Usual disclaimer: proto-KRACH is mostly an academic exercise, since it
makes little sense to rate teams based on so few games.

Now that everybody's played at least one official game, we can include
everybody in the proto-KRACH diagram, and the structure is pretty
manageable by now.  Harvard and Brown have only played each other, so
we can't compare them to anyone else.  The two other unbeaten, untied
teams (Maine and Dartmouth) are ranked infinitely higher than
everybody else.  The four winless, tieless teams (AIC, Princeton,
Yale, and Sacred Heart are at the bottom.  The only subtlety is that
Army and Bentley have only beaten or tied each other and AIC, which
puts them in their own group infinitely worse than the main pack and
infinitely better than AIC.  Note that in the only games in that
group, Army took three of four points from Bentley, so their KRACH
(for the purposes of that group) is three times Bentley's.  The
remaining 48 teams can be assigned finite KRACH ratings on the basis
of games among them.

    +---------------+     +---------------+
    | Me 100.0 .974 |     | Da 100.0 .974 |
    +---------------+     +---------------+
            |                     |
            V                     V
 +-----------------------------------------------+
 | SC  6117 .915   Pv 314.0 .680   HC 35.13 .405 |
 | Mi  2088 .863   MD 265.1 .660   Mr 34.95 .405 |
 | Wi 976.5 .803   Ck 168.7 .603   Mk 34.42 .403 |
 | CC 885.8 .794   Qn 155.2 .592   LS 25.86 .370 |
 | Mh 867.8 .792   BG 147.5 .585   AF 23.58 .360 | +---------------+
 | BU 844.5 .790   Vt 147.2 .585   SL 23.44 .360 | | Bn 100.0 .509 |
 | MT 774.1 .781   AH 119.9 .559   BS 21.66 .351 | +---------------+
 | ND 686.0 .769   Mn 104.6 .541   WS 17.36 .329 |         |
 | NM 640.0 .762   Ni 104.1 .540   Fi 17.16 .328 |         V
 | MA 561.5 .748   AA 75.28 .499   Ca 13.62 .306 | +---------------+
 | NH 426.6 .717   RP 73.98 .496   Cg 9.634 .276 | | Ha 100.0 .491 |
 | BC 386.9 .705   Ct 60.61 .471   FS 4.063 .216 | +---------------+
 | Nt 381.7 .704   MS 57.14 .464   NE 3.497 .207 |
 | DU 366.6 .699   Mm 54.78 .459   WM 3.183 .202 |
 | Un 336.1 .689   ML 52.99 .455   Cr 1.061 .157 |
 | OS 334.4 .688   Ak 49.22 .445   NO 1.016 .156 |
 +-----------------------------------------------+
        |                |            \         \
        V                |             \         \
+---------------+        |              \         \
| Ar 173.2 .075 |        |               \         \
| By 57.74 .066 |        V                V         V
+---------------++---------------++---------------++---------------+
        |        | Pn 100.0 .061 || Ya 100.0 .061 || SH 100.0 .061 |
        V        +---------------++---------------++---------------+
+---------------+
| AI 100.0 .044 |
+---------------+

Note that the current ratings predict that Union will take 100% of the
points from Bentley, so if Union wins, all the ratings will remain
exactly the same, while if Bentley gets a win or tie, the Army/Bentley
group will be drawn into the main pack.
                                          John Whelan, Cornell '91
                                                 [log in to unmask]
                                     http://www.amurgsval.org/joe/

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