How to determine the precise offensive value of each player to your team

This post outlines how to determine the exact offensive value of all 4,485 Division 1 players in the country and represent it with one concise “Value Add.” I believe it is the small final piece of the huge jigsaw puzzle built by four people much, much, much smarter than myself. I’ll start with the 10 most valuable offensive players in the country this year, and then go through how we know that is the case:

Rank	Name	Team	ORtg	Repl	In play	%Poss	%Min	Value add
1	Jordan Taylor	Wisconsin	126.9	91.9	1.38	27.4	90.6	9.46%
2	Kemba Walker	Connecticut	116.7	90.8	1.29	31.4	92.4	8.29%
3	Jimmer Fredette	Brigham Young	114.5	92.7	1.23	36.4	88.5	7.56%
4	Charles Jenkins	Hofstra	123.5	96.1	1.28	28.4	92.3	7.46%
5	Noah Dahlman	Wofford	130.2	97.3	1.34	27.2	76.6	7.05%
6	Reggie Jackson	Boston College	119.9	92.3	1.30	27.1	85.4	6.93%
7	Derrick Williams	Arizona	122.7	92.7	1.32	28.7	74.1	6.90%
8	Ben Hansbrough	Notre Dame	120.5	91.8	1.31	25.0	87.1	6.81%
9	Mickey McConnell	St. Mary's	129.1	95.9	1.35	21.3	92.1	6.80%
10	Jared Sullinger	Ohio St.	120.4	92.5	1.30	27.0	78.9	6.44%

This post is probably too detailed to be of interest to 95% of our readers, but I need it as a reference to refer back to in future posts to make it clear that is a precise scientific measurement of the value add of each player. I can’t decide to weight offensive rebounds a little more because I don’t like that a Wisconsin player was actually slightly more valuable than the next best three players, Kemba Walker, Kyrie Irving (7.80% in the 11 games he played, but drops due to injury) and Jimmer Fredette. The fact is Jordan Taylor’s presence this year meant Wisconsin scored 9.46% more points than they would have if he had not played.

History
In 1977, Bill James’ Baseball Abstract finally started to utilize stats to determine how good players are rather than just look at the top batting averages each Sunday. Then in 2003, Moneyball revealed how a GM (Oakland's Billy Beane) could beat opposing teams with four times the salary money and scouts if he simply knew how to weight players’ stats to make decisions. That same year, Dean Oliver’s Basketball on Paper revealed with astounding accuracy how stats could determine how many points basketball players and teams could produce, and Ken Pomeroy created www.kenpom.com to organize every shred of information on each player, with annual summaries now in the Basketball Prospectus.

For a basic understanding of how much value a player adds, you can read my easlier post:

Best Offensive Players in Big East

However, for simplicity sake I left out the more complicated parts of the calculation out of that post. The following are the actual steps you have to go through to know precisely how valuable a player is to your offense.

How many points does a player generate per offensive trip (ORtg)
Luckily Oliver and Pomeroy have done the hard work for us by weighing how often Kemba Walker helps the team by making a shot, drawing a foul, setting up a teammate with an assist, grabbing an offensive rebound, or how often he hurts the team by turning the ball over or missing a shot. Read Basketball On Paper for the in depth explanation of how we know UConn scores 116.7 points for every 100 possessions when Kemba is involved. That’s a very good total, but neither Kemba or Jimmer Fredette are in the Top 100 in the country based purely on ORtg because they play tired and have to create shots against double teams to hold down their ratio against some players who only shoot when open and get plenty of breathers.

Replacement vs. Defense
The fact is we don’t know how valuable Kemba was until we know how many points replacements would have scored if Kemba didn’t play this year. The “average” player going up against the “average” defense this year produced 101.3 points per 100 trips down the court. However, Kemba had to overcome much tougher defenses, as the average defense UConn faced allowed only 96.2 points per 100 trips, meaning UConn faced the 4th toughest defenses of the 345 Division 1 teams (only Michigan State, Georgetown and Penn State faced tougher defense).

Replacement Player
However, an “average” player does not replace a player when he doesn’t play. Teams typically have an 8-man rotation, so if a player didn’t play it would be the 9th or 10th best player on a roster that typically takes the player’s place, in combination with other players being less effective due to having to do more (more tired, more defensive attention). James first noted that “average” players have value because they are better than “replacement” players, and that many a championship has been lost for lack of an average player at a key position (e.g. how much better would Marquette have been with an average Big East Center to play with the Three Amigos).

Therefore to determine how many points a typical replacement player would have produced, the first step is to identify the average replacement player. To this end, I broke down every player in the country based purely on minutes and their level of conference. There are 345 teams, so I treated the 1725 players who averaged the most minutes as Starters (345 X 5), then the 1035 who played the next most as in the Rotation (typically 6th, 7th and 8th men), and finally any other player who played at least four minutes a game as a replacement (typically the 9th or 10th man who gets in the rotation when someone is out).

Level	Teams	Starters	Rotation	Replacement	Sweats
BCS	73	365	219	128	237
Mid-Major	96	480	288	178	302
Other D1	176	880	528	414	466
Total	345	1725	1035	720	1005

It was the 128 “Replacement” players for BCS teams that give us the typical player who would replace a player who did not play. After quite a bit of math, I determined that multiplying the average defensive rating a player faced by 0.9435, we get the exact figure of how the 128 BCS Replacement players would have done in our player’s shoes. Against the tough defense played against Kemba, a typical BCS Replacement player would have produced on 90.8 points per 100 trips down the court.

While these 128 BCS Replacement players are 9th or 10th men in the BCS, they are actually producing almost as many points as your average starter in a lower D1 conference (1.03) or as a player in the rotation for a Mid-Major school (1.02). An actual Replacement player for a lower D1 school only produces 89% of the points of a BCS Replacement player, but to keep everyone on the same basis, we will compare every player to what a BCS Replacement player would have done in his shoes:

Level	BCS	Mid-Major	Other D1
Starters	1.15	1.09	1.03
Rotation	1.07	1.02	0.94
Replacement	1.00	0.94	0.89

Percent better than a Replacement Player (% > Replace)
So when Kemba was involved in the play, UConn scored 29% more points than they would have if a Replacement Player had been involved instead, so we note that as 1.29 (116.7 / 90.8 = 1.29).

Take charge players (%Pos)
While the 1.29 figure is a precise measurement of the % of points Kemba adds when he is involved in the play, the next step is to measure how often he takes control vs. one of the four other players on the court having to make a play.

Note that Mickey McConnell of St. Mary’s was actually slightly more likely to produce points than even Kemba when he is involved in the play. However, McConnell is not the play maker that Kemba is. McConnell is only involved in the play 21.3% of St. Mary’s trips down the court – meaning teammates that aren’t as good have to make the play 78.7% of the time. Kemba can produce a play or set up a teammate many trips, meaning the play goes through him 31.4% of the time he is on the court and lesser teammates only have to make the play 68.6% of the time. The formula that shows the actual impact a player has while he is on the court then is:

(WheninPlay * %Pos) + (100 - %Pos) = OnCourtWith5AveragePlayers

Finally, %Min played
Kemba’s Offensive Rating would have been much higher if he could have rested more than an average of 3 minutes a game, but a very tired Kemba was still much more valuable than a fresh Donnell Beverly coming into take his place. So the additional minutes a player can stay on the floor and still add any value helps the team even though it lowers his ORtg.

Note that Noah Dahlman was as dominant a force as Kemba when he was on the court. He called for the ball and scrapped inside, hitting his typical 60% from the floor en route to a 21 point, 9 rebound game that almost knocked BYU out in the opening round.

However, Dahlman wasn’t quite as dominant as Kemba because as a 6-foot-6 inch center, he needed about 10 minutes of rest a game to maintain his very high level of play. Those extra 7 minutes a game Kemba gave UConn made him more valuable than Dahlman overall, and the formula that measures the final factor - % of minutes played, is as follows:

(((OnCourtWith5AveragePlayers – 100)*(%Min * 0.01))/100) = Value Add

The percentage that comes from this formula is the % of points a player has added to his team’s results over the course of the season. The formula does not distinguish between a player being injured vs. not player well enough to be on the court. For example, Kyrie Irving played 68.95% of Duke’s minutes in the 11 games he was healthy, and had a Value Add of 7.8% to Duke during those 11 games. That makes him one of only six players in the country with a Value Add of 7% or higher. However, because of the 26 games he was out with an injury, Irving only played 20.5% of Duke’s overall minutes, and therefore his actual value add for the season was 2.32%, good for 365th best of the 4,485 players.

Bell Curve of Talent
Looking at the breakdown of Value Adds, we see that we are looking at the end of the bell curve we see in almost all sports. There are always very few players who are much, much more valuable than average, then a little group that are much better, etc., until we get down to most players who are about average. As you can see, most Division 1 players (the 1489 plus the 997 in the last two categories) have a 0% because they do not add offensive points. Here is the number of players that fall into each Value Add range:

Players	% in range	Value Add Ranges and Notes
5	0.11%	7% or higher Value Add: 1 in 1000 add more than 7% to their team's total scoring
30	0.67%	5 to 7% Value Add: Fewer than 1% of all players can add >5% to team's scoring
173	3.86%	3 to 5% Value Add: Still in the top 5% of all players if you add 3%
753	16.79%	1 to 3% Value Add: Just over 1 in 5 players are in one of top categories
1038	23.14%	Some Value Add, but less than 1%: Another 23% add some scoring
1489	33.20%	0% Value Add: 33% do not help offense, but still play due to defensive ability,etc.
997	22.23%	0% Value Add, less than 4 min a game: 22% play fewer than 4 minutes a game

Precise vs. Potential/Good
Of course, we can only have precise measurements of how good a player was in the past, not his potential for future greatness. The two often correspond fairly closely since having great talent makes it more likely you produce great results. For example 20 of the top 30 players in Value Add this year are projected to go in the NBA Draft while obviously a great college player like Dahlman isn’t likely to play center in the NBA at 6-foot-6. I have to admit I didn’t know who Charles Jenkins of Hofstra was until the formula showed he was the 4th most valuable offensive player in the country this year, and then I looked and saw who is projected to be the 28th college player drafted.

There are others like Yancy Gates who is expected to be picked next year, but did not realize his potential last year as the 315th most valuable player in the country.

Defensive Value
Finally, keep in mind that this is a precise measurement of OFFENSIVE value add. The fact that Derrick Williams and Jared Sullinger are also dominant defensive players inside means they might have been the two most valuable overall players in the country (and they are projected to be the 2nd pick in the NBA draft this year and next respectively). We could add to the formula that Sullinger dominates the defensive glass by grabbing an incredible 26.2% of all opponents’ misses (Williams also great at 21.7%) and other defensive stats, but that would take us away from our precise measurement and start making the process subjective.

“You can’t measure everything!”
Of course, the counter argument is that there are still things that are not measured – the nice pick that helped a team, or throwing a pass to a guy 30 feet from the basket with one second on the shot clock so he gets blamed for the missed shot. This is true, however in the scope of things, these small factors are like saying, “you didn’t credit the player for getting hit by a pitch four times this year,” when in fact that was probably balanced out by a few times of hitting into a double play in the clutch.

The fact is that what Oliver laid out in 2003 has proven to be amazingly accurate every year, just like the Oakland As success on a tiny budget defied logic until author Michael Lewis wrote Moneyball and let Beane's secrets out so that the Yankees and Red Sox could start using the same statistics.