A reader, Kanishka Kacker, writes to me about Cricket:
Now, very often, there are certain decisions to be made regarding whether a given batter was out or not, where it is very hard for the umpire to decide. In situations like this, some players are known to walk off the field if they know they are “out” without waiting for the umpire’s decision. Other players don’t, waiting to see the umpire’s decision.
Here is a reason given by one former Australian batsman, Michael Slater, as to why “walking” is irrational:
(this is from Mukul Kesavan’s excellent book “Men in White”)
“The pragmatic argument against walking was concisely stated by former Australian batsman Michael Slater. If you walk every time you’re out and are also given out a few times when you’re not (as is likely to happen for any career of a respectable length), things don’t even out. So, in a competitive team game, walking is, at the very least, irrational behavior. Secondarily, there is a strong likelihood that your opponents don’t walk, so every time you do, you put yourself or your team at risk.”
What do you think?
Let me begin by saying that the only thing I know about Cricket is that “Ricky Ponting” was either the right or the wrong answer to the final question in Slumdog Millionaire. Nevertheless, I will venture some answers because there are general principles at work here.
- First of all, it would be wrong to completely discount plain old honor. Kids have sportsmanship drilled into their heads from the first time they start playing, and anyone good enough to play professionally started at a time when he or she was young enough to believe that honor means something. That can be a hard doctrine to shake. Plus, as players get older and compete in at more selective levels, some of that selection is on the basis of sportsmanship. So there is some marginal selection for honorable players to make it to the highest levels.
- There is a strategic aspect to honor. It induces reciprocity in your opponent through the threat of shame. If you are honorable and walk, then when it comes time for your opponent to do the same, he has added pressure to follow suit or else appear less honorable than you. Even if he has no intrinsic honor, he may want to avoid that shame in the eyes of his fans.
- But to get to the raw strategic aspects, reputation can play a role. If a player is known to walk whenever he is out then by not walking he signals that he is not out. In those moments of indecision by the umpire, this can tip the balance and get him to make a favorable call. You might think that umpires would not be swayed by such a tactic but note that if the player has a solid reputation for walking then it is in the umpire’s interest to use this information.
- And anyway remember that the umpire doesn’t have the luxury to deliberate. When he’s on the fence, any little nudge can tilt him to a decision.
- Most importantly, a player’s reputation will have an effect on the crowd and their reactions influence umpires. If the fans know that he walks when he’s out and this time he didn’t walk they will let the umpire have it if he calls him out.
- There is a related tactic in baseball which is wh
ere the manager kicks dirt onto the umpire’s shoes to show his displeasure with the call. It is known that this will never influence the current decision but it is believed to have the effect of “getting into the umpire’s head” potentially influencing later decisions. - Finally, it is important to keep in mind that a player walks not because he knows he is out but because he is reasonably certain that the umpire is going to decide that he is out whether or not he walks. The player may be certain that he is not out but only because he is in a privileged position on the field where he can determine that. If the umpire didn’t have the same view, it would be pointless to try and persuade. Instead he should walk and invest in his reputation for the next time when the umpire is truly on the fence.
Cheap Talk 
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June 15, 2011 at 4:12 pm
kanishka
Thanks for replying. Your points are interesting.
The reason I find it interesting is because a lot of the post focuses on reputation.
Suppose, then, that one views the walking decision as containing information about the honour of a player. One very important development in the history of the game is the advent of the on-field camera which starts sometime in the 1980s, and by the mid-90s was being used to adjudicate decisions difficult to make on-field. In the pre-camera age, clearly, the decision to walk or not conveys information about the honour of the player but, and I believe this is important, this is a non-verifiable event. In the spirit of Barzel (1982), this is non-verifiable because it was too costly to verify. With the advent of the on-field camera, this cost reduces dramatically. Now it is clear if the player is cheating or not. So, if honour is important, one should see more players walking in the post-camera age.
June 15, 2011 at 4:16 pm
MMP
kanishka: i don’t think that’s an apples to apples to comparison because while costs of verification have gone down, the stakes have gone up by much more (billion dollar sport versus refuge of the old boys)… indeed there’s a related theory that ‘walkers’ only walk when the game isn’t that important/ on the line, and don’t walk in (say) the finals of the world cup… this lends even more weight to this idea that they’re trying to build reputation to use if they see fit at some point.
June 15, 2011 at 4:17 pm
kanishka
In cricket, #6 would be met with cancellation of match fees, and maybe even suspension. Even mild forms of showing dissent – just looking at the umpire or at your bat for instance after a close call – is considered sacrilege, conditional on the event that the batsman is given out.
June 15, 2011 at 4:28 pm
kanishka
@MMP
Yes, the stakes have increased, I have in mind some vague notion of an “average” game not finals.
In any case, one could always include some measure of stakes as a variable in the regression. The dependent variable I have in mind is some measure of a player’s honour.
I don’t mean to say that lowered monitoring cost is the only reason, but I do believe that it is quite important. In fact, the author – Mukul Kesavan – writes later on that with the on-field cameras the decision to walk or not becomes somewhat irrelevant if one only considers the sort of reasoning implied by Michael Slater above – because now you can be caught out as the camera sees all.
June 15, 2011 at 4:47 pm
MMP
kanishka- jeff won’t get this, but you will. it’s a beautiful story of manipulating the ump…. so apparently this fast bowler in county cricket was getting his wrist position wrong, ball was slipping toward leg. asian batsman on strike was happily flicking them away and making good runs…
between overs, a few times, this fielder walked up to the ump and was just generally chatting, and at some point he said “oh you know this batsman is just so skilled, keeps flicking balls from middle and off through leg. it’s great to watch.” the ump nodded and changed the subject. few overs later, ball hits pad, ball probably headed down leg, ump gives it out! can’t remember who this was about…
June 15, 2011 at 5:00 pm
David Pinto
To use another baseball example, players who are known to swing at balls in the strike zone and take balls out of the strike zone tend to get the benefit of the doubt from umpires when they don’t swing. If batters swing at balls out side of the strike zone, they are less likely to get the call when they take a border line pitch.
June 16, 2011 at 4:13 am
Another Kanishka
I think we can see the bite to the reputation argument in the case of bowlers. In cricket bowlers have a decision to appeal or not (a batsman can’t be out if there in no appeal). Given this (from points 2 and 3) above a bowler with a “good” reputation is much more likely to get a close call from the umpire. There are clear example of this in international cricket – some bowlers (e.g., Harbhajan Singh) who appeal for anything close whether or not they believe it is out, while others (e.g. Glenn McGrath) who only appeal when they think it is out. Without reputation, appealing (assumed costless) on every delivery is clearly a dominating strategy. Except that is just ‘not cricket’!
June 16, 2011 at 7:12 am
Rajiv Sethi
I’m a bit late in responding to this post…
Here’s a wonderful article on walking that highlights reputational concerns:
http://www.telegraph.co.uk/sport/cricket/2383875/County-Report-More-batsmen-should-walk-in-Laras-footsteps.html
Jeff, you’ll enjoy it. Here’s an extract:
“The umpires talk among themselves about who is on [the list of walkers], and occasionally base their decisions on it. For instance, if there is a vehement appeal against a batsman renowned as a walker then the umpire is more likely to veer on the side of not out. But even in this regard one umpire expressed some hesitation. “They can be the ones who can ‘do’ you. They can use their reputation and get a fine edge and stay there.”
Lara, by the way, is one of the greatest batsmen in the history of the game and has the highest score ever made in a test match (and also the third highest).
June 16, 2011 at 10:24 am
Kanishka
it is interesting that the economists talk about honour, while the (admittedly sole) cricketer talks in terms of rationality.
June 16, 2011 at 1:59 pm
Sid
I was thinking if the umpiring guideline “give the benefit of doubt to the batsman” could, in fact, result in fewer batsman walking.
Every batsmen enters a game with a ‘reputation’: As a ‘walker’ or a ‘non walker’. A walker always walks when out, and a non-walker never walks. Assume that the umpire knows the reputation of the batsmen. Now, faced with a walker, the umpire basically lets him make the decision, and the batsman get exactly what he deserves – out when he is actually out and not out when he is actually not out.
When a non walker is batting, the umpire relies entirely on his private signal to make his decision. This could result in two kinds of errors – giving the batsman out when he is not out (Type 1) and give the batsman not out when he is out (Type 2). Given that doubts are resolved in favour of the batsman, each batsman can increase his batting time by not walking and letting the umpire make the decision.
To support this equilibrium, the following beliefs of the umpire might work: Since the correctness of the decision is always verifiable after the game, any player who didn’t walk when out is believed to be a non walker for the rest of his career – in effect, a walker has to consistently ‘prove’ himself to maintain his reputation and even one instance of ‘taking advantage’ of his reputation would result in a complete erosion of his built up reputation. Further the umpires also believe “once a non walker, always a non walker”. Also off the equilibrium path, if a non walker chooses to walk, the umpire does not revise his estimate of the player’s reputation.
Your thoughts?