains basically unchanged, if marginally more in favor of the bowler than it was in the 2016-21 period. This means that the virtual delivery in the animated visualization on your television set will continue to show the ball clipping the bails and HawkEye or VirtualEye returning “Umpire’s Call”. Its just that this will happen less often.

Sadly for the ICC, “less often” is a mathematical idea. And the superstars who have campaigned relentlessly against ‘Umpires Call’ for five years have shown themselves to be immune to those.

I predict that this will be revisited further in two to three years.

A Cricketing View

The New LBW Rule In DRS