Rethinking the TAPE Index

Even though the Tournament is still going on, I'm already in the process of putting together the projections for the 2015 season. If all goes as planned, I'll have them up and ready to go on the Tuesday morning following the National Championship game.

Next year poses a bit of a problem for my system, though. From the beginning, the TAPE ratings and most of the other adjusted stats here have been indexed to a hypothetical average BCS conference team. The thinking behind this was that teams from the six BCS leagues who finished with .500 conference records were generally right around the bubble cut line for the NCAA Tournament, so a TAPE rating better than .500 (or 9.0) would indicate a Tourney-caliber team.

For the first six years, that was simple enough: I just included all the teams from the ACC, Big East, Big Ten, Big Twelve, Pac-12 (or Pac-10), and SEC in the index. When the Big East split last summer, I made the decision to include both the new Big East and the American Athletic Conference in the index. Doing so added some strong teams who hadn't been in the index before--Butler, Creighton, Memphis, and Xavier--but also meant that the likes of Central Florida and Houston would be included as well. In this case, the good outweighed the bad.

For 2015, though, there would be a tough choice as to whether or not to consider the AmCon worthy of inclusion in the index. Louisville and Rutgers are leaving on July 1 for the ACC and Big Ten, respectively, and they'll be replaced by East Carolina, Tulane, and Tulsa. Are those three teams really worthy of consideration as major basketball teams? Probably not. On the other hand, should UConn, Memphis, and Cincinnati be considered mid-majors?

The solution is to abandon conference affiliation as a consideration for inclusion in the index altogether. Instead of indexing everything to an average of an ever-changing number of power conference-affiliated teams, from this point forward each season's ratings will be based on an average of the top 100 teams over the preceding 5 years. The change has already been made for the current season's ratings as of this morning's update.

The following teams (with their 5-year ranking in parentheses) are included in the index for 2014:

Akron (84)	Duke (3)	Marquette (19)	Oklahoma (61)	Texas (24)
Alabama (53)	Florida (15)	Maryland (49)	Oklahoma St. (46)	Texas A&M (51)
Arizona (30)	Florida St. (42)	Memphis (31)	Old Dominion (90)	Tulsa (80)
Arizona St. (59)	George Mason (91)	Miami (FL) (37)	Oregon (78)	UAB (74)
Arkansas (98)	Georgetown (12)	Michigan (20)	Penn St. (76)	UCLA (39)
Baylor (25)	Georgia (92)	Michigan St. (8)	Pittsburgh (13)	UNLV (36)
Belmont (64)	Georgia Tech (82)	Minnesota (26)	Providence (87)	USC (73)
Boston Coll. (94)	Gonzaga (10)	Mississippi (58)	Purdue (16)	Utah St. (50)
Butler (44)	Harvard (100)	Mississippi St. (95)	Richmond (68)	UTEP (81)
BYU (14)	Illinois (35)	Missouri (9)	Saint Louis (71)	Vanderbilt (47)
California (33)	Illinois St. (85)	Murray St. (86)	San Diego St. (28)	VCU (45)
Cincinnati (48)	Indiana (52)	N.C. State (56)	Seton Hall (65)	Villanova (22)
Clemson (43)	Iona (93)	Nebraska (77)	South Florida (89)	Virginia (63)
Cleveland St. (99)	Iowa (75)	New Mexico (29)	Southern Miss (66)	Virginia Tech (67)
Colorado (72)	Iowa St. (55)	North Carolina (11)	St. John's (83)	Washington (21)
Colorado St. (79)	Kansas (1)	Northern Iowa (69)	St. Mary's (32)	Washington St. (62)
Connecticut (18)	Kansas St. (17)	Northwestern (70)	Stanford (57)	West Virginia (23)
Creighton (54)	Kentucky (5)	Notre Dame (34)	Syracuse (4)	Wichita St. (40)
Davidson (88)	La Salle (97)	Ohio (96)	Temple (38)	Wisconsin (7)
Dayton (60)	Louisville (6)	Ohio St. (2)	Tennessee (41)	Xavier (27)

For the 2015 season, Boston College, Cleveland State, Davidson, George Mason, Illinois State, and Mississippi State will drop out of the index and be replaced by Boise State, Middle Tennessee, New Mexico State, Princeton, St. Bonaventure, and St. Joseph's.

Preseason TAPE Rankings Are Up

This is sure to look foolish by, oh, the second weekend of November or so, but this season I'm going to be publishing a preseason version of the TAPE ratings. The preseason ratings were compiled by projecting each individual player's offensive and defensive PAPER ratings and playing time for the upcoming season based on typical development curves. 

Those development curves are based on the average year-over-year improvement for players at each position in each conference. Ideally, I would be able to use a group of similar players to project out each individual, but since my player stats database only has three seasons' worth of data in it at the moment, this is the next-best thing.

(The list of players included in the rankings can be found in this spreadsheet. It's obviously hard to keep up with the comings and goings of 344 teams, so it's entirely possible that I've missed an incoming transfer here or included a player who's been dismissed from his team there. If you notice any of those cases, please let me know and I'll adjust everything accordingly.)

The astute reader will notice that for most teams the number of expected minutes falls well short of the 200 total floor minutes per game each team will log. That's because the only individuals listed are returning players, incoming transfers, and incoming RSCI Top-50 (or Top-100 for non-BCS conferences) players. The remaining minutes are projected to be filled by generic incoming freshmen.

Some notes on the rankings:

• The Big Ten looks to be absolutely stacked at the top, with four teams in the Top Ten (#1 Ohio State, #2 Purdue, #8 Wisconsin, and #9 Michigan State), and three more in the Top 25 (#12 Northwestern, #16 Indiana, and #18 Michigan). 
• The ACC has nine teams--everyone but Georgia Tech, Boston College and Wake Forest--that should contend for NCAA Tournament bids, but only Duke and Carolina project in the Top 25.
• Frank Haith might have walked into a great situation at #3 Missouri. The rest of the Big 12 looks like it might have a down year.
• A couple of interesting teams appear poised to rise to the top of the SEC: Alabama and South Carolina. Anthony Grant could have a nationally-elite team in just his third year in Tuscaloosa, while the Gamecocks look like a fringe Top 25 team in what's likely a make-or-break year for Darrin Horn.
• Looking for a mid-major team that might do big things? Try Indiana State, Oral Roberts, Harvard, Wichita State, or South Dakota State.

Hope That Payday Was Worth It (Plus: Bonus Nerd Content!)

This is why you don't play games at 6 o'clock in the damn morning: Monmouth, playing on the road at St. Peter's, hit just 10 of 47 attempts from the floor on their way to a mind-bogglingly low 34 points in 65 possessions. So maybe agreeing to tip off a road game 45 minutes before sunrise wasn't the best idea in the world.

Speaking of St. Peter's, you may have noticed that they're the #1 team in the early season TAPE rankings. Are the Peacocks really that good? Probably not.

See, this year I've added an adjustment into TAPE that will account for the point in the season a given contest takes place. I know that some other systems weight for recent performance, and I wanted to find out whether that would make TAPE better. I couldn't find any evidence that it would, though. The season is too short and there are just too many random fluctuations around the mean in a given team's season to suss out any trends.

What I did find, though, was that there are certain trends that seem to apply across the board as the season progresses. The most notable of these is that the pace of games slows as the season progresses. Games in November are about three possessions faster than those played in March. This was sort of a big deal for TAPE, because it was built on the assumption that the overall environment of college basketball was fairly static throughout the season.

So I started drilling down into the component categories of the possession model to find out whether those varied over the course of the season as well, and, sure enough, lots of them did. Turnover rate, not surprisingly, is higher in November than in February; field goal shooting improves as the season goes along; offensive rebounding rate actually gets worse over the course of the season.

What's really interesting is that in some categories, there's much more change for either the home or away side. Home teams, for example, are very consistent throughout the season in terms of turnover rate and shooting percentages, while away teams get much better at both as the season progresses. (I'm pretty sure this is the source of my frustration in predicting games last season, when TAPE would be consistently high on its projection of total points scored and consistently low by a couple points on its projection of the visiting team's score.)

So that brings us back to St. Peter's. They had the good fortune of playing what might turn out to be their best game of the season on the road in their first game of the season. Once everyone gets a few games under their belts, that one game won't mean as much. Right now, though, it's all TAPE knows about the Peacocks.

Tournament Overview: Big XII

Can't see the table? Click here.

Despite being a slight underdog in a potential head-to-head matchup in the conference finals, Missouri has a better chance of winning the championship than does Kansas. How's that possible? The Tigers match up much better against their five other possible finals opponents--the ones they'd match up with 57% of the time--than do the Jayhawks.

In Wednesday's first round games TAPE likes Nebraska over Baylor by less than a point (65.3 to 64.5 in 64.7 possessions). This matchup is about as even as it gets, with the Bears holding slight edges in shooting, rebounding, and getting to the line but giving it all back with turnovers.

Colorado-Texas is the biggest mismatch in the first round of any BCS conference tournament. TAPE likes the Longhorns to win 83.3% of the time by a margin of nearly 13 points (70 to 57.1 in 62.6 possessions) while dominating every facet of the game.

Travis Ford's resurgent Cowboys are 10-point TAPE favorites over Iowa State (77.1 to 67.3 in 69.5 possessions). Fun fact: Pittsburgh's DeJuan Blair's offensive rebound rate (23.7%) is almost as high as Oklahoma State's (26.8%) and is higher than Iowa State's (23.0%).

The nightcap could turn into a free throw exhibition for the Aggies. A&M went to the line almost 26 times a game in conference play, and the Red Raiders' opponents averaged 28 free throws per game. TAPE thinks A&M will shoot 29 free throws--but make just 20 of them--on their way to a 6-point victory (77.4 to 71.2 in 70.3 possessions).

The table of all possible matchups:

Minor Changes

The TAPE rankings page has been changed. Most of the clutter that didn't really mean anything (like pythagorean winning percentages) or can be found a million different places on the 'net (like actual records) has been replaced with clutter that is unique to this site. Along with each team's adjusted offensive and defensive points per possession (the OFF and DEF columns), I've now included offensive and defensive Four Factors. Just as before, all statistics are adjusted to reflect neutral-court performance against an average BCS-conference opponent.

Today's Games: 1/14/2009

I've finally located and fixed the bug that was causing the point spreads to be underestimated, and I figured now was as good a time as any to finally get a post up explaining just how TAPE and TAPE projections work.

If you're a baseball stathead or you're familiar with Ken Pomeroy's ratings, you've probably heard of the Log5 method for predicting the outcome of a given event. Simply put, it says that a team's expected winning percentage in a given game can be predicted using the following formula:

Where T is the team's winning percentage and P is the opponent's winning percentage. So if you have a full baseball season's worth of data, or a really good adjusted ratings system like KenPom's (or even the TAPE ratings), you can get a pretty good handle on what the odds are for a given game.

There's a much more powerful variation on the theme of Log5, though, and it's way more useful. Instead of having an implied mean of .500 for all teams, the following formula (which I stumbled upon here) has league average as its own variable:

In this case, the formula gives the expected batting average for a hitter with a batting average of B facing a pitcher with a batting-average-against of P in a league where the overall batting average for all players is L. The good news for us is that it works just as well in basketball as it does in baseball. Field goal percentage, rebounding percentage, the ratio of three-point attempts to field goal attempts, and anything else that is (or can be) expressed as a number between zero and 1 can be predicted with a suitable degree of accuracy using the above formula.

Using this method and a table of each team's double-neutral (i.e. what the team would be expected to do on a neutral court against average competition) values in a number of categories, it's possible to not only predict teams' performances in any given category, but also, using a probablistic model of a possession, to build a complete predicted line score for any matchup.

The full slate of games is after the jump.

Tipoff	Visitors	TAPE Predicts			Home	Line	O/U	%	Conf.
6:30 PM	Michigan St.	71.9	at	69.3	Penn St.	+6.0	136	57.4%	BigTen
7:00 PM	Binghamton	65.2	at	70.3	Albany			64.5%	A-East
	Holy Cross	56.2	at	54.7	Army			54.6%	Pat
	Sacred Heart	67.2	at	61.7	Bryant			65.2%
	Elon	53.9	at	84.4	Davidson	-23.5	137.5	98.6%	SoCon
	Hofstra	58.7	at	63.0	Drexel	-4.0	122	62.5%	CAA
	Geo. Washington	60.6	at	78.8	Duquesne	-10.5	146	90.1%	A-10
	Duke	79.2	at	67.1	Georgia Tech	+12.0	148.5	80.0%	ACC
	Maine	59.6	at	62.7	Hartford			59.0%	A-East
	N.C. Wilmington	67.2	at	91.3	James Madison	-15	153.5	94.8%	CAA
	Bowling Green	63.5	at	68.0	Kent St.	-7.5	135	62.7%	MAC
	Colgate	62.5	at	66.6	Lafayette			61.7%	Pat
	Navy	69.8	at	74.5	Lehigh			62.7%	Pat
	N.J.I.T.	45.8	at	71.4	Loyola (MD)			97.3%
	Ohio	55.0	at	67.8	Miami (OH)	-9.0	122	83.2%	MAC
	UMBC	65.1	vs	60.1	New Hampshire			64.9%	A-East
	Temple	71.7	at	65.8	Pennsylvania	+9.0	138.5	66.3%
	South Florida	51.5	at	74.7	Pittsburgh	-21.0	131	95.8%	B-East
	S. Carolina St.	58.4	at	63.1	Savannah St.			63.8%
	St. Joseph's	67.0	at	64.9	St. Bonaventure	+4.5	137	56.2%	A-10
	VCU	75.7	at	67.0	Towson	+9.0	135.5	72.8%	CAA
	Richmond	64.2	at	69.1	Virginia Tech	-8.0	131	64.2%
	Toledo	57.2	at	64.1	W. Michigan	-10.0	124.5	69.7%	MAC
	George Mason	61.7	at	56.7	William & Mary	+6.0	122.5	65.0%	CAA
	Gardner-Webb	66.9	at	66.3	Winthrop			51.6%	B-Sou
7:30 PM	Bucknell	56.7	at	70.2	American			83.9%	Pat
	Vermont	70.7	at	73.2	Boston U.			56.7%	A-East
	La Salle	69.3	at	76.4	Charlotte	-5.0	145	69.1%	A-10
	Rutgers	59.9	at	70.1	Cincinnati	-9.0	130	77.1%	B-East
	Fordham	48.8	at	77.1	Dayton	-21.0	125.5	98.1%	A-10
	Syracuse	67.2	at	78.8	Georgetown	-6.5	142.5	79.2%	B-East
	Texas Pan Amer.	63.6	at	61.3	N.C. Central			56.9%
	UTSA	66.7	at	67.1	Nicholls St.			51.3%	S'land
8:00 PM	Florida	70.0	at	69.7	Auburn	+3.0	138	50.8%	SEC
	Stephen F. Austin	66.2	at	51.5	Central Arkansas			87.3%	S'land
	Nebraska	60.8	at	57.1	Iowa St.	+1.5	120	61.2%	Big 12
	South Carolina	70.6	at	74.1	LSU	-3.5	144	59.6%	SEC
	Arkansas	74.3	at	80.7	Mississippi	-1.5	146.5	66.9%	SEC
	Alabama	62.6	at	72.7	Mississippi St.	-7.0	136	76.2%	SEC
	SMU	63.6	at	65.3	Rice	-3.0	130	55.0%	C-USA
	Massachusetts	59.7	at	66.3	Saint Louis	-3.5	129	69.0%	A-10
	Northwestern St.	68.4	at	85.0	SE Louisiana			87.4%	S'land
	Texas St.	75.4	at	77.0	Texas A&M C.C.			54.4%	S'land
	Southern Miss	62.7	at	56.5	Tulane	+3.0	123	68.4%	C-USA
	Lamar	75.3	at	81.5	TX Arlington			66.4%	S'land
	Georgia	58.2	at	71.9	Vanderbilt	-10.5	132	83.4%	SEC
	Marshall	55.8	vs	77.4	West Virginia	-15.5	136	94.6%
	San Diego St.	76.4	at	67.9	Wyoming	+6.0	139	72.3%	MWC
8:05 PM	Southern Ill.	60.3	at	72.8	Creighton	-10.5	129.5	81.9%	Valley
	Drake	64.0	at	74.5	Illinois St.	-8.5	136	77.1%	Valley
	Wichita St.	54.4	at	56.6	Missouri St.	-4.0	116	56.7%	Valley
8:30 PM	Michigan	61.6	at	70.5	Illinois	-7.0	127	74.5%	BigTen
9:00 PM	Wake Forest	80.4	at	75.4	Boston Coll.	+3.5	155.5	63.4%	ACC
	UNLV	73.3	at	68.3	Colorado St.	+7.5	140.5	63.7%	MWC
	Maryland	61.4	at	75.1	Miami (FL)	-6.5	141	83.0%	ACC
	Colorado	59.8	at	81.7	Missouri	-18.0	138	94.6%	Big 12
9:05 PM	Houston	71.7	at	74.3	UTEP	-4.5	149	57.1%	C-USA
9:30 PM	Baylor	71.6	at	69.0	Texas A&M	+1.5	139.5	57.4%	Big 12
10:00 PM	Utah	61.5	at	53.5	Air Force	+8.0	122	73.3%	MWC
	CSU Northridge	66.9	at	65.9	UC Riverside	-1.0	132.5	53.0%	B-West
Point spreads compiled from OddsShark.com.						Updated 11:42 PM EST

2009 TAPE is up

As you can see in the sidebar, TAPE is now being computed for the new season. It means absolutely nothing right now--nobody's connected enough for anything to make sense at this point--but it's at least a reference point. I've automated the process of spidering for all of the game data, so if everything goes as it should, TAPE should be up through the previous night's games by around 9 a.m. every day. You'll also notice the TAPE History link, which will take you to a page that shows the daily progression. That should be fun for tracking how teams do over the course of the next four months.

Also in the works for this year are full player stats for all of Division I. I'll be generating translated line scores for every player-game (which probably won't get published unless I move to a non-Google-Docs-based system) as well as season averages and totals for every player (which probably will be available). These will be based on the same framework that makes TAPE possible, and should allow for an apples-to-apples comparison of players across all of Division I. That, in turn, will make it possible to generate PAPER for every player in D-I. I'll have more on all of that as I roll the new features out.

TAPE: Raising the Bar

Up to this point, a team's TAPE has been a representation of their expected winning percentage against an average team. The problem is, with 341 teams in Division I, there are between 160 and 170 teams that are better than average at any given moment. Average teams, unless they're lucky enough to play in the Ivy League or the SWAC or the Patriot League or the MEAC, aren't even among the best teams in their own conference. Average teams are nowhere near the postseason radar. Using an average team as a reference point in a Division I ratings system just doesn't make any sense at all.

So, if average is out, what is in? Every year around this time, bubble talk begins in earnest. While an increasing number of mid-majors are getting bubble attention, most of the focus rightfully is on the teams from the six BCS conferences. (Yes, I do realize that it's silly to use a football term in a basketball context, but, really, what other nomenclature would work? "Power conference" sounds like a meeting of energy executives, and a "high major" is a marching band leader with an illegal smile, so, as much as I hate the sport with the funny-shaped ball, I'll stick with the BCS.) When it comes to assessing those teams, the most important bit of information seems to be whether or not they have a winning conference record.

With that in mind, TAPE has now been changed to reflect how each team would fare not against the average Division I team, but what their record might look like if they played their entire schedule against BCS-level competition. The number of teams with ratings better than .500 has dropped from 165 to 48. It just so happens that if the NCAA field was built using TAPE, the cut line for at-large bids would be .500. Neat, huh?

Tale of the TAPE

One of the things I was hoping to do with the site this season was to produce PAPER numbers for the entire season, not just the conference portion of the schedule. The problem with that is that schedules are so varied that it's hard to find a way to make an aples-to-apples comparison. I thought about using items that were already in the ACC database--specifically treating each opponent from a given conference as the same team--but rejected that idea pretty quickly. There's just too much variation in quality within conferences for that to work.

With no easy solution available, I decided to go big. I've entered all the linescore data from every game between Division I teams into the database and I've used that to adjust every team's offensive and defensive rates across all the statistical categories that relate to team scoring. That data, which represents what each team would have done over the course of the season if all games were played against a Division I-average opponent on a neutral floor, can be found here.

With all that done, it's just a matter of plugging numbers into the same probabilistic model used for PAPER to arrive at an estimate of the number of points each team in Division I would score and allow against neutral competition. The Pythagorean expectation derived from those numbers (an exponent of 9.2 maximizes the r-squared in this model) is the Team Adjusted Probabilistic Effectiveness, or, in keeping with the office supplies theme, TAPE. The current Top 25 (through the games of 1/21/08) are:


The full list of TAPE is available here. Other information on the spreadsheet includes each team's full raw winning percentage and Pythagorean expectation (exponent 8.5), as well as their adjusted records converting each opponent into a hypothetical average team.

Coming up next: using the component pieces of TAPE to predict the future.