The deeper states of mind of batsmen remain essentially mysterious. You'd have to search for a long time to find two players mentally stronger than Steve Waugh and Sachin Tendulkar, but they have their foibles too.
Even the Texas courts will not accept polygraph evidence, and yet Steve Waugh wants to see it in cricket [South Korea are said to use it on their football team - any player passing doubles their wages]. The lie detector's natural arena, though, is the piss-artists and pub stuntmen of the Jeremy Kyle Show, where his motley collection of gormless shaggers line up daily to try and beat it, no doubt armed with some facile tip or trick that they think will save their lying asses.
The reason that courts don't accept lie detectors is that they don't work on liars, especially liars who don't believe that they are lying, or that do it so often it's almost a version of their truth. Steve Waugh took a polygraph test and was impressed by the pressure it exerted on him, but that is because he's an honest man responding as an honest man does to the polygraph's psychology.
Waugh is typical of a particular kind of sportsman, one who loves empirical evidence. His belief built as he proved things to himself, as he worked his mind and his game out. Once he believed he didn't look back, as the curve of his cumulative average shows. He might have proved to himself that the lie detector works, but it's not the ICC's get out of jail card, nor is it the match-fixers' get into jail one.
Steve appeared to yield to one talisman as he grew older - that red cloth that rarely left his back pocket. Sachin Tendulkar has one too - his bat. After he'd departed Lord's with a viral infection of day four of the Test, Sky's cameras showed him returning the ground, in civvies but, as Nasser Hussain observed: 'Still carrying his bat with him. It never leaves his side - he won't leave it in the dressing room'.
Admittedly, Sachin's bat would be a grand prize for anyone, but he is a batter who invests emotion in the ones he likes. Many players are far less talented and far more pragmatic about the tool of their trade. Tendulkar of all men could probably make runs with Geoffrey's mother's stick of rhubarb, yet he wields the same bat until it packs up [his last probably made more Test hundreds than any bat ever shaved from the tree] and he still uses buckle-up pads. The great man has some mental props of his own. He is all too human, and all the more glorious for it.