Friday, September 4, 2009

Unthinkable Permutations



If you're like me, you're asking yourself, "What does the Atlanta Dream have to do to get to the playoffs? Can they get there without sweeping? Or should they just start buying tickets to Europe right now?"

There are all kinds of scenarios that can happen over the next four games. Better mathematical minds than mind have written about them. But that never stopped me before. Here's how we could finish over the next four games, and depending on each scenario, here's what that leaves us with.

4 wins, 0 losses: Atlanta is in automatically if they sweep - that would give them a 20-14 season. However, the best they can do is finish second to Indiana. Still, home court advantage in the opening round is not bad.

3 wins, 1 loss: The best Washington or Detroit can do is tie them in a 19-15 tie. This also puts Atlanta in automatically as Atlanta would be among the top four teams. But where would Atlanta finish?

If the tie is only with Detroit, Atlanta is in and finishes second as Atlanta has the better record against Detroit. If the tie is only with Washington, then this means that Washington must have beaten Atlanta in Atlanta's final game of the season. With both teams having a 2-2 record against each other then it goes to "best Eastern Conference record". Washington would have to sweep to get to 19-15 and they would definitely have a better record than Atlanta in the conference, so Atlanta would finish third and lose home court advantage.

If there's a 3-way finish between Atlanta, Detroit and Washington, it goes to best combined record against all tied teams.

Atlanta: 5-3
Washington: 4-3 (2-2 vs. Atlanta, 2-1 vs. Detroit)
Detroit: 2-5

This puts Atlanta in second, Washington in third and Detroit in fourth.

Obviously, if neither team could tie Atlanta's 19-15 resulting record, Atlanta finishes second.

2 wins, 2 losses: This would put Atlanta at 18-16, and makes the resulting picture a lot muddier. It gives Washington and Detroit a chance to actually finish ahead of Atlanta and for the Sky to at least tie Atlanta. If Washington sweeps, Detroit sweeps and Chicago sweeps...Atlanta is out. Atlanta was swept in all three games it played against the Sky, and those two teams would finish at 18-16 in a fourth-place fight. If Washington and Detroit finish ahead of Atlanta, but the Sky can't catch up, then the sixth-place Sun won't be able to catch up either and Atlanta squeaks in in fourth place.

If only Washington or Detroit finishes ahead of Atlanta, then there are all sorts of permutations. It would come down to who finished ahead of Atlanta and who tied them. If that doesn't happen, we have to imagine all the various ways teams could finish with an 18-16 record and end up tied with each other.

* Atlanta, Washington, Detroit, Chicago (complicated as Washington has games against both Chicago and Atlanta)
* Atlanta, Washington, Detroit (Atlanta finishes second in the Eastern Conference)
* Atlanta, Washington, Chicago (see the Atlanta-Washington-Detroit-Chicago scenario above)
* Atlanta, Washington (Washington wins)
* Atlanta, Detroit (Atlanta finshes second in the Eastern Conference)

1 win, 3 losses: See that Atlanta-Washington-Detroit-Chicago scenario where teams end up tied at 18-16? Well, if Atlanta finishes 17-17, Atlanta is going to need some luck. There is the possibility (mathematically) anyway of five teams being eligible for three playoff spots. Any combination of Atlanta, Washington, Detroit, Chicago, or Connecticut could be contending. It would be very possible for Atlanta to end up on the outside looking in depending on how the other teams finish.

0 wins, 4 losses: The nightmare scenario. This puts Atlanta at a 16-18 finish. Washington definitely finishes ahead of Atlanta, since for Atlanta to get swept Washington won their last game and this gives Washington the tie-breaker. The absolute best Atlanta could hope for is a third-or-fourth place finish.

Even New York could sweep its last four games and finish 16-18 along with Atlanta. My request? Get out your abacus and your slide rule if we go 0-4. And your rosary, if you carry one.

6 comments:

Patrick said...
This comment has been removed by the author.
pt said...

But how do you account for a scenario where multiple teams finish at 17-17? How does Atlanta win the tiebreaker?

pt said...

(forgot to add this)

Yup, if Atlanta were to be tied with Connecticut alone or with Chicago alone or with both together Atlanta would win the tiebreaker. But if there's a multiple-team logjam, my understanding is that the tiebreaker is "best record with games between all of the tied teams", and is there a mathematical assurance that Atlanta finishes at least fourth?

Anonymous said...

FYI if Dream wins tonight and Sky and Sun both lose, Dream clinch being in the playoffs....

Anonymous said...

Looking at your analysis I think some of your scenarios mention this but some do not....the funky situation is that many people involved in this chase play each other a lot so that there are some scenarios that just can't happen (e.g. both Chicago and Washington cannot sweep because they play each other just to note one that I think you already noted)

afoundingfan said...

This is making my head spin. I just wanna see my Dream here in the midwest!