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The contact patch size doesn't matter in that the weight per square inch goes up or down and therefore the traction available never changes. What a bigger contact patch helps with is the ability not to melt the rubber when the limits of traction are exceeded. Once the rubber starts to melt it is like driving on butter. So in the rain (or snow and ice) the narrow tire isn't melting and the smaller contact patch has an ability to poke through the standing water to the pavement.
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