The One-Seeds
That was a pretty dumb thing to say
I picked the top few teams that I thought might make #1 seeds, and did some analysis from their stats from Kenpom.com.
Anyways, here's my #1 seed bracketology: http://spreadsheets.google.com/pub?key=tdf4HIaf_vWtQhoNCxjHLdQ&single=true&gid=0&output=html
Time Left on Shot Clock
I expect a high standard deviation of this number for most teams, but it is interesting to look at.
Here's the results (internet explorer might be required, hopefully not)
Adjusted Player Offensive Ratings
The results are here.
(EDIT: the Usage% represents how much a teams' possessions a player ends up 'using' via shots/turnovers/etc. players under 20% are below average in usage. I will soon adjust only those who are above the 20% mark)
Texas v. UNC
this gives us an average of 8.97 for both teams
-a 68.2% chance that Carolina's final margin is between {-11 and -29}
Nathan's Statistical Rankings
Hopefully in January I will have a model adjusted including diminishing returns, consistency, and 'game point margin' which accurately reflects the 'real score' of a game, rather than one that was altered in the last 30 seconds to a game-insignificant-degree. (To do this, we will use Bill James' "time statistically over" stat from Statsheet.com).
UNC's terrible 2nd halves
Oliver-Adjusted PlusMinus
Theoretically Correct RPI, Part I
WPct = .500 + A - B (http://www.diamond-mind.com/articles/playoff2002.htm) which means: Team's Win% = .5 + Real Win% - Opponents' Real Win%
Therefore, a team's "real" win% roughly equals:
Rwin%=Twin%-.5+(OTwin%-.5+O.OTwin%)
=Twin%+O.Twin%+O.OTwin%-1 This shows us that a teams' win%, opponents' win%, & opponents' opponents' win% are all roughly EQUALLY weighted in figuring out their 'real' value.
So a better simple RPI would be RPI= Team's Winning % + Opponents' Winning + Opponents' Opponents' Win% -1
In the next post, we will examine the 'normally-adjusted' version.
Fixing the current models...
Win%=????
Win%=NormsDist(Point Margin/Standard Deviation of Point Margin)
Chance of Win%=Normsdist(Predicted Point Margin/Standard Deviation of Actual Minus Predicted Point Margins of both Teams)
Fixing errors & improving accuracy
Here, I will lay out the foundations of my current, modified EMA (or Efficiency Margin Added).
This shows each player's increase in the points per possession his team scores on the floor.
First, I gotta define a few things:
ON = PlusMinus (+/-) while a player is on the court
OFF = PlusMinus (+/-) while a player is off the court
Net = The points a player scores, minus the points his man scores
Min%=percent of game a player plays in, or percent of minutes played
here are two basic estimations for how much one player helps his teammates (which I call TMA, or Teammate Margin Added). This is a factor based on their substitution, i.e. how many points a team stands to benefit by a player being in (how good they are on the court minus how good they are off the court).
TMA1=2 x (Teammates' Net While On Court - Teammates' Average Net)
^for this one, we estimate that they add just as much as they do on the court as their team loses when they are off the court
and
TMA2=Teammates' Net While On Court - (4/5 x OFF)
^i.e. their four teammates make up roughly 4/5 of the point margin while a player is off the court
So we get our estimated Teammate Margin Added (eTMA) by averaging these two estimates.
now, we need to find out what a players' Net is, adjusted for how good his teammates are (adjusted Net, or aNet)
aNet=Net-(1/4) x (All Teammates' Total eTMA)x Min%
The 1/4 multiplier is because each player helps a sum total of four teammates while on the court.
Then, a players' overall Point Margin Added (PMA) simply adds our two estimates:
PMA=eTMA+aNet
and per possession, we calculate EMA as
EMA=PMA/(Team Possessions Played x Min%)
Top 25 NBA Players
Nathan's Most Efficient Basketball Players | |||||
THA/48=Teammate Help Added Every 48 Minutes Played | |||||
PHA/48=Personal Help Added Every 48 Minutes Played | |||||
Player # | Player | THA/48 | PHA/48 | THA+PHA/48 | |
1 | MIA | Wade | 1.49 | 23.19 | 24.68 |
2 | CLE | James | 2.00 | 22.59 | 24.59 |
3 | BOS | Garnett | 1.36 | 20.76 | 22.13 |
4 | NOH | Paul | 3.98 | 12.85 | 16.83 |
5 | PHO | Nash | 1.95 | 14.33 | 16.28 |
6 | UTA | Kirilenko | -1.26 | 16.25 | 14.99 |
7 | LAL | Odom | 8.55 | 4.81 | 13.36 |
8 | PHO | Stoudemire | -5.81 | 18.53 | 12.72 |
9 | PHO | O'Neal | -2.88 | 15.10 | 12.22 |
10 | HOU | Yao | 2.48 | 9.19 | 11.67 |
11 | CHI | Gordon | 0.59 | 10.97 | 11.56 |
12 | ORL | Howard | -2.23 | 13.58 | 11.36 |
13 | CLE | Ilgauskas | 6.98 | 3.80 | 10.78 |
14 | PHO | Hill | 2.52 | 8.22 | 10.74 |
15 | DET | Hamilton | -2.79 | 13.48 | 10.69 |
16 | LAL | Bryant | 0.21 | 9.99 | 10.21 |
17 | DET | Wallace | 6.69 | 3.25 | 9.95 |
18 | BOS | R.Allen | 1.99 | 6.98 | 8.97 |
19 | CHI | Noah | 5.34 | 3.58 | 8.92 |
20 | LAL | Bynum | -1.07 | 9.66 | 8.59 |
21 | POR | Roy | 0.33 | 8.14 | 8.47 |
22 | IND | Granger | -1.82 | 10.29 | 8.47 |
23 | UTA | Millsap | 2.49 | 5.69 | 8.19 |
24 | PHI | Iguodala | 4.90 | 3.19 | 8.09 |
25 | MIL | Sessions | -4.55 | 12.38 | 7.83 |
FM=Final Margin (of your team)
Net=points scored - points scored by your man
Min%=percent of minutes played
+/-=PlusMinus=point margin change while you're on the floor
OFF=point margin change while you're off the floor
2 categories:
1) Teammate Help Added=THA
THA=(1-Min%)x(FM-Net)-(4/5)x(OFF)
TS THA=Team Sum THA=Combined THA of entire team
2) Personal Help Added=PHA
PHA=Net-(TS THA-THA)*Min%
SHA=Sum Help Added=THA+PHA
SHAPP=Sum Help Added Per Possession=(THA+PHA)/(Team Possessions Played x Minute%)
GameAdjusted SHAPP=SHAPP-(Team Efficiency Margin/5)
Player's Efficiency Margin, Explained
How it works:
Edit: BUT ALAS, there is one problem with this formula. As a players' minute% reach 100%, the only value that comes into question is their Net Points (that is to say, their intangibles become zero). So our BEST GUESS for how much a player helps a team that also plays every minute of the game is simply their Actual Plus/Minus (PMa). So our best guess is a weight between the prior formula and their amount of minutes played:
Best NBA players
here tis:
http://dl.getdropbox.com/u/241759/nbastuff.html
Using the Four Factors (and Pace and FT%) to Estimate Point Margin/Efficiency Margin!
Here's a quick primer of definitions:
Poss=Possessions
eFG%=Effective Field Goal Percentage
(FG%=Field Goal Percent)
OR%=Offensive Rebound percentage
TO%=Turnover percent
The first thing we need to find is Free Throws Attempted! We can estimate it thusly:
From this we can get:
FGA=FTA/FTR
After doing this for both teams, you can predict a point margin (or estimate one from a previous game).
To find the efficiency of a team, simply divide the final score by possessions played!
No seriously, check it out:
Premises:
1) Possession change (the calculation for total possessions) can only happen in the following ways: when a team gets a defensive rebound, when the ball is turned over, when the ball goes in the hoop. Also, we estimate that .475 percent of the time a free throw is attempted, a possession ends.
2) We can represent Field Goal Attempt possession changes in the following way: FGA*(FG%+(1-FG%)*(1-OR%))
That is to say, when you make a shot (FG% means when the ball goes in) and when you miss it (1-FG%) and don't get an offensive rebound, (1-OR%) the other team gets the ball next.
Possessions=FGA*(FG%+(1-FG%)*(1-OR%))+.475*FTA+TO
4) Unfortunately, the four factors do not offer us FG%, but a close number, eFG%, so we can turn the formula into this:
This gives us:
Possessions=FTA/FTR*(eFG%+(1-eFG%)*(1-OR%))+.475*FTA+(TO%*Poss)
6) Factor it and use algebra!
(Possessions-(TO%*Poss))/((1/FTR)*(eFG%+(1-eFG%)*(1-OR%))+.475)=FTA
For me, it helps us predict the final score MORE accurately. Kenpom only keeps adjusted stats for offensive and defensive efficiencies....however, this might not be a very accurate representation of how a team works. For example, if one team REALLY relies on not fouling teams (like Uconn did this season) to make up for a stinky factor (like Uconn did with not forcing turnovers), they are more likely to fare poorly against good teams that are good at drawing fouls (like Georgetown, Syracuse, and Michigan St.).
And so we move forward!
Fixing Kenpom.....
1) that Memphis' best defenses (and Gonzaga's best offenses) came from absolutely crushing terrible teams. Beating Poop St. by 9000 or my Cat by 2390209 isn't exactly an important stat, kenpom.
My prediction
Carolina by 7
74 possessions,
| EFG % | TO% | OR% | FTR |
north carolina | 50.94 | 17.07 | 32.37 | 42.68 |
michigan st. | 48.26 | 20.69 | 37.03 | 32.48 |
North Carolina - 77% from FT
Michigan St - 71% from FT
In order for Michigan State to win (by two)
| EFG % | TO% | OR% | FTR |
north carolina | 48.9 | 17.75 | 31.08 | 40.97 |
michigan st. | 50.19 | 19.86 | 38.51 | 33.78 |
Michigan St. - 71% from FT
The Probability of Having a Good Run
(((1-to%)*(1-nofga%)*FG%+(1-to%)*(1-nofga%)*(1-fg%)*or%fg%)*2*eFG%/100)^3
Not predicting the unpredictable.
Consistency shows how often a team plays as expected. More accurately, you might call it how well Ken Pomeroy's stats (adjusted by me) can predict a team.
(16 and 15 seeds not included)
| team | standard deviation from expected point margin |
1 | cornell | 12.96 |
2 | western kentucky | 12.59 |
3 | louisville | 12.55 |
4 | michigan st. | 12.41 |
5 | north carolina | 12.31 |
6 | louisiana st. | 12.14 |
7 | arizona st. | 12.11 |
8 | west virginia | 11.94 |
9 | clemson | 11.74 |
10 | marquette | 11.56 |
11 | gonzaga | 11.55 |
12 | tennessee | 11.35 |
13 | kansas | 11.28 |
14 | akron | 11.27 |
15 | maryland | 10.98 |
16 | wake forest | 10.74 |
17 | michigan | 10.73 |
18 | missouri | 10.63 |
19 | northern iowa | 10.34 |
20 | boston college | 10.28 |
21 | syracuse | 10.26 |
22 | brigham young | 10.22 |
23 | mississippi st. | 10.18 |
24 | UCLA | 10.17 |
25 | illinois | 10.08 |
Some things to note.
Info on The Bracket-Maker
The day has come!
Five bucks!
Ok, now here's the picture you need to see:
Oh my goodness....
• Big Ten (7): Michigan State, Illinois, Purdue, Wisconsin, Minnesota, Michigan, Ohio State
• Big East (6): Pittsburgh, Connecticut, Villanova, Syracuse, Marquette, West Virginia
• ACC (6): North Carolina, Duke, Wake Forest, Clemson, Florida State, Boston College
And Penn State is only four teams off the bubble.
The Big Ten qualifiers just have a ton of losses and some random wins against BETTER teams (UCLA, Duke, Louisville).
Overrated/Underrated, continued.
wahoo!
Weighted Goodness
LAZY
Top 10 Kenpom Teams, Sorted by Laziness | ||
(Correlation and slope of Actual-Expected Defensive efficiency and Actual-Expected Offensive efficiency) | ||
(higher is lazier) | ||
Provable Laziness Factor (slope x R value) | ||
1 | Pittsburgh | 0.39 |
2 | Connecticut | 0.17 |
3 | Memphis | 0.12 |
4 | Duke | 0.11 |
5 | UCLA | 0.1 |
6 | Kansas | 0.02 |
7 | West Virginia | 0.02 |
8 | North Carolina | 0.01 |
9 | Gonzaga | 0 |
10 | Louisville | 0 |