The importance of tread pattern on cycle tyres
On surfaces that will move under your tyre eg mud, some tread is useful. But on asphalt/tarmac/road the tyre 'moulds' to the road surface. Cycle tyres will not aquaplane (see link below) and
any tread will merely serve to reduce the rubber in contact with the road and therefore reduce grip. Given the forces involved it is unlikely that there will be any performance merit or loss whichever way round tyres are mounted, irrespective of 'drive arrow' markings. The latter have been put there, much as the tread has, to meet customers' expectations, and possibly for aesthetic reasons (to avoid the 'look he's put the tyres on back-to-front' comments from the incognoscenti).
To explore and seek a few figures:
For a given rider, bike and any load, the total mass will be supported by the contact area x pressure (both tyres) irrespective of the width of or circumference of the tyre. The wider the tyre (for given pressure and load) the 'shorter' the contact area ellipse. So for example on 28mm tyres the loaded contact patch is circa 20mm wide. If the total load is 100kg, split 40/60 (front/rear) and tyre pressures are 70psi and 105 psi, then the contact area for each tyre is ~8cm
2 and this ellipse is 2cm wide and about 5cm long. If you ran them at the same pressures (you wouldn't) the contact area of a wide tyre eg 2+" would be almost a circle.
http://www.bretonbikes.com/homepage...he-importance-of-tread-pattern-on-cycle-tyres