Statistics: Frequency vs Possessions

After I posted Ray's piece I took a look at the SEC Hoops: The Good. The Bad. The Dirty. Blog to see what those guys were up to. They organized data for the entire South East Conference -- teams and players -- and begun to publish a series of "minutes per..." statistics for individual SEC players. For convenience I will call these frequency stats, they suggest "how frequently" a particular player will perform some action (an FGA, an FTA, a foul, a steal, etc.) to distinguish them from per capita (per game) stats -- how frequently will a particular player/team perform a particular act/task over the course of a game, and possession-based stats. Ironically, all are refinements, an end product of some process that begins with the same grist -- the raw data produced by individuals and teams when they play the game. The differences however extend beyond simply the computations and organization, to what they might suggest about a player (or his team) and ultimately to how they can be employed for analysis of personal and team performance.

Consider the compilations of Minutes per Field Goal Attempt Ray produced in his latest Guest Post for the 2008 Villanova squad. The players making up the regular rotation were listed from most frequent shooter (rising sophomore Corey Fisher) to least frequent shooter (rising junior Reggie Redding). I know (using no more than a calculator...or a good estimate) that if he played an entire game Corey Stokes would have taken about 13 FGAs while Reggie Redding would have taken about 8. By comparing Corey Fisher to Scottie Reynolds, I would know that Fish would most likely take the shot (by a small margin...), but that putting both on the floor together would generate a whopping 30.5 FGAs over the course of a 40 minute game. Consider that Villanova averaged (ahhh -- a per capita stat...) 57.5 FGAs per game, the two would have accounted for 53% of the Wildcat's FGAs. What can that tell us about a line up that put both Fish and Reynolds on the floor simultaneously? I have reproduced Ray's table below, but added a third column of the Shot%, a possession-based stat that calculates the probability that a particular player will take the shot.

Player	MpFGA	Shot%
Corey Fisher	2.46	27.5
Malcolm Grant	2.74	22.4
Scottie Reynolds	2.81	24.3
Corey Stokes	2.94	21.9
Casiem Drummond	3.39	20.5
Antonio Pena	3.68	18.8
Dwayne Anderson	4.40	16.0
Shane Clark	4.47	17.6
Dante Cunningham	4.77	17.3
Reggie Redding	5.13	13.3

Shot% and MpFGA do appear to "track", but there is not an exact correlation. If I add Fisher's and Reynold's Shot% I get 51.8, very close to the 40 minute, per capita calculation I did earlier. I can tell by looking at Shot% that a four guard lineup with Drummond in the middle would have been very problematic for the team (the sum of the Shot% for Fisher, Grant, Reynolds, Stokes and Drummond is 116.6 -- the team would have needed two basketballs to maintain everyone's shot rate. The relationship between MpFGA and Shot% is less obvious when I compared the Big East's Top 10 Scorers:

Rnk	Player	School	MpFGA	Shot%
1.	L. Harangody	Notre Dame	1.79	35.6
2.	S. Young	Pittsburgh	2.28	29.0
3.	D. Jones	South Florida	2.63	25.5
4.	B. Laing	Seton Hall	2.72	25.4
5.	D. Vaughn	Cincinnati	2.58	27.6
6.	J. Flynn	Syracuse	2.80	22.7
7.	K. Gransberry	South Florida	2.76	27.3
8.	D. Green	Syracuse	2.36	28.2
9.	D. Burns	DePaul	2.33	29.5
10.	A.J. Price	UConn	2.68	24.4

"Luke Harangody takes a lot of shots" was my first thought when I saw Ray's numbers, putting his MpFGA up against his Shot%, and I have a very good idea of how significant Harangody's role is with respect to Notre Dame's offense. His 35.6% by the way, earned Harangody a #6 ranking overall in D1 according to Pomeroy's Notre Dame Scouting Report. And "Luke Harangody takes a lot of shots relative to his teammates" was my first thought when I saw Harangody's Shot%. Each statistic (MpFGA and Shot%) suggest something about an individual player's tendency to hoist shots (attempt field goals), but MpFGA measures that tendency against time, while Shot% measures it against the other players on the court (at the time the player is shooting...). Which explains why any correlation between an individual's MpFGA and Shot% breaks down with respect to the players in the Top Ten list. How can Jonny Flynn and Kentrall Gransberry, shooting at about the same frequency (2.20 vs 2.76) have a nearly 5% "gap" in their respective Shot% (22.7 vs 27.3)? The answer is the number of possessions (and by implication, shots) the team each plays on typically gets in a game. South Florida had about 67 possessions per game (according to Pomeroy's South Florida Scout Page), while Syracuse (per Pomeroy) had nearly 73.

That each of the Top Ten Scorers should be very efficient offensively is a given (he would not have been allowed to function in the role without demonstrating efficient scoring...), and the table below (same as the one above, just added the player's eFG% & ORtg to the other numbers...):

Rnk	Player	School	MpFGA	Shot%	eFG%	ORtg
1.	L. Harangody	Notre Dame	1.79	35.6	57.1	114.9
2.	S. Young	Pittsburgh	2.28	29.0	54.7	110.1
3.	D. Jones	South Florida	2.63	25.5	53.9	112.2
4.	B. Laing	Seton Hall	2.72	25.4	49.4	106.6
5.	D. Vaughn	Cincinnati	2.58	27.6	55.5	109.5
6.	J. Flynn	Syracuse	2.80	22.7	52.6	112.9
7.	K. Gransberry	South Florida	2.76	27.3	52.8	102.6
8.	D. Green	Syracuse	2.36	28.2	50.5	105.4
9.	D. Burns	DePaul	2.33	29.5	48.6	107.6
10.	A.J. Price	UConn	2.68	24.4	50.8	114.4

Notice that while all of the players listed were indeed efficient shooters (eFG%s nearly 50.0 or better) but all also efficiently generated points for their respective teams (ORtgs > 100). It is no coincidence that all but one of the players who had ORtgs > 110 played on teams that played in a post season tournament (NIT/NCAA). When we look at those same numbers for last season's Wildcat squad what can we learn?

Player	MpFGA	Shot%	eFG%	ORtg
Corey Fisher	2.46	27.5	43.3	94.1
Malcolm Grant	2.74	22.4	53.4	113.2
Scottie Reynolds	2.81	24.3	51.1	105.6
Corey Stokes	2.94	21.9	47.5	101.8
Casiem Drummond	3.39	20.5	52.4	104.4
Antonio Pena	3.68	18.8	46.5	95.4
Dwayne Anderson	4.40	16.0	57.6	114.9
Shane Clark	4.47	17.6	48.3	111.1
Dante Cunningham	4.77	17.3	54.4	104.1
Reggie Redding	5.13	13.3	42.5	99.7

The keys to progress next season may well come down to improvements by the (then sophomores) Fisher, Stokes and Pena. Fisher will need better judgement on when to shoot (and cut back a bit...) and work on setting up teammates. Stokes and Pena will have to become better scorers. Each, along with Drummond, may not get as many opportunities to shoot, but they will have to score more efficiently when they have the ball.