Not to start a grammar war on these here boards, but I think "me" is correct here, since it's being used as the object of a preposition. You wouldn't say "There isn't a bigger Michigan fan around I."
For the record, my dad taught me that in the Harvard - Yale rivalry, it was always MIT that got the last laugh.
We may have missed our last 6 free throws, but only 1 (!) of these misses took place in the last 15 minutes of the game and 3 of them were in the first half.
After the Tacopants transfer, I was worried about having to face him in the upcoming years. It's about time we signed a recruit who can cover the guy. Sounds like this Robot is up to the task.
You forgot to mention GPA (2.7 - I don't think he's mastered those humanities courses).
The travelling salesman problem is a little bit different. The goal there is to find the minimum-weight Hamiltonian cycle (passes through all vertices). TSP is NP-complete, so it's difficult to solve it in any speed.
Here, we are looking for the minimum-weight path. This can be solved in about V^3 steps (where V is the number of vertices=teams) using Floyd-Warshall (http://en.wikipedia.org/wiki/Floyd_Warshall). As several people have already suggested, adjusting the weights for the strength of the win (i.e. mixing the two approaches) might be an improvement. OT wins should be weighted less than everything else, though (winning by 8 in 4OT is not more dominant than a one touchdown win in regulation).
I think your issues are relevant. I'd guess that most years, the graph even for the Big Ten is somewhere between strongly connected and acyclic. Resolving these problems is probably the most important obstacle towards finding a consistently workable ranking. The main goal is to reduce the graph somehow to a single directed path in the most representative way. With that in mind, one idea is to keep deleting the edge with lowest weight until the graph is acyclic. Then use either some adaptation of the "strong wins" ranking or (maybe better) an adaptation of topological sort.
Sadly, I don't know how to do any actual coding, so I can't implement any of these things myself. I'd definitely like to see more things in this vein.
Teams don't play each other twice in the regular season (that would be stupid).
Division A has 7 teams, Division B has 6 teams (bylaw 17.9.5.2 (c) requires each division to have at least six schools), each play round-robin.
Questions:
Can we schedule such that each team in the conference plays the same number of games?
Failing in the above, can we schedule such that each team plays the same number of conference games as the other teams in its division?
The answer to both is yes, but only if there are either zero crossover games or 42, which would be round-robin for the entire conference (and result in 12 conference, 0 OOC games for each team).
Why? Looking at the requirement for question 2 (for question 1 to be fulfilled, question 2 must be also), we would have each team in division A play, say n crossovers. That means there are 7n crossovers in total. In particular, the number of crossover games is divisible by 7. On the other hand, by considering division B, we can see that the number of crossover games is divisible by 6. Since we have at least 0 crossovers and at most 42 (by assumption 1) & 7 and 6 are relatively prime, the only choices are, in fact, 0 and 42.
Interestingly, the same problem wouldn't necessarily exist for a 15-team conference, since it could be split 9/6 (although this is definitely undesirable, especially since the only other solutions would involve 10 and 8 conference games OR 12 and 11 conference games for teams in the large and small divisions, respectively.
\end{math}
In light of the above, I'd say the only reasonable option (involving a championship game) would be to base the division championship on in-division games only and maybe factor crossover games into a possible tiebreaker.
The question that this all raises is how the MAC does it. They have 13 teams in a 7/6 split, each playing 8 games. However, Miami (NTM) and Akron, both in the East division, didn't play each other last year, so I don't really understand how that qualifies as round robin (this is one example I found, there should be others).
If Pac-10 expects their new members to start playing in 2012, then does this suggest the Big Ten wants to stop here (don't need as much time to organize things)? Or is Delany just a much better commish than Scott?
Meanwhile, Barry Alvarez giving an interview on BTN from a cruise right now.
IIRC they tried to get the one hit ruled an error (which it should have been), but MLB wouldn't reverse the call.
At the very least, the scorer could rule it an error and at least salvage a no-hitter. I doubt that Selig will do the right thing and call it a perfect game. Remember, this is the guy who stopped the all-star game once in a tie after 11 innings!
I'm all for instant replay, but they need to find a more reliable way to implement it (tennis's seems pretty much infallible) -- high-speed cameras pointed at each base would be a start. I've seen several home run calls made wrong on replay. The current system is just enough to allow the crew to get some bad calls wrong twice while not enough to correct some (I have one in mind) other really awful calls.
Rachel Strassner was named the director of compliance for the Western Michigan University athletic department in June of 2008. Prior to joining WMU, Strassner was a compliance assistant at the University of Michigan.
I agree that the two deserve to be fired, but in the current situation, it might be better to wait or do something else more quietly. As for possible mitigating factors, name a party involved and I can think of a scenario damning to that party while making everyone else seem innocent. In particular, the theory that Labadie and Draper were getting hit from both sides might have merit, but it's still not enough to excuse the facts we have in front of us. After all, they hardly needed s-a input (perhaps a little from the coaches) to compile the job descriptions. This is especially true for the first version (Exhibit 3, which, probably unfortunately, is short enough for everyone to read).
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Not to start a grammar war on these here boards, but I think "me" is correct here, since it's being used as the object of a preposition. You wouldn't say "There isn't a bigger Michigan fan around I."
For the record, my dad taught me that in the Harvard - Yale rivalry, it was always MIT that got the last laugh.
You two are arguing about nothing.
We may have missed our last 6 free throws, but only 1 (!) of these misses took place in the last 15 minutes of the game and 3 of them were in the first half.
Please don't pull the fire alarm AGAIN.
After the Tacopants transfer, I was worried about having to face him in the upcoming years. It's about time we signed a recruit who can cover the guy. Sounds like this Robot is up to the task.
You forgot to mention GPA (2.7 - I don't think he's mastered those humanities courses).
You've got it exactly. I'm still planning on learning how to do this stuff eventually...
The travelling salesman problem is a little bit different. The goal there is to find the minimum-weight Hamiltonian cycle (passes through all vertices). TSP is NP-complete, so it's difficult to solve it in any speed.
Here, we are looking for the minimum-weight path. This can be solved in about V^3 steps (where V is the number of vertices=teams) using Floyd-Warshall (http://en.wikipedia.org/wiki/Floyd_Warshall). As several people have already suggested, adjusting the weights for the strength of the win (i.e. mixing the two approaches) might be an improvement. OT wins should be weighted less than everything else, though (winning by 8 in 4OT is not more dominant than a one touchdown win in regulation).
I think your issues are relevant. I'd guess that most years, the graph even for the Big Ten is somewhere between strongly connected and acyclic. Resolving these problems is probably the most important obstacle towards finding a consistently workable ranking. The main goal is to reduce the graph somehow to a single directed path in the most representative way. With that in mind, one idea is to keep deleting the edge with lowest weight until the graph is acyclic. Then use either some adaptation of the "strong wins" ranking or (maybe better) an adaptation of topological sort.
Sadly, I don't know how to do any actual coding, so I can't implement any of these things myself. I'd definitely like to see more things in this vein.
\begin{math}
Assuming:
Questions:
The answer to both is yes, but only if there are either zero crossover games or 42, which would be round-robin for the entire conference (and result in 12 conference, 0 OOC games for each team).
Why? Looking at the requirement for question 2 (for question 1 to be fulfilled, question 2 must be also), we would have each team in division A play, say n crossovers. That means there are 7n crossovers in total. In particular, the number of crossover games is divisible by 7. On the other hand, by considering division B, we can see that the number of crossover games is divisible by 6. Since we have at least 0 crossovers and at most 42 (by assumption 1) & 7 and 6 are relatively prime, the only choices are, in fact, 0 and 42.
Interestingly, the same problem wouldn't necessarily exist for a 15-team conference, since it could be split 9/6 (although this is definitely undesirable, especially since the only other solutions would involve 10 and 8 conference games OR 12 and 11 conference games for teams in the large and small divisions, respectively.
\end{math}
In light of the above, I'd say the only reasonable option (involving a championship game) would be to base the division championship on in-division games only and maybe factor crossover games into a possible tiebreaker.
The question that this all raises is how the MAC does it. They have 13 teams in a 7/6 split, each playing 8 games. However, Miami (NTM) and Akron, both in the East division, didn't play each other last year, so I don't really understand how that qualifies as round robin (this is one example I found, there should be others).
Hmm...
If Pac-10 expects their new members to start playing in 2012, then does this suggest the Big Ten wants to stop here (don't need as much time to organize things)? Or is Delany just a much better commish than Scott?
Meanwhile, Barry Alvarez giving an interview on BTN from a cruise right now.
IIRC they tried to get the one hit ruled an error (which it should have been), but MLB wouldn't reverse the call.
At the very least, the scorer could rule it an error and at least salvage a no-hitter. I doubt that Selig will do the right thing and call it a perfect game. Remember, this is the guy who stopped the all-star game once in a tie after 11 innings!
I'm all for instant replay, but they need to find a more reliable way to implement it (tennis's seems pretty much infallible) -- high-speed cameras pointed at each base would be a start. I've seen several home run calls made wrong on replay. The current system is just enough to allow the crew to get some bad calls wrong twice while not enough to correct some (I have one in mind) other really awful calls.
This is what happened to Strassner:
http://www.wmubroncos.com/ViewArticle.dbml?DB_OEM_ID=4600&ATCLID=1553927
I agree that the two deserve to be fired, but in the current situation, it might be better to wait or do something else more quietly. As for possible mitigating factors, name a party involved and I can think of a scenario damning to that party while making everyone else seem innocent. In particular, the theory that Labadie and Draper were getting hit from both sides might have merit, but it's still not enough to excuse the facts we have in front of us. After all, they hardly needed s-a input (perhaps a little from the coaches) to compile the job descriptions. This is especially true for the first version (Exhibit 3, which, probably unfortunately, is short enough for everyone to read).
Great job, Brian, on leafing through all of this.
That was my first guess, but it still could have played out like this:
Reporter: What if [insert bad scenario - i.e. bad 2010 season, Rodriguez either fired or might be after Hayes would commit]?
Hayes: I don't think I can put myself in that (hypothetical) situation (which you brought up).