The centre of the tread is usually the first place a rider looks for wear, but its pattern alone does not tell the whole story. On many city and road bicycle tires, a shallower pattern need not mean immediate replacement; the knobs of a mountain-bike tire matter more for traction. A useful inspection follows the tire all the way around and includes the sidewalls, not just the strip that contacts the road.
One clear replacement point is when the puncture-protection layer or the casing threads become visible beneath the rubber. Some performance road tires also have small tread-wear dimples, with marks on the sidewall showing where to find them. These indicators are model-specific, so check the tire you actually have. Examine both sidewalls for cracks and abrasion as well: they can deteriorate before the centre tread appears completely worn.
Riding for a long time at insufficient pressure makes the sidewalls flex excessively and may shorten their life. Use a gauge and keep pressure within the range stated for the tire. There is no universal replacement mileage, since load, road surface, temperature and riding style all affect wear. Especially before another wet-season ride, a few minutes spent inspecting the whole circumference tells you more than the odometer alone.