DRS for LBW

[K]

I posted about DRS on Day 1 of the Boxing Day Test. And what happened on Days 3-4 was a great example!! Of course I was right.


On Tuesday 26, I wrote:

There's no sign the umpiring has got worse. And batters have no reason to complain. They get the chance to review!! They get a second chance batters never got in the old days!

There's no "raffle"! If you run out of reviews (e.g. Oz run out 'cos FTB Smith blows one, reviewing his plumb LBW decision), it's your own fault!!

And we have the insanity of Warner and FTB whingeing when DRS agrees with the ump. Sheesh, how can you whinge when the umpire and DRS both say it was hitting the stumps?


And the DRS rules have always been in the batters' favour. That's why the whingeing of FTB and Warner makes no sense. The scary thing is if the crazy sh** FTB and Warner say misleads the public.

DRS always works to favour the batters.

If the ump gives "not out" and tracking says it's hitting by 3.5cm (3.5cm of ball is hitting wicket), it won't overrule the ump ("umpire's call"). But if the ump gives "out" and tracking says it's missing by 1mm, it overrules the ump ("not out")!!!

Batters have to be really stupid to whinge with those rules. Pity the poor bowlers.


Wu, December 29:

'Pakistan also had four reviews turned down on umpire’s call, the two costliest coming in Australia’s second innings when Mitch Marsh was on 40 and Steve Smith on 25.

In both cases, the delivery was found to be clipping the stumps but because the initial decision was not out more than half the ball needed to be hitting for the decision to be overturned.'

(The Age)

Ramsey, December 29:

'Pakistan's team director Mohammad Hafeez has blamed "inconsistent umpiring and the curse of technology" for the 79-run loss to Australia, adding his team played better cricket and would have been rewarded with a different result but for the offending officialdom.

While the contentious dismissal of ... Mohammed Rizwan ... was the lightning rod for Hafeez's grievance, he pointed to other decisions throughout the second Test.

The former allrounder didn't cite individual examples but alluded to the number of 'umpire's call' outcomes from on-field reviews that were a feature of the game...
...

"The ball hitting the stump is always out - why it's umpires call, I never understand that. A lot of areas need to be addressed for the betterment of cricket.

"Our Pakistan team played better than the other team in general."
...

But the visitors can also point to the four reviews deemed to be umpire's call all that all fell in Australia's favour, while the hosts also benefited from some crucial line-ball decisions – most notably lbw shouts against Marsh (on 25) and Smith (on 40) during their stand – which were decided by a hair's breadth.

In turn, Australia can cite the successful review that overturned an on-field lbw verdict from Nathan Lyon's bowling against Pakistan skipper Shan Masood on 12 (he went on to top score with 60) earlier today as another of those 50-50 calls that left one camp scratching their heads in bemusement.'

(cricket.com.au)

[K]

[Pies4shaw]

DRS ball-tracking for lbw is just a projection. It isn't 100% accurate. It's just a probability model with error at the margins. It may help to say that the error on the height of the bounce is much greater than the error on the line of the delivery. In both cases, though, the way DRS operates is the same (even though it should be much more conservative on bounce and respect the umpire's call - as to whether a ball is going to travel within the height of or over the sumps - in many more cases).

Consequently - and despite the differential statistical error with "height versus line", the laws allow for the uncertainty of the projection at the margins.

When it's a line-ball, you go with the umpire's call. It supports the umpire in marginal calls, both for decisions given out that "shouldn't" have been, as well as for decisions given not out that "should" have been out. What it's intended to do is rule out "howlers" - the "not out" when the ball is going to hit half-way up middle stump and the "out" when the ball has moved too much and is actually going past the stumps a few inches wide of leg stump. It doesn't rule out all howlers, of course - there was a famous example where Elgar was given out by a South African umpire against India a few years back and, on review, DRS said the ball was going over the stumps. No-one at the ground thought that - not even Elgar. But there are likely fewer than there used to be, so it's a useful system.

If the ball-trajectory were shown as a probability spread (eg, a band 3 balls wide, showing the "hot" central part of the spread, as well as the alternative projections outside that central spread), rather than as a specific representation of a cricket ball in flight, it would be easier to understand. What the "umpire's call" identifies is that - on the probability spread - the ball is about as likely to hit as to miss the stumps. The representation - a ball half of which hits the stumps - does damage to the probability analysis: there isn't one "certain" path where the ball is definitely half-hitting. If there were, that would obviously be out - everyone knows that if half the ball hits the stumps, the bails will fall. What the representation of a single, defnitie ball-trajectory actually disrupts is the true position that the ball will hit the stumps about half the time and miss the other half.

It's the same issue that underlies other common statistical "failures", such as election projections based on opinion polls. Put simply, if an opinion poll (assuming the poll is otherwise viable and accurate) shows one candidate to be an overwhelming favourite, that doesn't mean that the other candidate will not win. It usually means that the likelihood of a particular candidate winning based on the projection is 70/30 - or even 90/10. Even at 90/10 - what we would call an overwhelming favourite if we were gambling - the other guy gets up on one election in every 10. This is why the approach Nate Silver took at fivethirtyeight.com (before he sold the business) was very helpful - he identified the spread of reasonably likely possibilities in graphical form: really, when the opinion polls "fail", they typically only appear to have failed because journalists like to make a single prediction, rather than look at the likelihood of particular outcomes.

You can test this yourself with games of chance. Texas Hold-em is a good one. The chance of making an inside straight when you have the other 4 cards after the flop is about 1 in 11 (and in many cases, that "statistic" is too high - one only has partial knowledge and chances are that one or more of the 4 "outs" you can win with have already been dealt to someone else). Consequently, it is unsurprising that those straights almost never come in - and, for that reason, it is usually a terrible idea to go all-in on what is a generally remote off-chance. They do come in sometimes, though - which is why poker is a game of chance: for every 10 people who end up looking like idiots when they go all-in and end up with AKQJ and an unhelpful 2 or the like (which another player pairs), one (equally-stupid) person will look like they have special knowledge and are unbeatable with that AKQJ10.

As a very practical real-life example, I had a pocket pair of 8s yesterday and, for situational reasons, went "all-in" before the flop. So did another player. They had two aces - my heart sank when they showed before the flop because we all know they are very likely to win against - well, anything, but certainly - a pair of 8s. In fact, the board flopped the other two eights, so I made 4 of a kind. A few rounds later (I play a lot of poker), I went big with an A8 suited (looking for the flush - see previous discussion) - and the other three eights came by the river. Is the moral to go all-in when you have a pair of 8s or A8 suited? No, the moral is to recognise that that's happened twice in one day and will likely never happen again. I know that the odds of being dealt two aces in your hand are 220-1. I have no idea what the odds of losing to four 8s are when you have two aces - but they must be very slim (probably in the thousands to one, I'd guess) - it simply isn't a statistic you need to know to play poker. The statistic the other player needed to know was that AA is the best starting hand in poker - but it only wins about 30% of all hands in which it is held. So, they couldn't afford to go all-in, in the context of that table on that day.

On the other hand, the chance of making a flush when you have 4 of the 5 cards you need after the flop is about 35% (subject to the same vaguary about whether the remaining cards in the suit you want are actually in the deck). Most people who are playing poker think of that, rightly, as pretty much a coin toss - it's a bit more likely that you won't get the flush (but only a bit more likely) and most people are not troubled betting on the flush coming up (in general terms, specific game situations aside). Equally, when you see two or 3 spades on the board after the flop and you don't have any, it isn't rocket science to work out that there's a big chance that another player will get the spade flush, so you moderate your betting on the pair of aces you hold in your hand - because chances are you're about to be taken down by somebody holding the 2 and 5 of spades.

Silver (who, as it happens, is also a fine poker player) applied that understanding of probability to polling and instead of saying, eg, Democrats 55%/Republicans 45%, so Democrats will win, started saying "70/30 - it's a coin toss with a slightly bad coin - the mob who look way behind actually win 3 out of every 10 elections on these numbers").

To close the loop, "ball-tracking" doesn't track the ball - it just identifies a notional sinlge line that presents as a certainty that which is inherently uncertain. It isn't that every possibility shows 50% of the ball hitting the stump - the actual position is that the possibilities are that the ball will either hit or miss. Understood that way, "umpire's call" makes reasonable sense. It also needs to be understood that the specific line of the specific "ball-tracking" isn't even the most likely line - it's just a single representation of the variation of many, many potential outcomes.

Put another way, Hafeez simply doesn't understand how the system works. We all agree that the ball that would actually be hitting the stump is (all other things being equal) always out - but that isn't what DRS shows. It shows that about half the time the ball will miss. In fact, if you think about it, it could as easily be said that it is actually quite unfair to batsmen to give them out when the true projection is that the ball is going to miss the stumps with that specific delivery about half the time.

[lazzadesilva]

Great analysis Pies4shaw, makes a hell of a lot of sense to me.

[Pies4shaw]

^ Thanks, lazza. I put a lot of thought into that. I hope it was both interesting and useful.

[Pies4shaw]

Once again, DRS reversed a howler by the umpire against Cummins. To the naked eye, it plainly looked like Cummins had Babar Azam dead in front of leg stump, about half-way up. He was given not out but, on review, the dcecision was corrected and the batsman was given out. Here's Cricinfo's description of the ball:

[K]

FTB Smith and Warner just make themselves look stupid when they have hissy fits about their LBWs.

In the Slogathon WC, Zampa said when FTB and Warner get out, he tries to escape the dressing room... 'Cos they always have hissy fits.

And Oz's last great batsman, Ponting, said in the field the captain should "never trust Smith and Labuschagne" 'cos they reckon everything's out.


So FTB is doubly crazy. Thinks everything's out as a fielder. But thinks he's never out. Even when the ump and DRS agree it's crashing into the stumps.

Do FTB & Warner even know how DRS works? Warner whinged that it was never explained to the players. Shouldn't one of the Oz coaches make sure an ICC explanation gets to the players?

[Pies4shaw]

Perhaps while they're at it, the ICC might explain it to you.