The ICC have made their annual adjustments to playing conditions and in addition to their usual futile tinkering with ODIs, there is actually some stuff of note.
The biggest is probably that the ICC have given approval for Day/Night Tests provided both sides agree to the hours and type and colour of the ball. I’m not happy with this and I’m less happy that Australia have already said they would be keen to play D/N Tests. I do understand the need to reach out to audiences with Test cricket and I can just about understand it in places with sharply declining Test attendances. But I very much hope they are never implemented in England and I would rather they weren’t in Australia either. In places where Test cricket is still strong they should stick to the traditional red ball and sunlight.
The worse change is to the DRS, however. After India blocked it’s universal application, the ICC still made a tweak to the umpire’s call margin. They have widened the umpire’s call margin for the ball hitting the pad to half a stump width, the same as the margin for the HawkEye projection. But this betrays an utter ignorance of how a margin of uncertainty actually works. The margin of uncertainty regarding where the ball hits the pad is related to the accuracy of the cameras and nothing more. There certainly is one, but it will depend on the specific technology and is almost certainly smaller than half a stump width. And it is definitely smaller than the margin of uncertainty for where the ball hits (or misses) the stumps because by nature the uncertainty increases the farther into the future one tries to predict! What ought to happen in both cases is that the on-screen graphic should just show the uncertainty as it shows the path of the ball and that should be used to determine umpire’s call. Nothing else makes sense. Using the same, completely made-up margin for both is utterly ridiculous and all it will do is increase the controversy about the results. Given the influence the BCCI had, however, that may be the point.
Defensive Indifference 
Cricket boards and tv companies are obviously eager about day/night tests. I wonder are players equally eager?
I am not against it in principle but Im afraid d/n test would take some hardship from the game. No midday sun and stifling heat, no zinc ointment, no dripping sweat, no red spots on trousers…
Lets see how the first d/n test series turns out.
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What I suspect from the various day/night first class matches that have been played is that the more physical hardships will be replaced by more subtle annoyances. The players have said that it is hard to pick up the seam position on the pink balls (though the ones currently used will have to improve before any D/N Test can be played anyway) and there is also apparently a problem with dew as well. There also has been discussion of the twilight conditions causing problems. What I suspect (and it is only a suspicion) is that the problems with the ball especially will mean that we won’t actually see D/N Tests for a few years.
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I don’t really see dew as a problem. No more than cloud cover, intermittent rain, heat or wind. The ball is the big issue and won’t be resolved soon. Another is the backlash against having all day-night games. A lot of people will object to late nights on Saturday or Sunday. In theory you can play D/N weeknights and day on the weekend, but in practice they won’t, partly because they are fools, and partly because players will object to an 11am start after a 10pm finish.
On projections. It would be nice if the ICC (or MCC) actually defined what constitutes “hitting in line”. Because it is not necessarily the same as hitting the stumps, where any part of the ball would be sufficient. I do think you are wrong about projection error though. Projections are based on a series of points, which allows a line-fitting that will reduce the sampling error of a single point. Whereas a single point might be blurred. Moreover, where the ball hits the pad is also a projection, and a more complex one, because it is based on the last frame, projected onto the position of the pad, where the impact point in the z-direction has to be estimated. It is method dependent, but I suspect the margin of error on impact is much bigger
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You’re right that dew itself probably won’t be more of a problem then to what players are used, but I think the fact that they won’t have experience dealing with it the way the have other conditions will make it more of a problem, at least for a time.
You’re right that some more clarity on the laws themselves would help, but the way I have seen HawkEye used in the past suggests that ‘in line’ refers to the centre of the ball and the outside of the stumps. Certainly this is the way it is used for determining whether the ball pitched in line and the wording of the laws is the same for pitching in line and hitting in line (‘between wicket and wicket’).
The reason projections necessarily have a larger margin of uncertainty, however, is that although they do use several points, each of those points has its own margin of uncertainty. The line fitting does not reduce this, but actually /amplifies/ it as they all have to be taken into account. There is a /slight/ projection involved in the point of impact, but a much smaller one. But regardless of how large that uncertainty is the larger projection must use that as its starting point, meaning that it still must have a larger margin of uncertainty.
And either way, the method the ICC have decided on is hardly a scientific assessment of the accuracy of the technology and more just deciding on something that seems about right. It’s like when schoolchildren are told to just use 5% as their uncertainty, regardless of how big it may be. But at least the schoolchildren have the excuse of still learning and needing to focus on the concept rather than the specifics; the ICC don’t.
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The laws are very ambiguous on whether the centre of the ball is taken as the pitching point, or an area, of which some part of the area must be in line. I might have to write to the MCC and see what they say.
I agree on the ICC. Their maths related work is always terrible. They ought to be able to test the measurement uncertainty, and use that to calculate a line-fit uncertainty. But the review system is so clunky anyway the margin of error is largely political.
Either way though, I don’t agree on calculating the uncertainty. Individual points have a margin of error that might be quite large (say 2mm), equivalent to samples in a political poll. But a line fit through twenty consecutive points will give a very accurate position from end to end, and on the projection. (You can test this with line fitting in excel). It won’t always be more accurate because there can be issues with the end-points, but it will generally be constrained. Measurement uncertainty is more problematic than projection uncertainty – though as you state, it affects both.
Projection on impact is definitely a big problem. Hawkeye has no way of estimating impact from what I’ve seen, (I believe the operator makes a judgement) so it is guessing from the final known point to the next expected (but missing) point based on speed. The stumps don’t move, so accuracy of 3-5mm is probably pretty typical. I’d be surprised if the accuracy at impact, because it is being estimated on the z-axis, is better than 10-20mm.
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The laws most certainly are ambiguous; my point was only that the way the ICC have interpreted them up to now is more clear.
But with respect to uncertainty, there is a very big difference between using something like the line fit on a graph and projecting real world movement. A line fit assumes that there /is/ a line to fit which when dealing with a mathematical graph is a fair assumption. But that is not the case with something like HawkEye where a real world object is being measured. In this case uncertainties most certainly do propagate; it’s very well established physics.
The nice thing about impact though is that the ball comes very close to a dead stop, at least for a very brief instant and the distance from the final known point is going to be very small, certainly much smaller than the distance from the last known point to the stumps. The z-axis should not come into play either, since all that is being determined is whether the impact is inside the line or not.
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Rules for mathematical propagation of uncertainty are given here and I think the best example I can give for the physical propagation of uncertainty as it relates to this is a variation of the standard frictionless object. In an effort to predict where is will be in five seconds you measure the object as it slides by and note that at t=0s its position is 10+/-0.2m and at t=1s its position is 15+/-0.2m. Its (constant in this case) velocity is then given by (x2-x1)/(t2-t1). Since uncertainties are summed in subtraction this gives v=5+/-0.4m/s. In this case x=v*t, so at t=5s x=25+/-2m. As you can see the uncertainty has increased tenfold from the original measurement uncertainty. Obviously the process for HawkEye will be somewhat different, but the underlying physical principle still holds.
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Your formula is 100% correct. If you only have two points. Which we don’t. And it explodes if we project well into the future, which we aren’t. The projection of the line is comparatively short (1-2m) having travelled 5-8m. Errors are reduced with a larger sample size, for the same reason the standard error of a least square fit of a linear line will be smaller than the measurement error of a single point. The projected standard error for a curve will be two curves bounded by a) the inner edges of the standard deviation of end-points and the outer edge of the standard deviation of the centre and b) vice versa. For a straight line a linear line from the left to right bounds and vice versa. The error will propogate, particularly if a player is a long way down the pitch, but it is smaller than the multiplication of measurement error over distance.
The calculation of physical uncertainty with two points is identical to a line-fit with two points, by the by. Since the measurement uncertainty is identical to the standard deviation. With multiple points the SD is smaller, and therefore the propogation is not as large,
On impact. The ball only stops if it strikes perpendicular to the pad, which is not always the case. Using the post-impact point where there is a deflection will introduce all sorts of errors (and again see the Tendulkar dismissal in my link for how, the next frame is markedly to the left). The ball is travelling in the direction of the z-axis, with points 400mm apart. Given no impact point, but a missing sample, that gives an uncertainty of 400mm in the z-direction. The z-axis doesn’t matter, true, but if in a typical dismissal with the ball travelling at 10 degrees to the perpendicular, uncertainty in the z-position (or time if you prefer) translates to sin(10)*400 on the x-axis, or 69mm. Obviously -Eye makes an estimate of impact point, but it is still approximately 1/6 of the error in the z-direction, and there is no way they are accurate to within 50mm in that direction, given the curvature of the pads, obscured vision, etc.
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My example explodes, but only because I chose numbers that meant that I would not have to deal with annoying decimals. Essentially the dimensions are exaggerated for clarity, but as I said the underlying principle still holds that the uncertainty will increase as you go farther into time and it also holds regardless of how many points you use. You seem to be making the point that more measurements decrease uncertainty and that is true, but you have to remember that we are not just trying to express the uncertainty of a single measurement at and endpoint in time, we are trying to project the position at some point in the future. No matter how precise you get the initial measurement it is always going to increase again due to multiplying it by a time factor. In fact it’s actually /worse/ with something like HawkEye because there are external forces acting on the ball which puts a t^2 into play and mean that only the points after the ball has pitched are relevant. But even without all that there is still the basic physics that says that uncertainty will /always/ increase as one projects into the future.
You misunderstand my objections to a line-fit: the problem is that its measurement is not analogous to the measurement of the motion of a physical object. With a line fit one has a single dependent variable being measured directly. In the measurement of an object moving in three dimensions there are no fewer than /nine/ dependent variables only three of which can be measured directly. In a line fit one is trying to find the mathematical line that demonstrates the pattern underlying the data. With HawkEye one is trying to find a physical path that is at best defined by multiple implicit equations, but may not even be defined in a way we can formalise.
With respect to the z-axis, I thought you were referring to /height/ (with line and length being x and y) so that was why I considered it irrelevant. If it’s distance from the bowler then your point makes more sense. And I know that it does not come to a full stop, that was why I said ‘very close’. But I think you are being a little bit harsh on the technology. If one knew /nothing/ about where the ball had been intercepted then yes the uncertainty would be about 5cm. (Given that the ball slows down after pitching the z-uncertainty is closer to 30cm.) The system would also be almost useless as the ball would almost have to hit in front of middle to be given out. But the reason why I mentioned that the ball comes almost to complete stop upon impact is that one can measure /that/ point which will have /very/ close to the same z-value as where the ball was intercepted. In theory it would be exactly the same as the ball does come to a full stop in the z-direction, but the technological limitations mean that it is unlikely to be caught before it had rebounded slightly. But HawkEye uses 106 FPS which means that the ball is certainly not going to rebound 40cm in 0.01s to give the same uncertainty that you did. Even if one assumes that the ball comes off the pad at 10m/s (which I suspect is very much on the high end of the scale) then that gives an uncertainty in the z-direction now under 100mm. As you rightly pointed out, that translates into an uncertainty in the x-direction of about 16mm. That’s still a decent amount, but less than half a stump and as I said it’s on the high end of the scale.
Every situation will be different, of course and some will have a larger uncertainty than others. But that’s just another reason why the ICC should not use one single margin for umpire’s call. And it also does not change the fact mentioned above that the uncertainty will increase as one tries to project further forward.
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I’m not sure we are disputing much anymore.
I don’t dispute that errors will propagate, and sometimes explode significantly. Only that the e being propagated will generally be smaller (prob. 0.5-1mm) than the measurement error of any particular point (prob. 1-2mm). Depending on how many points are available.
I’m glad you are on board with the issues in determining impact time. I’ll note here that a propagated error of 2mm needs to have double the propagation length versus path length to exceed 16mm. Which was my original point: uncertainty of impact position is as large, as uncertainty of stump position.
I agree completely that uncertainty depends on particular circumstances, and that the ICC has not thought it through properly. Obviously that depends on circumstances, and the system/frame-rate/resolution being used. Most uncertainty is, I think, from 10-20mm which is nothing. But if a batsman is hit 600mm after pitching 4000mm down the pitch, then the projection path will be 10x the line-fit, which is going to translate to 40mm or more.
I don’t agree on the distinction with a line-fit. A line-fit takes measurements in the x-y plane and fits a function of x-y. In this case we are taking measurements in x-y-z and fitting two lines, One in the x-z plane, and one in the y-z plane. The former being the only one that matters for determining the line. The latter, height. Measurement error is different, insofar as it is not normally distributed – being a rounding error – but they are essentially equivalent. Being curves and not linear functions does increase the propagation error, but only where the ball is swinging markedly.
I’m interested enough in trying to determine exact margins to write about this, so perhaps we should leave it here and return when I have some graphics.
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Fair enough. There are some more things I have to say, especially on the distinction between real life and a line-fit. But they can wait.
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