I take Precision as my main Tree because the attack speed is very useful in Warwick's kit making his passive(Eternal Hunger) stronger because his Autos deal bonus magic damage and when he is below 50% HP he heals with every auto so the AS helps him deal more damage and heal more it also gives his ult more DPS. Press the attack also helps with the same things the rest of the precision runes are the strongest in their tier and you will see most Precision champs running the same setup.

Triumph: I take this one because it saves my *** a lot(by giving you 12% missing hp back after a kill/assist, works good in sticky situations or if your diving) and it also gives you extra gold which is always nice on a champ like Warwick who wants to snowball super fast and end the game before he gets out scaled, if your cocky you can probably take presence of mind

Legend: alacrity: I take this one because like I said before taking AS on Warwick really does help him out but I don't think legend: Bloodline would be horrible either

Coup de grace: This one is pretty much the only one in this tier Warwick can take as it works so well with your W(Blood Hunt) which can give you some insane pressure.

Ultimate Hat: I don't usually build too much CDR on Warwick so the extra CDR on your ultimate is very nice of course a lot of people prefer Waterwalking since it can give you, even more, MS and more adaptive damage in the river which can help with team fighting near objectives like baron and dragon but its up to personal preference.

celerity: this just gives you even more MS and more adaptive damage (the more ms you have the more adaptive damage it gives you).