Rating Systems and March Madness Brackets, Part I

March Madness is big business, not just for the NCAA and its member schools, but for media outlets and the billions of dollars and hours spent every year filling out brackets. With all the numbers and all the money involved, it would be negligent for Rational Pastime to stay out of the discussion.

Lots of us like to look at the different ratings systems for bracket information, especially when it comes to upsets. Of course, the ratings systems don't agree with each other. Let's take a look at three ratings systems that are among the most influential and well known: Pomeroy, Lunardi RPI and NCAA Official RPI.*

We'll have more rating systems tomorrow, but if you have any requests please post them in comments.

The table below is the result of an attempt to quantify the "chalkiness" of the three rating systems in question. Basically, I composed brackets for all three systems in which the higher ranked team always wins. For each round, I added up the seed differentials of all the predicted upsets. I then calculated a weighted sum of the seed differentials in each round multiplied by 1 for the field of sixty-four, 2 for the field of thirty-two, 4 for the Sweet Sixteen and 8 for the Elite 8. Lower scores equal more chalk.

Upset Index (Seed Differential * [2 ^ Round / 2])
	Field 64	Field 32	Sweet 16	Elite 8	Overall
Pomeroy	25	0	12	0	37
Lunardi	25	8	40	8	81
NCAA*	9	16	4	24	53
Mean	20	8	19	11	57

*NCAA Official RPI numbers are not yet updated for Sunday's games, so take their preliminary numbers with a grain of salt.

A couple of interesting things jump out. First, Pomeroy is the chalkiest of the three rating systems, including the NCAA Official RPI. This is somewhat surprising, since presumably the selection committee partially relies on the latter system. However, this may be due to the NCAA numbers not yet factoring in Duke's ACC tournament victory, among other Sunday results.

Second, Lunardi's RPI system is by far the least chalky, and it's not even close. Most of the Lunardi system's renegade streak results from Sweet Sixteen matchups.

Third, Pomeroy's system picks no matchups in the round of thirty-two or Elite Eight. Ignoring the events of yesterdays' Selection Show, I might suggest that the lack of chalkiness in the Pomeroy bracket is a sign that the NCAA Selection Committee is becoming more rational in their selections. However, certain inclusions, omissions, and the general tenor of Jay Bilas' Twitter feed convinced me otherwise. 

You can check out each upset that the systems predict in the table below. All three systems pick a 12-5 upset, but they don't agree on which. Lunardi predicts two, which seems high but we'll see. Perhaps more notably, only Pomeroy picks any 10-7 upsets (he picks 2). This seems unusually chalky, but we'll see.

Pomeroy: 37
Field 64	Field 32	Sweet 16	Elite 8
Marquette (11)	None	Syracuse (3)	None
Xavier (6)		North Carolina (2)
Illinois (9)		Purdue (3)
UNLV (8)		Notre Dame (2)
FSU (10)		BYU (3)
Texas A&M (7)		Florida (2)
Old Dominion (9)
Butler (8)
Utah St (12)
Kansas St (5)
Gonzaga (11)
St. Johns (6)
Michigan St (10)
UCLA (7)
Lunardi RPI (ESPN Insider): 81
Field 64	Field 32	Sweet 16	Elite 8
Clemson (12)	Georgetown (6)	Syracuse (3)	Texas (4)
West Virginia (5)	Purdue (3)	North Carolina (2)	Connecticut (3)
Marquette (11)	Kansas St (5)	Texas (4)
Xavier (6)	Wisconsin (4)	Duke (1)
Memphis (12)		Connecticut (3)
Arizona (5)		San Diego St (2)
Missouri (11)		Kansas St (5)
Cinci (6)		Pittsburgh (1)
Old Dominion (9)		BYU (3)
Butler (8)		Florida (2)
NCAA Official RPI: 53*
Field 64	Field 32	Sweet 16	Elite 8
Tennessee (9)	Utah St (12)	BYU (3)	San Diego St (2)
Michigan (8)	Wisconsin (4)	Florida (2)	Duke (1)
Old Dominion (9)			BYU (3)
Butler (8)			Pitt (1)
Utah St (12)
Kansas St (5)
*NCAA Official RPI not updated for Sunday Games

We'll have more on different rating systems, and hopefully updated NCAA RPI numbers, tomorrow.

Image Credit: Wikipedia