The True Value of the Four Factors

Dean Oliver's four-factors are well-understood in how they impact the game.

To figure this out, people usually run a regression of game or team four-factors versus efficiency.

We find the following, roughly:

	raw coefficients
OeFG%	1.32
OTO%	-1.19
OOR%	0.63
OFTM/FGA	0.17
DeFG%	-1.32
DTO%	1.19
DOR%	-0.63
DFTR	-0.11

However, to say that these are the proper weights for each of these is to assume that each of these is just as controlled by the offense as the defense. Ken Pomeroy has been blogging on the subject and it got me thinking: there is no way that these can be the true (relative) PREDICTIVE values for four-factors.

I ran a LOOCV test for each 2010-11 NCAA team, for each game they played (for both teams).

In layman's terms: I looked at each game, then averaged all the four factors for the other games a team played.

The results look may only slightly different. The difference is, in fact, huge.

	predictive coef
OeFG%	1.27
OTO%	-1.71
OOR%	0.73
OFTM/FGA	0.17
DeFG%	-1.11
DTO%	0.99
DOR%	-0.62
DFTR	-0.19

The differences can be outlined here (x = predictive / raw) :

	x
OeFG%	96%
OTO%	144%
OOR%	116%
OFTM/FGA	103%
DeFG%	84%
DTO%	83%
DOR%	99%
DFTR	174%

This is now the basis for my ratings. The strength of schedule part is a bit of a guess, but the results are so different no matter what I do, I can't really tell if it's working :)

All this to say: Murray State is actually more overrated than we thought (#227 in offensive TO%, somehow).

Conference Bias in the Polls: No Mountain-West Love

"The Nation's Best Point Guard" apparently.

I did a very quick study on how conferences/teams are underrated or overrated in the polls.

First, I combined the ESPN and AP Polls from Monday.

Here's a simple formula based on regression to add the vote totals from both polls for NCAA basketball:

Total Adjusted Votes= AP votes + (2*ESPN Votes+26)

The top-27 in this method is shown left.

All teams worse than #27 were given a simple "#40" as a placeholder . I then compared each of these team's rankings to my own ranking system, which is very similar to Ken Pomeroy's...I can just fiddle with it as I please :). From this, it's pretty easy to see that teams that have won a lot of close games are overrated and vice versa (if you trust us stat-geeks on the principle of 'luck').

To convert Luck (Win% - Expected Win%) to ranking deviation (Poll rank - my rank), I found the following easy equation:
Expected Ranking Deviation = 140 * Luck% - 0.38

So for each conference, I found the average luck of my top 49 (I stopped at 49 because that's where Murray is ranked) and found the following. I split the rankings into three categories

-Murray State (the only OVC team here, and the most overrated team in the country)
-Conferences (with at least 2 listed teams in the poll)
-Other Conferences (the total of each of the conferences with one bid)
 

Like so:

	#	Top 40 Avg Luck
Murray State	1	0.138
A10	2	0.016
WCC	3	0.009
MVC	2	0.004
Other Mid-Majors	5	-0.002
BE	9	-0.002
MWC	2	-0.007
B12	6	-0.012
ACC	5	-0.014
P12	2	-0.033
B10	6	-0.040
SEC	4	-0.048

Then I used the Expected Ranking Deviation formula to come up with each 'conference's average expected ranking deviation:

	#	ExpRkDiff
Murray State	1	18.9
A10	2	1.9
WCC	3	0.9
MVC	2	0.1
Other Mid-Majors	5	-0.7
BE	9	-0.7
MWC	2	-1.4
B12	6	-2.0
ACC	5	-2.4
P12	2	-5.0
B10	6	-6.0
SEC	4	-7.1

Then I simply subtracted each team's Expected Ranking Difference from their Actual Ranking Difference to give us an estimate of conference bias. The results are pretty intuitive:

	#	Top 40 Luck	ExpRkDiff	ActualRkDiff	Bias
Murray State	1	0.138	18.9	33.0	14.1
B10	6	-0.040	-6.0	-2.0	4.0
BE	9	-0.002	-0.7	3.0	3.7
ACC	5	-0.014	-2.4	1.2	3.6
SEC	4	-0.048	-7.1	-7.0	0.1
WCC	3	0.009	0.9	-0.7	-1.6
MVC	2	0.004	0.1	-1.5	-1.6
B12	6	-0.012	-2.0	-4.3	-2.3
P12	2	-0.033	-5.0	-8.0	-3.0
Other Mid-Majors	5	-0.002	-0.7	-5.4	-4.7
A10	2	0.016	1.9	-6.5	-8.4
MWC	2	-0.007	-1.4	-12.0	-10.6

The only real surprise to my eyes is the Big 12 having a bias of -2.3. Murray State is overrated by their ridiculously easy schedule which they haven't beaten to a pulp. The only four other overrateds are the rest of the power conferences minus the Pac-12, who is still in "recovery mode."

The Journey of Jeremy Lin

Via InfographicWorld

Click image to enlarge

Source: Infographic World

How To Adjust Game Results for Garbage Time (NCAA)

UNC's Blue Steel scrubs. Photo 100% stolen from ESPN.com

There is a fairly straightforward, rule-of-thumb way that I have used in the past to adjust for "garbage time" - basically an effective way of smoothing out the end of games where:

a) the scrubs begin playing
b) teams try and make a comeback despite a mighty deficit...tons of free throw shooting that could skew the point margin in either team's favor
c) the winning team doesn't care about playing anymore, really...
d) etc

Bill James (of baseball stats fame) introduced his own simple metric that StatSheet.com uses, and succeeds rather invariably: Lead "Safeness." Bill James also refers to Coach K as "the human typo" in that article. I love him.





Anyways, the math is pretty straightforward (I remove the bit about who has the ball to make it easier to calculate, as it averages to zero):

     (Point Margin - 3)^2  /  Seconds Remaining = % Safe


So we do a little algebra, and we can quickly estimate point margin when the lead became 100% safe:

     Point Margin =Sqrt(seconds remaining when safe) + 3


Which we then use to forecast the rest of the game, ignoring how it actually played out:

     Adjusted Final Margin = [sqrt(Seconds Remaining when safe)+3] x 40 / [40-(Seconds Remaining when safe/60)]


You can easily find "seconds remaining when safe" via StatSheet.com. For example, last night's UNC-Wake Forest Game was "statistically over" with 3:48 left to go. Plus this in to my handy-dandy spreadsheet, and you get:

Point Margin When Safe: ~18
Adjusted Final Point Margin: 20

So while the Heels only won by 15, they had plenty of room to let the game slide in the final minutes - if they had played with the same quality all the way through they would have won by around 20.