Scoring Rules (2012)

This is an explanation of why the particular scoring rules for 2012 have been adopted. The problems we had with last year were:

• In Jeremy's bracket contest, there is an inherent balance between getting a lot of points for an upset and, if you're wrong, getting 0 points for subsequent games. In this contest, by design you can't be completely out of a game, so this heavily skews results in favor of picking upsets. Note that that was the winning strategy for both the #1 and #2 entries last year.
• In the occasional scenario where a low seed makes it to the final four (like #8 Butler in 2011 or both #5 Butler and #5 Michigan State in 2010), it's worth a disproportionate number of points. You can see this effect by the spike in the average points per game for round 4 below.
• The contest is pretty much over before the final four games, especially since dropping the seed multiplier makes the game really low scoring.

To fix this, the rules will be changed as follows:

• The value of the seed drops over time, so the Seed term is now essentially Seed / (Round+1). (The actual expression is more like floor(1+(Seed-1)/(Round+1)).) A #8 in round 4 would only be worth 2, and a #5 is only worth 1.
• To increase the effect of subsequent rounds, the Round term has been changed from 5, 10, 15, ..., to 5, 15, 25, ..., which is expressed as (10*Round - 5).

Using the past few years as data points, you get the following distributions:

2011 Rules: 5 * Round * (Round <= 4 ? Seed : 1)	2012 Rules: (10 * Round - 5) * (Seed / (Round+1))

How That Would Change Results

By applying those rules to last year's contest, the new results would be:

User	Bot Name	New Score	Change In Rank
Michael O'Halloran	There's No Need to Fear	1105.000	same
Darrel Hutchins	Fibs, Lies, and Statistics	920.318	+2
Darrel Hutchins	Big Stuff	914.974	same
Brent Cox	PastPerformance	908.409	+3
Stock	Low Seed Wins	895.000	-3
Michael O'Halloran	Bot-tastic	868.206	+3
Stock	Coin Flip	862.500	-1
Rick Bassham	Random	861.616	-3
Stock	High Seed Wins	830.000	+4
Daniel Reid	Random	823.781	+2
Stock	Split the Middle	773.535	same
Darrel Hutchins	Déjà Vu	767.500	-2
Daniel Reid	Contrarian	765.000	+1
David Jones	Human Bracket	739.000	-2
David Jones	High Seed Mostly Wins	738.869	same
David Jones	Using Statistics	735.276	same
Brent Cox	SOLOOLT	725.000	+1
Brent Cox	Haven'tISeenYouBefore?	722.417	-1
Daniel Reid	Contrarian 2	675.000	same
Michael O'Halloran	Modified RPI	670.000	same

This shows "There's No Need To Fear" clearly dominating the competition. The last round is only worth 55 points, so it would have been over by then. The idea that a "low seed wins" variant can do so well is still troubling. I do like how much closer the rest of the field looks, though.