Why was Space Shuttle Atlantis selected for Mir docking so frequently?

In this answer @RussellBorogove discussed the frequency of dockings of each space shuttle with the Mir space station. I've summarized those frequencies, total number of missions flown, and year of first and last flight below.

Not counting the Enterprise and the Challenger (lost early in its expected life) there are four shuttles that span the period over which Mir docking missions were carried out.

Of the 9 dockings, 7 were made by the Atlantis. I've done a rough calculation tossing nine balls into four equal bins repeatedly, and then calculated roughly how many times the maximum number of balls in a given bin would be $N_{max}$. The probability that 7 of 9 balls would end up in any one bin is less than 0.5%. So I think the high frequency of Atlantis-Mir docking is not likely to have been just a statistical fluke, although it's not impossible.

Were there any reasons why NASA would have used Atlantis for such a large fraction of all the Shuttle-Mir dockings?

Enterprise: 0 /  0 (1977-2012, model only)
Columbia:   0 / 28 (1981-2003, lost)
Challenger: 0 / 10 (1983-1986, lost)
Discovery:  1 / 34 (1984-2011)
Atlantis:   7 / 33 (1985-2011)
Endeavour:  1 / 25 (1992-2011)

With 1,000,000 tries:
Nmax  %
---- ----
3   37.2
4   43.2
5   15.6
6    3.5
7    0.5
8   <0.1

import numpy as np
from collections import Counter

n_tries = 100000 # I used a million for the question

# shamelessly inefficient way to do this
bob = np.random.randint(4, size=9*n_tries).reshape(9, -1)
qq  = [max(Counter(thing).values()) for thing in bob.T]
a,b = np.histogram(qq, bins=range(11))

for A, B in zip(a, b[:-1]):
print B, float(A)/a.sum()

• Note that balls in bins isn't a good model, here. It assumes that missions were assigned to shuttles independently and uniformly at random but that defintely wasn't the case. For example, in the 100+ missions flown from 1985 onwards, there were only a handful of instances where the same shuttle flew two consecutive missions. Commented May 25, 2019 at 10:55
• @DavidRicherby In order to head off bothersome comments like "Why do you think it is 'so frequently?'" I made a quick estimate of what "random" might look like precisely to show that the real distribution isn't random! So I think your comment misses the point.
– uhoh
Commented May 25, 2019 at 12:19
• But all you showed is that the distribution doesn't match a model that is already completely implausible. You don't need statistics to refute somebody who suggests "Maybe they just picked a shuttle uniformly at random, independently of any previous flights." And your refutation says nothing about a much more plausible "it's random" hypothesis such as "Maybe Mir missions just happened to be performed at times when Atlantis was the next shuttle to fly." Anyway, I don't to get into a big argument about this -- it doesn't affect the underlying question (which is a good one) or the answer (ditto). Commented May 25, 2019 at 12:58
• @DavidRicherby I think you are reading something into the question that's not there.
– uhoh
Commented May 25, 2019 at 14:29