How Did David Robinson Perform Against Elite Centers?

The David Robinson-Hakeem Olajuwon debate can be summarized easily: In head to head matchups, Olajuwon outperformed Robinson (especially in the playoffs). Against everybody else, Robinson was better. So, who was better?

That's a question I'm not going to answer right now. However, one argument (which has many variants) that is often made in the context of this argument is, "David Robinson played really well against bad teams, but didn't show up when he was facing another great player." I was interested to see if that was true, so I looked at all of the games Robinson played against Hakeem Olajuwon, Patrick Ewing, Shaquille O'Neal, Alonzo Mourning, and Dikembe Mutombo (the great centers of the 90s) during his (and partially their) prime (1989-90 through 1997-98*).
*Except for games against Hakeem in 1997-98, when Hakeem was clearly not in his prime.

Warning: Lots of stats ahead!

Robinson faced Hakeem 38 times, including 6 playoff games. The Spurs went 22-16 in those games, losing the playoff series in 6.
David Robinson (vs Hakeem Olajuwon)
MPG: 40
PPG: 22
ORB: 3.8
DRB: 8.0
RPG: 11.8
APG: 3.2
SPG: 1.9
BPG: 3.3
TOG: 3.7
FG% .476
FT% .731
TS% .547
Hakeem Olajuwon (vs David Robinson)
MPG: 40
PPG: 27
ORB: 3.4
DRB: 8.7
RPG: 12.2
APG: 3.6
SPG: 1.8
BPG: 3.5
TOG: 3.2
FG% .470
FT% .788
TS% .526
If you remove the playoff numbers from the totals, Hakeem loses almost 2 points a game and 15 points of TS%, leaving them with close to equivalent production. Hakeem played great defense against Robinson, forcing him into worse shooting and more turnovers than usual.

David Robinson faced Patrick Ewing 14 times in those 9 years. The Spurs went 8-6 in those games.
David Robinson (vs Patrick Ewing)
MPG: 39
PPG: 26
ORB: 3.4
DRB: 6.8
RPG: 10.2
APG: 3.0
SPG: 1.8
BPG: 3.2
TOG: 3.6
FG% .518
FT% .653
TS% .563
Patrick Ewing (vs David Robinson)
MPG: 38
PPG: 23
ORB: 2.4
DRB: 8.9
RPG: 11.3
APG: 2.7
SPG: 1.1
BPG: 3.0
TOG: 3.6
FG% .435
FT% .682
TS% .463
Ewing, like Olajuwon, forced Robinson into a lot of turnovers, but Robinson had a much easier time scoring against Ewing than against Hakeem. On the other end, Ewing's efficiency plummeted against Robinson.

David Robinson faced the young Shaquille O'Neal 9 times when he was with Orlando and Los Angeles. The Spurs went 5-4 in those games.
David Robinson (vs young Shaquille O'Neal)
MPG: 41
PPG: 28
ORB: 3.7
DRB: 8.3
RPG: 12.0
APG: 4.7
SPG: 2.7
BPG: 2.4
TOG: 2.6
FG% .473
FT% .796
TS% .554
Shaquille O'Neal (vs David Robinson)
MPG: 39
PPG: 26
ORB: 3.3
DRB: 9.3
RPG: 12.7
APG: 1.8
SPG: 0.7
BPG: 2.0
TOG: 3.9
FG% .514
FT% .578
TS% .540
Once Robinson hit his mid 30s, and Shaq was at his absolute best, Shaq started to dominate. But before those years, I think Robinson outplayed Shaq in head to head situations.

David Robinson faced Alonzo Mourning 1o times when he was with the Hornets and Heat. The Spurs went 6-4 in those games.
David Robinson (vs Alonzo Mourning)
MPG: 35
PPG: 29
ORB: 3.0
DRB: 7.3
RPG: 10.3
APG: 2.5
SPG: 1.5
BPG: 2.0
TOG: 2.4
FG% .553
FT% .781
TS% .620
Alonzo Mourning (vs David Robinson)
MPG: 35
PPG: 21
ORB: 2.4
DRB: 6.0
RPG: 8.4
APG: 1.6
SPG: 0.8
BPG: 2.8
TOG: 2.7
FG% .507
FT% .689
TS% .570
Neither really stopped the other, but Robinson easily outperformed Mourning in these games. In the next two years, when Mourning was at his best, the two faced each other once, and Robinson outplayed him (in a Heat win).

David Robinson faced Dikembe Mutombo 28 times when he was with the Nuggets and Hawks, including a three game sweep against Denver in the 95 playoffs. The Spurs went 22-6 in these games. As Mutombo was something of a defensive specialist, I'm only going to give Robinson's statistics. If you're curious, Mutombo averaged 11 points/game in these matchups.
David Robinson (vs Dikembe Mutombo)
MPG: 37
PPG: 24
ORB: 2.5
DRB: 7.8
RPG: 10.3
APG: 2.9
SPG: 1.6
BPG: 3.8
TOG: 2.1
FG% .487
FT% .757
TS% .567

In 99 games (against these 5 centers), during his prime, Robinson averaged over 24 points a game, and 11 rebounds a game, with a true shooting percentage of .564% (.494% from the field). Those are impressive numbers to put up against top flight centers, and they lead me to conclude that the "Robinson only performed well against bad teams" argument is wrong.