Ok, we know that 1 and 2 are the placingest posts in the game:
1 - 5.6
2 - 5.6
3 - 6.1
4 - 7.5
5 - 9.2
6 - 12.6
7 - 12.0
8 - 13.4
As in, overall in spec 7 games, post 1 comes in second 1 out every
5.6 times.
So, if 3 wins, we can say 31, 32 are most likely. 4 wins, 41,
42, 5 wins, 51, 52 etc. But beginning with post 6 and peaking
at post 8, we see 1 and 2 being edged by other numbers. Since
1 and 2 start out the game, and clearly have the best chance of
amassing points, why does this happen?
Tiger's answer seems to accept the assumption that 1 and 2 are
still best in the first round runout cases. Because runouts constitute
over half of all post 8 wins, it makes good sense to verify that
belief.
To test this out we could either evaluate all possible sequences
(sounds like work) or modify a simulation so that 8 runs it every
time. I went with the Q & D option B and found consistent exacta
results like this:
81 - 6.2
82 - 6.2
83 - 5.2
84 - 4.9
85 - 5.6
86 - 10.4
87 - 168.7
Wow. Something is happening right in the first round that strongly
favors 4, 3 and 5. That something is actually a combination of
factors.
First, the playoff rules. The key rule is "The order in which
they were defeated". In the case of all teams having 1 point,
the 1 or 2 will end up in the third pair, while 4 and 5 are in
the first pair. Anybody who has looked into 3 post playoffs knows
that the third group or post has a 25% chance as opposed to the
37.5% chance
for the first groups.
Also, in a 3 team playoff with each team having 2 points, the
1 or 2 is again third, while our top dog 4 is up first.
Next, in the event that the top score is 2, for 1 and 2 there
could still be a 3 way playoff. But for post 3, it is guaranteed
that only 1 other post can have 2.
Finally if 1 or 2 have 3 points, there is still a chance to be
tied with post 5, which require a playoff point. But for posts
3 and 4, 3 points is an automatic place.
So, combining runout playoff factors that help 4, 3, and 5 with
those that hurt 1 and 2, along with what Tiger said, shows
us why 81 and 82 fall behind.
