Analyzing the RPI Bonus

OK. I've gone and answered my own question and done an anlysis of the '03 and '04 tourney selection to determine the constraints on the bonuses. I used the following model:

HOME = h
NEUTRAL = h + d
ROAD = h + 2d

i.e. The bonus values are equally spaced. I suspect this is true, and its the way everyone always talks about the bonuses.

I used the following additional constraint: h <= d.
Also, I assumed 0 < h <= d <= 0.005

From now on I'll multiply everything by 1000.

No one has ever suggested otherwise. I don't think my analysis changes if I relax this, until the very end.

The 02-03 season had no teams on the TUC bubble with bonus wins. Simplifies things.

[www.slack.net] for final PWR results.

1	Cornell (E)  	28	0.5958
2	CO College (W) 	27	0.5913
3	Minnesota (W) 	25	0.591
4	New Hampshire (H) 	25	0.5894
5	Boston Univ (H) 	24	0.5854
6	Maine (H) 	23	0.5807
7	Ferris State (C) 	22	0.566
8	Boston Coll (H) 	21	0.5792
9	Michigan (C) 	21	0.5689
10	North Dakota (W) 	18	0.5574
11	Ohio State (C) 	17	0.5497
12	Harvard (E) 	16	0.5583
13	MSU-Mankato (W) 	16	0.5528
14	St Cloud (W) 	15	0.5507
15	Providence (H) 	14	0.5444

Mankato-St Cloud: Since #1 overall Cornell played Mankato, not SCSU, we can assume St Cloud actually won this comparison and moved up to #13 overall (We were forced to play 13 or 14 since 2 other 1 seeds were WCHA teams and 13&14 were WCHA teams).

St Cloud had 1 Road win. The RPI difference was 2.04.

Thus, h + 2d > 2.04

St. Cloud-Harvard: Harvard was a 3 seed, SCSU a 4 seed. If this comparison flipped, then SCSU would have been a 3 seed, and we'd have played Wayne State or Mercyhurst and the comittee would have been spared a lot of sniping about #1 playing #14 instead of #16. But, it clearly didn't flip.

SCSU - 1 road win, not enough to make up the 7.59 difference in RPI
Thus h + 2d < 7.59

We can also predict how the Providence-Denver and Providence-Mankato comparisons worked out, but it turns out the the 03-04 tourney provides stronger constraints, so I won't bother.

JTW doesn't provide a final PWR for 03-04 that accounts for all the AutoQualifiers as TUCs. So nowhere to link. But the top of the standings were:

North Dakota 0.602499 29 Bo 0 0 Mi
Boston College 0.5926742 29 0 Ma 0 Mi
Maine 0.5922233 29 0 0 No Mi
Minnesota 0.5812356 27 0 0 0 0

The 03-04 season had only Mercyhurst near the TUC bubble with a Road Bonus win. They had RPI = 0.4894. For Mercyhurst to be a TUC that implies:

h + 2d > 10.6
But above, we saw h + 2d < 7.59, so Mercyhurst did not become a TUC.

The only interesting piece here is that UND was the #1 seed overall, BC #2. This is clear from the final four seedings where UND was setup to play Minn, not Maine. Thus, the BC-UND comparison did not flip. It could have.

BC had 1 ROAD, 2 NEUTRAL. (3h + 4d)
UND had 1 HOME. (h)
The RPI diff is 9.8

Thus, 3h+4d-h < 9.8
or
2h + 4d < 9.8
or
h + 2d < 4.9 (also, confirming Mercyhurst was not a TUC)

Put it all together:

2.04 < h + 2d < 4.9
h <= d
h > 0
d > 0

Gives a nice little quadralateral in the h-d plane where allowed bonuses live.

The corner points of the shape are, and their bonuses, which I've written backwards)

h d
--- ---
0 1.02 (0-1-2)
0 2.45 (0-2.5-5)
0.67 0.67 (0.67 - 1.33 - 2)
1.63 1.63 (1.63 - 3.26 - 4.85)

Note that 1-3-5 is excluded by the BC-UND comparison last year.

Now to get setup for the game.

[Q]CrazyLarry Wrote:
JTW doesn't provide a final PWR for 03-04 that accounts for all the AutoQualifiers as TUCs. So nowhere to link. But the top of the standings were:
[/q]

You should be able to do this with last year's DIY script.

Larry points out that last year, the BC-UND comparison showed that the committee did not use a .005/.003/.001 bonus. We can also reject the .005/.003/.001 bonus hypothesis for this season . If the NCAA had used a .005/.003/.001 bonus this year, then Harvard and BU would have been a 2 and 4 seeds, respectively, because the bonus would have flipped the Harvard-UNH and the Maine-BU comparions.

The seedings this year are consistent with a .003/.002/.001 bonus. Something in between the two commonly assumed RPI bonus options (.0040/.0025/.0010), would also have made Harvard a 2 seed and BU a 4 seed. A .004/.003/.002 bonus would have made Harvard a 2 seed, but kept BU as a 3 seed.

If the bonus points are consistent across seasons, as they appear to be so far, then it seems reasonable to assume, as many had already, that the committee uses a .003/.002/.001 bonus.

Of course, with the committee doing their "We voted and made DU the #2 overall," thing, I'm not so sure we can keep doing this and know for certain, which is why I have not gone back and done the analysis for this year.

On the Selection Show is was very clear that there was discussion on whether Cornell or Minnesota got the last #1 seed. There is no reasonable set of bonuses that would (there is a vanishing set that involves the bonus for a home win being essentially zero, something like 0-2-4, I forget exactly)

1) Give BC overall #1
2) Give DU and CC the same PWR score
3) Give Cornell and Minnesota the same PWR score

So, that means, that the comitee wasn't going on straight PWR score, and wasn't wasn't using direct comparisons. If we can't guarantee that, then we can't say anything at all.

[sarcasm] Thanks Adam, you asked for a little wiggling, eh... Careful what you wish for. Not that I think you're wrong, but no-one else ever wiggles quite the way you want them to...