Top 25 talk

[magicman]

Biggest Gainers in this week's Poll:

1.   Wabash +135 pts
2.   UW-Whitewater  +117 pts
3.   Hope   +83 pts
4.   Puget Sound  +67 pts
5.   MIT   +59 pts
6.   Franklin & Marshall  +57 pts
7.   Virginia Wesleyan   + 54 pts
8.   Augustana   +52 pts
9.   Williams    +49 pts
9.   St. Thomas  +49 pts
10. Birmingham-So.  +47 pts
11. Oswego St.  +46 pts


Biggest Losers:

1.   Wooster    -310 pts
2.   Buffalo St  -156 pts
3.   Wheaton   -133 pts
4.   Amherst   -119 pts
5.   WPI         -106 pts
6.   Whitworth  -78 pts
6.   William Paterson 78 pts
8.   UW-Stevens Point  -54 pts
9.   Hobart    -29 pts
10. Rochester -21 pts (but went from #24 to #23)
11. Baldwin-Wallace  -11 pts     

[augie_superfan]

For those who have not seen this yet, here is a new computer poll - D3 Basketball Index - created by poster augie_superfan...

https://sites.google.com/site/d3basketballindex/


You will see this has Hope #1.

I'm sure augie superfan himself would agree that with a sample size of 2, the statistical meaning of that ranking is not very high. They are being rewarded because they haven't really played any bad d3 teams (Wheaton only had 1 other d3 loss, and Carthage only has 2). Those rankings don't take into account non-d3 games. What if we ranked every team based on their top 2 d3 results? Probably wouldn't mean a whole lot, right?  Hope's computer ranking won't mean more until they have more d3 games. I'm sure some voters are being cautious for this very reason.

You see some other manifestations of this low sample size phenomenon with other teams also, like 1-2 Lewis and Clark at #22 and 1-1 George Fox at #29. If those teams were undefeated they would also likely be in the top 5 of the computer rankings, but would anyone really be arguing for them to be ranked higher in the human poll? Probably not.

Further, Hope's rating is really being pumped up by the 30 point win vs. Carthage. Because they have only played two games, and won both, the computer model is trying to justify the final margins. In other words, and simplified for explanatory purposes, the model needs to account for the final spreads in Hope's games by assigning the team a proper rating. Since it doesn't have a lot of data to go on from Hope, based on the other results from Carthage and IWU, the rating for Carthage is about 7 and for IWU is about 20. Therefore, to reconcile their margins of victory, Hope's rating must be about 30 (the difference in the teams ratings is the expected final margin). If Hope had only beaten Carriage by single-figures, I would expect their ranking to fall to the teens, which goes to show how shaky their current ranking in the computer poll is.

Leave it to an MIT guy to explain it better than I could have myself.  Out of curiosity, I re-ran the rankings by taking out all margin-of-victory information.  So all the system used was win/loss and the location of the game.  Hopefully this weekend I'll have time to add these rankings to the site for comparison but here are the top 10 for those interested:

#1   Hope
#2   Whitworth
#3   Lycoming
#4   Puget Sound
#5   Wabash
#6   Edgewood
#7   George Fox
#8   UW-Whitewater
#9   Grinnell
#10 UW-River Falls

[Hugenerd]

I will still have to point out that N is equal to 2 for Hope.

Also note that George Fox at 1-1 has moved to #7.

Small samples sizes are a statisticians enemy. Its tough to make strong conclusions.

[smedindy]

I don't think you need to take out the MOV info. That's quite crucial info, though you may need to put in some diminishing returns. Some teams just need a few more D-3 games in their belt, but I think the premise is sound!

[augie_superfan]

I will still have to point out that N still equals 2 for Hope.

Also note that George Fox at 1-1 has moved to #7.

Small samples sizes are a statisticians enemy. Its tough to make strong conclusions.

It's true that the sample size is small at the moment meaning you can argue that Hope has played above their level and are maybe overranked in the system.  But to play devil's advocate, how do we know that's true?  Only time will tell but as of this instant, I think it's giving an accurate measure of where Hope should be ranked.  I feel a little bit better with the ranking seeing that Massey has them ranked #3 in the power ranking.  That includes all their other games against NAIA and D1 teams.  Now, they may be getting a decent bump from the D1 game (one reason I left those out of my system).  Unfortunately for my system's sake, Hope doesn't play another D3 game until 12/29 vs. Marietta so they should stay near the top of my rankings unless Wheaton and Carthage fall.

[augie_superfan]

I don't think you need to take out the MOV info. That's quite crucial info, though you may need to put in some diminishing returns. Some teams just need a few more D-3 games in their belt, but I think the premise is sound!

Have no fear, the MOV info is going nowhere....was just taking it out to show that Hope's ranking stayed the same in this case

[Hugenerd]

I don't think you need to take out the MOV info. That's quite crucial info, though you may need to put in some diminishing returns. Some teams just need a few more D-3 games in their belt, but I think the premise is sound!

Have no fear, the MOV info is going nowhere....was just taking it out to show that Hope's ranking stayed the same in this case

Unfortunately, the number of games they played against d3 opponents did not change. So if you were to put a confidence interval on that rating, it would be huge (by the way, can you calculate a standard deviation, or uncertainty, in your model in any way?).

[Hugenerd]

Also, here are Massey's ratings, for comparison:

http://masseyratings.com/rate.php?lg=cb&yr=2012&sub=NCAA%20III&mid=1

Massey does take into account all games, and they still have Hope #2, although their strength of schedule is really getting pushed up by some of their non-d3 opponents (a 20 point loss to a D1 program can be much more impressive than a win vs. A D3 opponent to the computer model).

Also, for those of you hating on MITs SOS, Massey has 2 of the 3 schools ranked ahead of them in the human poll, VA Wesleyan and Middlebury, as having lower SOS' than MIT.

[augie_superfan]

I don't think you need to take out the MOV info. That's quite crucial info, though you may need to put in some diminishing returns. Some teams just need a few more D-3 games in their belt, but I think the premise is sound!

Have no fear, the MOV info is going nowhere....was just taking it out to show that Hope's ranking stayed the same in this case

Unfortunately, the number of games they played against d3 opponents did not change. So if you were to put a confidence interval on that rating, it would be huge (by the way, can you calculate a standard deviation, or uncertainty, in your model in any way?).

Well one thing that I can do is look at each team individually and see for each game what the predicted score would be based on the two teams rankings and then I obviously have the actual result.  Now, the whole premise of the system is to even out the "overrankings" and "underrankings" to net out at 0.  So I can get a standard deviation for each team based on the distribution for all their games.  Obviously you'd have more confidence in a team's ranking is all their games score differences were small versus large.  I'm just not sure how to use that standard deviation quantity and relate it to the team's actual ranking...but worth thinking about.

When trying to optimize the system using last year's games, I did look at every game and how far off the predictions were and what the standard deviations were for those distributions and minimized both of those numbers while not predicting my game prediction percentage.

[augie_superfan]

Also, for those of you hating on MITs SOS, Massey has 2 of the 3 schools ranked ahead of them in the human poll, VA Wesleyan and Middlebury, as having lower SOS' than MIT.

One thing that I worry about most in my ranking system is that it over-penalizes for playing weak teams.  It's all taken into account automatically so I would have to counteract that with a small multiplier to very weak teams.  Unfortunately, this seems completely counterintuitive and did produce worse prediction results so I left it out of this year's system but it may be something to revisit in the future.  MIT may be a good team to follow with respects to this but their conference schedule should make up for the currently low SOS.

[Hugenerd]

Agreed

Don't worry about variance if its not readily available.  Even if standard deviation was identical for all teams, your df would be 1 (n-1) and therefore t-stat would be huge when calculating a CI for N only equal to 2 (not to mention small sqrt(N) term in denominator). Just going back to my old point that there is not a lot of certainty in any quantity when sample size is 2.

[augie_superfan]

Just going back to my old point that there is not a lot of certainty in any quantity when sample size is 2.

Agreed

[smedindy]

Small samples sizes are a statisticians enemy. Its tough to make strong conclusions.

Yet ink-stained wretches and announcers will take 10 at-bats or 4 2/3 innings and say 'conclusive proof!"

[Hugenerd]

Small samples sizes are a statisticians enemy. Its tough to make strong conclusions.

Yet ink-stained wretches and announcers will take 10 at-bats or 4 2/3 innings and say 'conclusive proof!"

No one ever accused an announcer of being a statistician.

[mailsy]

Reading these posts, makes me understand why I was a history major.