Danny Ainge’s deals for Ray Allen and, subsequently, Kevin Garnett are what made the Celtics relevant again over the past three seasons.

However, it’s been Ainge’s drafting prowess that has ultimately made that possible.

Without Al Jefferson, taken with the 15th overall pick back in 2004, Boston isn’t able to swing the deal for K.G.

Without Rajon Rondo, who was drafted 21st overall by Ainge in 2006, the Celtics wouldn’t have hung a banner three years ago and come within a quarter of doing so again this past season.

Ainge’s track record has been impressive. There have been second-rounders such as Ryan Gomes, Leon Powe and Glen Davis, as well as late first-rounders that include Delonte West and Rondo.

On Thursday night, Ainge and the Celtics brass will try and hit a home run with the No. 19 overall pick — if they don’t deal it away.

The C’s needs are virtually endless, due to their age.

In fact, Ainge could use just about anything — which likely mean’s he’ll go with who he believes to be the top player on the board.

The good, old top available player.

The dilemma could be the fact that the top player is 6-foot athletic point guard Eric Bledsoe — which satisfies the least need on the Celtics roster.

Even though it’s a weak crop of point guards, there’s a chance that Bledsoe, who was forced to play shooting guard alongside likely No. 1 overall pick John Wall at Kentucky last season, could be around when the Celtics are on the clock.

Bledsoe is a strong, athletic and tough player who shot 40 percent from beyond the arc a year ago. He’s not ready to step in immediately and even if he was, it’ll be difficult imagining a backcourt of two midgets such as Rondo and Bledsoe.

But then again, Ainge may opt to go with a guy he knows can play in the NBA rather than taking a risk on a big man with potential.

And that’s what’ll likely be staring at when No. 19 rolls around.

Ainge may see a trio of long and talented 7-footers in Marshall freshman Hassan Whiteside, Florida State’s Solomon Alabi and VCU sophomore Larry Sanders.

Whiteside is a skilled, immature forward who compares to Washington Wizards Andray Blatche — a guy who did virtually nothing his first two seasons in the NBA while he matured before putting up 14.1 points and 6.3 boards last season — his fifth in the league.

Florida State’s Solomon Alabi, may also be on the board and would give Boston a different look than the somewhat-plodding Kendrick Perkins, but sources indicate Ainge will likely pass on both Whiteside and Alabi.

Then there’s 6-foot-9, 270-pound Daniel Orton — yet another Kentucky product (the Wildcats will likely have five go in the first round) — who may be on the board. Orton came out after one season in which he averaged just three points and three rebounds and multiple sources indicate that Kentucky John Calipari didn’t care if Orton returned for his sophomore season.

Pass.

The Celtics could certainly use a replacement for the 35-year-old Allen, who is an unrestricted free agent — and a couple of scoring wings that may be in the mix are Kansas’ Xavier Henry, Oklahoma State junior James Anderson, Xavier sophomore Jordan Crawford and Memphis sophomore Elliot Williams.

Texas’ athletic 6-foot-8, 225-pound combo forward Damion James, Fresno’s 6-foot-9 Paul George and Clemson’s 6-foot-7 undersized power forward Trevor Booker are others who could be in play when No. 19 rolls around. James is an active and relentless rebounder who may be caught in-between positions while George has shot up mock draft boards due to impressive individual workouts. Booker is a terrific athlete who is projected to go late in the first round.

Beyond the top couple of picks, there’s plenty of uncertainty and not a ton of disparity with this year’s NBA Draft.

But I’ll take my chances with Ainge given his track record.

EIGHT GUYS THAT COULD BE IN PLAY FOR BOSTON AT NO. 19

Damion James, 6-8, 225, F, Sr., Texas

James Anderson, 6-6, 210, SG, Jr., Oklahoma State

Jordan Crawford, 6-4 ½, 200, SG, Soph., Xavier

Eric Bledsoe, 6-1 ½, 190, PG, Fr., Kentucky

Paul George, 6-9, 215, F, Soph., Fresno

Avery Bradley, 6-3, 180, G, Fr., Texas

Xavier Henry, 6-6, 210, SG, Fr., Kansas

Trevor Booker, 6-7, 240, PF, Sr., Clemson