Liverpool’s boys basketball team could not have asked for a more exciting arrival at the midway point of its regular-season schedule. Jesse Gates delivered a 3-point shot as the buzzer sounded in Tuesday night’s game at Nottingham, allowing the Warriors to beat the Bulldogs 51-48. The Gates shot climaxed a dramatic Liverpool rally. It trailed 43-35 going into the fourth quarter and, despite some attempts to fight back, still stared at an eight-point deficit, 48-40, with 3:30 left. In such a situation, its helps to have someone like Gates — who, if things are desperate, can offer something grand. That’s exactly what he did here. Fouled twice, Gates sank three of four three throws, cutting the margin to 48-43. After a defensive stop, the Warriors got the ball back and, with 1:46 left, Gates flashed opened for a 3-pointer — and sank it, making the score 48-46 with a lot of time to do something about it. Again, Nottingham couldn’t build the lead back up — and when Cam Jones broke free for a lay-up with 30 seconds to play, the two sides were tied 48-48. Shut out all through this homestretch, the Bulldogs tried to set up a winning shot — but never got to that point, Liverpool pressuring and forcing a tie-up, getting the ball back on the alternating possession. Now the Warriors called time-out. Nottingham anticipated the Warriors’ original strategy — get the ball to Gates inside — and forced him outside. Still, Gates fought his way open, caught a pass and, from 29 feet out, shot it just as the clock hit zero. It swished, and Liverpool won. For a while, it didn’t look like any late excitement was needed. The Warriors led, 15-5, after one period, but went cold in the second quarter as Nottingham bolted ahead 22-20, then kept adding to its advantage before the wild ending. Gates, overall, had 29 points, more than half the Warriors’ output. Adam Misener, the next-highest scorer, had just six points. Jawan Simmons led Nottingham with 15 points.