Greetings... I may be new to this list, but as a statistician, I jump
at the chance to collect some interesting data. One of my pet peeves
about college sports is that everybody seems to jump on winning percentages
without considering the strength of the opposition upon which the
winning percentage was based. So I thought I'd try my rating procedure
out on last season's scores and see who looked best once you did
adjust for strength of opposition. Here's what I found. Comments?
My comments are below the table (yes guys, it's a long message!)
Rating W L T Pct
==========================================================
1 Maine 13.430 40 1 2 0.953
2 Michigan 11.736 29 7 2 0.789
3 Lake Superior 11.701 29 8 5 0.750
4 Boston U 11.688 28 9 2 0.744
5 Miami 11.411 27 9 5 0.720
6 Minn-Duluth 11.101 28 11 2 0.707
7 Harvard 10.998 22 6 3 0.758
8 Minnesota 10.745 22 12 8 0.619
9 Wisconsin 10.740 24 15 3 0.607
10 Michigan State 10.689 22 14 2 0.605
11 Clarkson 10.602 20 10 5 0.643
12 N Michigan 10.501 21 18 4 0.535
13 Western Michigan 10.486 20 16 2 0.553
14 Ferris State 10.443 20 16 4 0.550
15 Michigan Tech 10.405 17 15 5 0.527
16 UMass-Lowell 10.368 20 17 2 0.538
17 RPI 10.326 20 11 4 0.629
18 New Hampshire 10.305 18 17 3 0.513
19 Denver 10.280 18 17 2 0.514
20 Alaska-Fairbanks 10.279 18 11 2 0.613
21 Brown 10.260 16 12 3 0.565
22 Providence 10.194 16 16 4 0.500
23 Bowling Green 10.148 18 21 1 0.463
24 St Lawrence 10.138 17 12 3 0.578
25 St Cloud 10.018 15 18 3 0.458
26 Alaska-Anchorage 9.932 15 12 4 0.548
27 Yale 9.925 15 12 4 0.548
28 Merrimack 9.775 14 20 2 0.417
29 Kent 9.664 12 21 3 0.375
30 North Dakota 9.572 12 26 1 0.321
31 Northeastern 9.534 10 24 1 0.300
32 Boston College 9.516 8 24 5 0.284
33 Vermont 9.395 11 16 3 0.417
34 Dartmouth 9.359 11 16 0 0.407
35 Colgate 9.270 11 18 2 0.387
36 Illinois-Chicago 9.248 9 25 2 0.278
37 Princeton 9.194 8 17 3 0.339
38 Colorado College 8.977 8 28 0 0.222
39 Notre Dame 8.830 7 27 2 0.222
40 Ala-Huntsville 8.566 4 11 1 0.281
41 Cornell 8.470 6 19 1 0.250
42 Ohio State 8.400 4 30 2 0.139
43 Mankato State 7.909 2 14 3 0.184
44 Union 7.868 3 21 0 0.125
45 Air Force 7.768 2 17 2 0.143
Actually, for these scores, the winning percentages are not so bad. Though
if you look down the list, the first three teams with winning percentages
better than their ratings suggest are Harvard, Clarkson, RPI. Interesting,
no? (Sorry, ECAC fans.) And of course, you don't need any sophisticated
methods to see that Maine were miles better than the rest. At the bottom,
Mankato State got a better win-loss record than Ohio State, but against
weaker teams, so the two switch places on the rating scale.
Data notes: I took the file of scores out of the archives and removed all
the games for any team that played less than ten times (so as to exclude
Canadian colleges, touring European teams etc., and, as it happened, Army
but not Air Force). Hence the overall W-L-T's differ a bit from the
ones in the archives.
Algorithm notes: The ratings only depend on wins, not scores. The basis
is an ugly formula (known to statisticians as the "logistic transformation")
which relates a rating difference to the probability that one team will beat
another. For example, Michigan and Michigan State differ by 1.047 rating
points, which translates into a 74% probability of Michigan defeating
Michigan State if they meet. The ratings are then chosen so that the
expected number of wins for each team, as found from the probabilities,
match the number of wins each team actually got. (This automatically
takes care of the opposition factor: if your schedule has a bunch of
tough teams, you won't be expected to win many, so if you don't, it's
no big deal --- but if you do, you get a big-time rating.)
Sorry for the hard reading in the last paragraph, but I try to convince
people that I know what I'm doing!
--
Ken Butler
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