Watching the Celtics get thumped by the Cavaliers Wednesday night, then dropping last night’s game to Atlanta, would leave you with the impression that they have a few problems to fix. The one that’s been nagging the longest is Boston’s poor showing on the defensive glass. Cleveland, playing without Tristan Thompson, managed 13 offensive rebounds against Boston. The Hawks put up the same number one night later. On the season, Boston ranks 28th in defensive rebound percentage and that inability to finish possessions has short-circuited an otherwise solid defense (they foul a little too much but are about league average in forcing turnovers and rank fifth in defensive effective field goal percentage).

The team rebounding struggles have often been laid at the feet of Al Horford, partly because his individual numbers aren’t strong but also because the Hawks suffered from the same problem last season with Horford manning the middle.

Horford’s defensive rebound percentage this season is 18.3, a mark that ranks in roughly the 25th percentile among centers. This is about in line with Horford’s numbers from the past three seasons, but it’s a huge drop-off from the beginning of his career — across his first seven seasons, Horford has a defensive rebound percentage of 23.5, which would rank in roughly the 60th percentile this season. In short, Horford’s rebounding has devolved over the course of his career which begs the question of whether it’s related to aging and a decline in athleticism or whether it’s something more contextual about the role Horford plays.

Getting a rebound involves requires two steps — getting yourself close enough to the ball to get your hands on it, and then actually taking the rebound away from anyone else in the area. We can look at how Horford compares to his peers in those two areas using the NBA’s player tracking statistics.

Defensive rebound chances are anytime a player is within 3.5 feet of a defensive rebound (roughly within an arm’s length for some with a 7-foot wingspan). Defensive rebound conversion percentage is just the percentage of times a player converts a rebound chance into an actual rebound. The graph below covers all centers who played at least 1000 minutes in any of the last four seasons.

Horford’s conversion percentage has bobbed up and down over the past three years but he’s not a catastrophe in that regard. However, he has consistently ranked towards the bottom of all centers in defensive rebound chances per 36 minutes. If we average together multiple seasons for all the players on that graph, Horford ranks in the 54th percentile in defensive rebound conversion percentage and the 28th percentile in defensive rebound chances per 36 minutes.

Getting in position to rebound is clearly what’s limiting Horford’s numbers but, again, it’s worth examining why that might be happening. These past two Celtics’ losses present a nice case study. The Cavaliers had 19 offensive rebound chances in their game and Horford had just nine defensive rebound chances, meaning for more than half of Cleveland’s offensive rebounds he either wasn’t on the floor or wasn’t with an arm’s length of the ball. If you watch video of each offensive rebound, you can see a few cases where he loses a battle to Kevin Love and at least one case where probably should have rotated over to a crashing Channing Frye. But, by my count, on five of those offensive rebounds, Horford was defending a player who was beyond the 3-point line, and twice it was his man who was shooting the 3.

We saw the same thing last night against the Hawks, where Atlanta had 13 offensive rebounds and Horford had just four defensive rebounds in 26 minutes. Of the Hawks’ 13 offensive rebounds, only six occurred while Horford was on the floor and for four of those six, he was guarding a player behind the 3-point line.

Per game, Horford defends 6.2 shots at least 15 feet from the basket — the most of any center. Of those, 3.6 are 3-pointers, the second-highest total defended by a center. Of course those are just the shots where he is the defender closest to the shooter. There are plenty of other possessions where Horford is defending a big beyond the 3-point line away from the action and a shot-attempt.

This trend is prevalent across the league — as bigs take more 3-pointers and outside jumpers, their defenders are pulled farther away from the basket. Boston’s defense is comfortable switching, Horford is extremely mobile for his position and so he often spends his time chasing stretchy bigs away from the paint. When he’s playing with another traditionalish big, Horford often takes the more mobile offensive player. He’s played just under half his minutes with Amir Johnson, who defends noticeably more interior shots (7.9 to 6.4) and post-up possessions (2.4 to 1.6) per 36 minutes. When Horford is the lone big in a small ball lineup, with someone like Jae Crowder at power forward, there’s even more of an advantage to be had if the offense can pull him out of the paint with a stretchy big, leaving the rim undefended.

This doesn’t explain away everything about Horford’s rebounding — his shots defended numbers on the perimeter weren’t nearly as extreme last season — but it’s part of the context this year. And this may be as close to an explanation as we can get. Horford has probably lost a step. At best, he’s probably an average rebounder at this point in his career. But playing in a defensive scheme that often pulls him away from the paint emphasizes his shortcomings.

Also, this goes without mentioning, but the lines of separation between good, bad and average are incredibly slim. Converting just one additional defensive rebound chance per game would be enough to move the Celtics from 27th in defensive rebound percentage to roughly 11th. Adding one additional rebounding chance per game to Horford’s total would move him from the 19th percentile among centers in defensive rebounding chances, to the 47th. Roughly one possession per game could be the difference between the Celtics and Horford being badly on the defensive glass or being average.

The thing is, when it comes to the playoffs, the importance of each of those individual possessions begins to increase. A half-dozen possessions can easily swing a series between two evenly matched teams. There’s not much the Celtics can do about their defensive rebounding problems at this point. They can pay attention, execute, communicate, fight like hell, but some of the problems are baked in. They can’t very will minimize Horford’s minutes because everything else he does is so important. Having strong rebounders on the wings, like Avery Bradley, Marcus Smart and Crowder, helps, but it might not be enough.

As they enter the playoffs, Boston’s weakness is defined. They just have to do their damndest to make a difference at the margins, pick up that extra rebound or two a night that covers it up. The good news, I suppose, is that everyone else has weaknesses too.