2015 NFL Statistics by Player and Team

I have downloaded stats for the recently completed 2015 NFL regular season from yahoo.com, cleaned the data, and saved the data in CSV format. The files are located here. If you prefer a github repository, check here. The column headers should be self-explanatory.

You will find seven CSV files, which you can open in Excel or Google Sheets:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. I have broken out attempted and made field goals by distance into separate columns for convenience.
• DEF: defensive stats by team.
• ST: special teams stats by team.

Enjoy!

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2014 NFL Statistics by Player and Team in Excel

I have downloaded stats for the recently completed 2014 NFL regular season from yahoo.com, cleaned the data, and saved in Excel and CSV formats. The files are located here. The column headers should be self-explanatory.

The Excel workbook has seven worksheets:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. I have broken out attempted and made field goals by distance into separate columns for convenience.
• DEF: defensive stats by team.
• ST: special teams stats by team.

The same folder also has separate CSV files for each position, which may be more helpful if you are a coder.

Fantasy Football Ratings 2014

I have prepared fantasy football ratings for the 2014 NFL season based on the data from last year’s season. I hope you will find them useful! You can download the ratings here.

These ratings are reasonable but flawed. The strengths of the ratings are:

• They are based on player performance from the 2013 season, using a somewhat standard fantasy scoring system. (6 points for touchdowns, -2 for turnovers, 1 point per 25 passing yards, 1 point per 10 passing yards, and reasonable scoring for kickers.)
• The ratings are comparable across positions because the rating means the expected number of fantasy points that a player will score compared to a “replacement level” player for that position. I call this “Fantasy Points Over Replacement”: FPOR.
• Touchdowns are a key contributor fantasy performance, but they are fickle: they often vary dramatically between players of the same overall skill level, and even between seasons for the same player. In a previous post I showed that passing and rushing touchdowns are lognormally distributed against the yards per attempt. I have accounted for this phenomenon in the rankings. Loosely speaking, this means that a player that scored an unexpectedly high number of touchdowns on 2013 will be projected to score fewer in 2014.
• The ratings do a rough correction for minor injuries. Players that play in 10 or more games in a season are rated according to the number of points they score per game. Therefore a player who missed, say, two games in 2013 due to injury is not disadvantaged compared to one that did not.

There are several weaknesses:

• I have data for several previous seasons but do not use it. This would stabilize the ratings, and we could probably account for maturation / aging of players from season-to-season.
• Rookies are not rated.
• We do not account for team changes. This factor is often very important as a backup for one team may end up as a starter for another, dramatically affecting fantasy performance. (I actually have a pretty good heuristic for accounting for this, but I have not implemented it in Python…only SAS and I no longer have access to a SAS license.)
• Players who missed a large portion of the 2013 season are essentially penalized for 2014, even if they are expected to return fully.
• I have not rated defense/special teams.

You may want to adjust the rankings accordingly. Here are the top 25 rated players (again, the full ratings are here):

Name	Position	RawPts	AdjPts	FPOR
LeSean McCoy	RB	278.6	199.3125	85.96875
Jamaal Charles	RB	308	194	80.65625
Josh Gordon	WR	218.6	176.3571429	71.57142857
Matt Forte	RB	261.3	177.46875	64.125
Calvin Johnson	WR	219.2	157.7142857	52.92857143
DeMarco Murray	RB	205.1	155.4642857	42.12053571
Reggie Bush	RB	185.2	153.4285714	40.08482143
Jimmy Graham	TE	217.5	113.90625	35.90625
Antonio Brown	WR	197.9	140.53125	35.74553571
Knowshon Moreno	RB	236.6	148.6875	35.34375
Adrian Peterson	RB	203.7	147.5357143	34.19196429
Marshawn Lynch	RB	239.3	145.59375	32.25
Le’Veon Bell	RB	171.9	142.9615385	29.61778846
Demaryius Thomas	WR	227	134.0625	29.27678571
A.J. Green	WR	208.6	133.6875	28.90178571
Eddie Lacy	RB	207.5	141.5	28.15625
Andre Johnson	WR	170.7	131.90625	27.12053571
Alshon Jeffery	WR	182.1	131.34375	26.55803571
Peyton Manning	QB	519.98	172.48125	22.18125
Stephen Gostkowski	K	176	176	22
Drew Brees	QB	435.68	172.2	21.9
Ryan Mathews	RB	184.4	133.5	20.15625
DeSean Jackson	WR	187.2	124.875	20.08928571
Pierre Garcon	WR	162.6	124.3125	19.52678571
Jordy Nelson	WR	179.4	123.1875	18.40178571

FPOR is the adjusted, cross-position score described earlier. RawPts is simply 2013 fantasy points. AdjPts are the points once touchdowns have been “corrected” and injuries accounted for.

We will see how the ratings work out! If I have time I will post a retrospective once the season is done.

2013 NFL Statistics by Player and Team in Excel

I have downloaded stats for the recently completed 2013 NFL regular season from yahoo.com, cleaned the data, and saved in Excel format. The files are located here. The column headers should be self-explanatory.

There are seven worksheets:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. For the yardage columns, the portion before the dash indicates FG made, the portion after attempted. So 4-5 means 4 made out of 5 from the distance range.
• DEF: defensive stats by team.
• ST: special teams stats by team.

The same folder also contains CSV files broken out for each position.

NFL Fantasy Football Statistics in CSV Format

You can find commonly used stats for NFL players in CSV format for the 2010, 2011, 2012 NFL seasons at this location.

For each season there are seven files:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. Attempts and made field goals are broken out by distance in separate columns.
• Def: defensive stats by team.
• ST: special teams stats by team.

Updated 8/21/2013: Added the 2010 season.

2012 Fantasy Football Prediction Model: Retrospective

Several months ago I laid out a simple model for forecasting fantasy football performance. My post included a table ranking players by value for draft purposes. Appropriately, in our league at Nielsen I used my own model to draft (selecting Ray Rice in the first round, followed by Victor Cruz and Wes Welker). I screwed up in a later round and accidentally selected Jason Whiten instead of Matt Ryan – but other than that I strictly followed the advice of my blog: always choose the highest ranked player from positions that needed to be filled.

So how did I do? Well, I finished third out of twelve – not bad. Let’s take a retrospective look at my model to see how accurately I predicted the 2012 fantasy football season.

My previous post provides actual 2012 statistics for all positions. I scored each player and compared to my projections. Note that my projections did not include players who did not participate in the 2011 season (e.g. Jamaal Charles) or rookies (e.g. RG III), so they are not included in the analysis. If I regard the difference between actual and projected fantasy points as “error”, then I can compute R^2 to summarize fit. I computed R^2 for two projections:

• Project 2012 points as equal to 2011 points (“2011” in the table below)
• Project 2012 points by adjusting 2011 points as described in my post (“Model”)

The results are as follows:

Pos	N	2011	Model
DEF	29	0.899414	0.899414
K	26	0.961511	0.961511
QB	31	0.909683	0.887465
RB	101	0.774406	0.797133
TE	78	0.81725	0.824893
WR	124	0.806109	0.810808

The overall R^2 for the model is around 0.852. I didn’t really dig into the details too much, but I think we can reasonably conclude that:

• Kickers and Defense are pretty darn stable (probably because they largely depend on the strength of the team and opposition, which does not generally massively change between seasons).
• RB performance was the hardest to predict.
• The model worked in the sense that most positions ended up with better R^2 than if I had simply used 2011 numbers.
• The exception is for the QB position, which perhaps implies that my assumptions about touchdown production do not apply to the QB position.

In the table below I compare the points per game projected by the model (Projected) with the actual number of fantasy points in 2012 (Actual) and the relative error. I highlight a row green when the relative error is less than 10%. If it is less than 25% it is yellow, and red otherwise.

Name	Pos	Projected	Actual	Rel. Err.
Drew Brees	QB	20.65682	21.59875	0.043611
Aaron Rodgers	QB	22.32247	21.35625	0.045243
Tom Brady	QB	20.06681	21.2675	0.056456
Cam Newton	QB	19.92028	20.17875	0.012809
Adrian Peterson	RB	13.7407	19.0875	0.280121
Matt Ryan	QB	15.70105	19.05375	0.17596
Tony Romo	QB	15.42652	17.18875	0.102522
Matthew Stafford	QB	18.70318	17.08	0.095034
Ben Roethlisberger	QB	14.58558	17.06154	0.145119
Arian Foster	RB	18.69446	16.38125	0.141211
Andy Dalton	QB	12.47327	15.6725	0.20413
Marshawn Lynch	RB	13.48645	15.4125	0.124967
Josh Freeman	QB	14.20246	15.40625	0.078137
Michael Vick	QB	21.37533	15.168	0.409239
Carson Palmer	QB	20.68852	14.688	0.408532
Eli Manning	QB	16.32711	14.5575	0.12156
Joe Flacco	QB	12.35432	14.555	0.151198
Kevin Kolb	QB	11.33343	14.12667	0.197728
Matt Schaub	QB	22.60787	13.96375	0.61904
Sam Bradford	QB	16.83711	13.92375	0.209236
Ray Rice	RB	17.53886	13.88125	0.263493
Calvin Johnson	WR	15.14139	13.775	0.099193
Brandon Marshall	WR	9.919735	13.55	0.267916
Ryan Fitzpatrick	QB	13.05769	13.35625	0.022354
C.J. Spiller	RB	7.19662	13.26875	0.457626
Philip Rivers	QB	14.7622	13.015	0.134245
Dez Bryant	WR	9.147546	13.0125	0.297019
Rob Gronkowski	TE	13.32919	13	0.025322
Stevan Ridley	RB	3.349849	12.4625	0.731206
A.J. Green	WR	9.735794	12.4375	0.217223
Demaryius Thomas	WR	6.994023	12.3375	0.433109
Jay Cutler	QB	20.61836	12.308	0.6752
Frank Gore	RB	10.8703	12.3	0.116236
Alex Smith	QB	12.57711	12.268	0.025197
LeSean McCoy	RB	16.10583	12.10833	0.330144
Christian Ponder	QB	14.64461	12.04375	0.215951
Jake Locker	QB	9.065129	12.01273	0.245373
Chicago Bears	DE	8.4375	11.875	0.289474
Matt Forte	RB	14.61648	11.82667	0.235892

2012 NFL Statistics by player and Team in CSV format

I have downloaded stats for the recently completed 2012 NFL regular season from yahoo.com, cleaned the data, and saved in CSV format. The files are located here. The column headers should be self-explanatory.

There are seven files:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. For the yardage columns, the first entry indicates FG made, the second attempted. So 4-5 means 4 made out of 5 from the distance range.
• Def: defensive stats by team.
• ST: special teams stats by team.

I have also provided a spreadsheet that combines all of the above.

Touchdowns are lognormally distributed

…well, not exactly. But it’s snappier if I put it that way.

What I really mean is: the number of pass attempts (or receptions, or carries) per touchdown is lognormally distributed, and that fact can be used to produce more stable fantasy football forecasts.

Click here to download the SAS source [estimate2.sas]

In my last two posts, I laid out simple fantasy football forecasting engines in SAS and R. An important component of a fantasy football score is the number of touchdowns scored by each player. Touchdowns can vary considerably among players with otherwise similar performance. For example, let’s look at the top three running backs from my previous post:

Name	Rush	Rush_Yds	Rush_Avg	Rush_TD	FFPts
Ray Rice	291	1364	4.7	12	292.8
LeSean McCoy	273	1309	4.8	17	280.4
Maurice Jones-Drew	343	1606	4.7	8	262

LeSean McCoy scored more than twice as many touchdowns as Maurice Jones-Drew. He scored several more than Ray Rice, but otherwise have very similar stats. The gut instinct that drives this post is that I don’t think LeSean McCoy is not going to score that many touchdowns this year!

How can I analyze touchdowns? I could simply draw a histogram of touchdowns per player, but that wouldn’t be very insightful. Players who get the ball more are more likely to score more touchdowns. So let’s control for that by dividing by the number of rushing attempts each player makes: let’s chart the touchdown rate. The histogram of rushing attempts per touchdown for the top 60 running backs in my 2011 dataset is interesting:

To my eye, it looks lognormally distributed. It’s not perfect, but it looks like a very reasonable approximation. A lognormal distribution makes sense – we expect that the distribution would be “heavy tailed” because going towards the left (1 touchdown per rush) is much harder than going to the right. Nobody scores every time they get the ball. Here is the SAS code that produces the histogram and the best fitting lognormal distribution. (I’m not doing this in R because I don’t know how to fit distributions in that environment. I am sure it is easy to do.)

** Plot a histogram, and save the lognormal distribution parameters. **;
proc univariate data=rb(obs=60) noprint;
  var Rush_Per_TD;
  histogram / lognormal nendpoints=15 cfill=blue outhistogram=rb_hist;
  ods output ParameterEstimates=rb_fit;
run;

The options for the “histogram” statement specify the distribution type, chart style, and an output dataset for the bins (which I then copied over to the free Excel 2013 preview to make a less-crappy looking chart). The “ods output” statement is a fancy way to save the lognormal parameters into a dataset for later use.

I can understand why there is a wide variation of values. Off the top of my head:

• Skill of the RB.
• Skill of the offensive line that blocks for the RB.
• How often the player gets carries near the goalline.
• Some teams call more red zone rush plays than others.
• Quality of opposition.
• Luck.
• Stuff like this. (This moment still burns…)

With these reasons in mind, I certainly don’t expect that all RBs will end up with the same rush/TD ratio in the long run. However, I think that it is likely that players on the ends of the distribution (either way) in 2011 are likely to be closer to the middle in 2012. Here’s what we can do: compute the conditional distribution function (cdf) for the fitted lognormal distribution for each player’s rush/TD ratio. This is a number between 0 and 1 that indicates “how extreme” the player is – 0 means all the way on the left. For example, LeSean McCoy is 0.0553 and is Maurice Jones- Drew is 0.5208. This means that LeSean McCoy is an outlier (close to 0), and MJD is not (close to 1/2).

To project next year’s ratio, I take a weighted average of the player’s binomial CDF and the middle of the distribution (0.5). I somewhat arbitrarily chose to take 2/3 times the CDF and add 1/3 times 0.5. This means that while I believe that players will regress to the mean somewhat, that I do believe that there are significant structural differences between players that will persevere from one season to the next.

Once I have the projected rush/TD figures, I can multiply by rushes and get a projected 2012 TD figure that I can use in fantasy scoring. If I take the rather large leap that touchdowns for all positions behave in this way, I can write a generic “normalizing” function that I can use for touchdowns at all positions.

** Recalibrate a variable with the assumption that it is lognormally distributed.   **;
** -- position: a dataset with player information. It should have a variable called **;
**              CalibrateVar.                                                       **;
** -- obscount: the number of observations to use for analysis.                     **;
** -- CalibrateVar: the variable under analysis.                                    **;
** The macro will create a new variable ending in _1 with the calibrated values.    **;
%macro Recalibrate(position, obscount, CalibrateVar);
  ** Sort the data by the initial score computed in my first post. **;
  proc sort data=&position;
    by descending FFPts0;
  run;

  ** Plot a histogram, and save the lognormal distribution parameters. **;
  proc univariate data=&position(obs=&obscount) noprint;
    var &CalibrateVar;
    histogram / lognormal nendpoints=15 cfill=blue outhistogram=&position._hist;
    ods output ParameterEstimates=&position._fit;
  run;

  ** Get the lognormal parameters into macro variables so I can use them for computation. **;
  data _null_;
    set &position._fit;
    if Parameter = 'Scale' then call symput('Scale', Estimate);
    if Parameter = 'Shape' then call symput('Shape', Estimate);
  run;

  ** Compute the projected values for each player using the distribution. **;
  data &position;
    set &position;
    LogNormCdf = cdf('LOGNORMAL', &CalibrateVar, &Scale, &Shape);
    &CalibrateVar._1 = quantile('LOGNORMAL', 0.67 * LogNormCdf + 0.33 * 0.5, &Scale, &Shape);
  run;

%mend;

A call to this macro looks like this:

%Recalibrate(rb, 60, Rush_Per_TD);

After this call I will have a variable called Rush_Per_TD1 in my rb dataset.

I have modified the forecasting engine to recalibrate touchdowns for all positions – see estimate2.sas. You can see below how the rankings change when I recalibrate: here are the top 20 running backs. Players in green moved up in the ratings after recalibration; players in red moved down. Unsurprisingly, LeSean McCoy moved down.

Pos	Name	Team	G	Rush	Rush_Yds	Rush_YG	Rush_Avg	Rush_TD	Rec	Rec_Yds	Rec_YG	Rec_Avg	Rec_Lng	YAC	Rec_1stD	Rec_TD	Fum	FumL	Rush_Per_TD	Rec_Per_TD	FFPts0	LogNormCdf	Rec_Per_TD_1	Rush_Per_TD_1	Rush_TD_1	Rec_TD_1	FFPts	FFPtsN	Rank New	Rank Old
RB	Ray Rice	BAL	16	291	1364	85.3	4.7	12	76	704	44	9.3	52	9.2	30	3	2	2	24.25	25.33333	292.8	0.183094	23.80672	29.76091	9.777928	3.192375	280.62182	158.7998	1	1
RB	Maurice Jones-Drew	JAC	16	343	1606	100.4	4.7	8	43	374	23.4	8.7	48	9.8	18	3	6	1	42.88	14.33333	262	0.520781	16.43331	42.43739	8.082496	2.616637	260.1947976	138.3728	2	3
RB	Arian Foster	HOU	13	278	1224	94.2	4.4	10	53	617	47.5	11.6	78	12.1	19	2	5	3	27.80	26.5	250.1	0.249994	24.51103	32.10521	8.65903	2.162292	243.0279329	121.2059	3	4
RB	LeSean McCoy	PHI	15	273	1309	87.3	4.8	17	48	315	21	6.6	26	8.8	18	3	1	1	16.06	16	280.4	0.05537	17.57991	25.27579	10.80085	2.730389	241.587431	119.7654	4	2
RB	Michael Turner	ATL	16	301	1340	83.8	4.5	11	17	168	10.5	9.9	32	8.8	8	0	3	2	27.36		212.8	0.241639		31.81053	9.462275	0	203.5736476	81.75161	5	6
RB	Marshawn Lynch	SEA	15	285	1204	80.3	4.2	12	28	212	14.1	7.6	26	8.1	8	1	3	2	23.75	28	215.6	0.173974	25.38375	29.44301	9.679716	1.103068	202.2967045	80.47466	6	5
RB	Steven Jackson	STL	15	260	1145	76.3	4.4	5	42	333	22.2	7.9	50	7.6	17	1	2	1	52.00	42	181.8	0.646438	31.61723	48.20039	5.394148	1.32839	186.1352231	64.31318	7	11
RB	Ryan Mathews	SDG	14	222	1091	77.9	4.9	6	50	455	32.5	9.1	42	9.3	18	0	5	2	37.00		186.6	0.422678		38.45808	5.77252	0	185.2351183	63.41308	8	8
RB	Michael Bush	OAK	16	256	977	61.1	3.8	7	37	418	26.1	11.3	55	9.4	14	1	1	1	36.57	37	185.5	0.415045	29.7855	38.16249	6.708157	1.242215	185.2022349	63.38019	9	9
RB	Darren Sproles	NOR	16	87	603	37.7	6.9	2	86	710	44.4	8.3	39	8.4	35	7	0	0	43.50	12.28571	185.3	0.530443	15.07624	42.85039	2.03032	5.70434	177.7079564	55.88591	10	10
RB	Reggie Bush	MIA	15	216	1086	72.4	5	6	43	296	19.7	6.9	34	7.6	12	1	4	2	36.00	43	176.2	0.404778	31.93509	37.76765	5.719181	1.346481	176.5939721	54.77193	11	13
RB	Matt Forte	CHI	12	203	997	83.1	4.9	3	52	490	40.8	9.4	56	8.8	19	1	2	2	67.67	52	168.7	0.793148	34.17389	56.47246	3.594673	1.521629	175.397812	53.57577	12	15
RB	Frank Gore	SFO	16	282	1211	75.7	4.3	8	17	114	7.1	6.7	13	6.1	5	0	2	2	35.25		176.5	0.391156		37.24835	7.570805	0	173.92483	52.10279	13	12
RB	Chris Johnson	TEN	16	262	1047	65.4	4	4	57	418	26.1	7.3	34	6.8	13	0	3	1	65.50		168.5	0.777213		55.46099	4.724041	0	172.8442456	51.0222	14	16
RB	Fred Jackson	BUF	10	170	934	93.4	5.5	6	39	442	44.2	11.3	49	12.8	13	0	2	2	28.33		169.6	0.26023		32.4672	5.236054	0	165.0163236	43.19428	15	14
RB	Adrian Peterson	MIN	12	208	970	80.8	4.7	12	18	139	11.6	7.7	22	7	5	1	1	0	17.33	18	188.9	0.071217	18.96808	25.84139	8.049102	0.948963	164.8883862	43.06634	16	7
RB	Shonn Greene	NYJ	16	253	1054	65.9	4.2	6	30	211	13.2	7	36	7.2	6	0	1	0	42.17		162.5	0.509643		41.96655	6.02861	0	162.6716623	40.84962	17	18
RB	Beanie Wells	ARI	14	245	1047	74.8	4.3	10	10	52	3.7	5.2	10	2.2	1	0	4	2	24.50		165.9	0.187692		29.92123	8.188167	0	155.0290026	33.20696	18	17
RB	Willis McGahee	DEN	15	249	1199	79.9	4.8	4	12	51	3.4	4.3	12	3.9	2	1	4	3	62.25	12	149	0.750944	14.89466	53.86313	4.622828	0.805658	151.5709151	29.74887	19	22
RB	Rashard Mendenhall	PIT	15	228	928	61.9	4.1	9	18	154	10.3	8.6	35	9.3	5	0	1	1	25.33		160.2	0.203174		30.46166	7.48482	0	151.1089178	29.28688	20	19

I actually used this as draft guidance (I selected Ray Rice with my first pick in a recent draft). Let’s see if it holds water!

Fantasy Football Player Forecasting in R

I rewrote my previous post in R, mainly because Paul Rubin mentioned the fact that SAS costs too much on Twitter:

Click here to download the R source [estimate.r]

The R code is a bit shorter (120 lines instead of 157), but they are basically the same complexity. I am following exactly the same logic as last time so I won’t go into the football part of it. I will simply highlight a couple of things about the code.

I rely on read.csv to read each input file into a data frame. Once I have a data frame, the primary operation is to “score” the position. Here is the code to score the running back position. The “within” statement makes it easy.

score.rb <- function(rb) {
  rb <- within(rb, {
    FFPts <- (Rush.TD + Rec.TD) * PtsTD + FumL * PtsFum + Rush.Yds / RushYdsPt + Rec.Yds / RecYdsPt
  })
  return(rb)
}

Remember from the last post that the next thing I do is to “normalize” the scores by subtracting the score of the projected worst starter on each team. This means sorting the players by score and picking one in a particular slot. Here’s how that works:

normalize <- function(p, count) {
  FFPtsMin <- as.numeric(p[with(p, order(-as.numeric(FFPts))), ][count,"FFPts"])
  p$FFPtsN <- apply(p,1,function(row) (as.numeric(row["FFPts"]) - FFPtsMin))
  return(p)
}

So by calling score.rb and normalize in sequence, I get final scores for the RB position. Once I score all of the positions, I simply need to join the data frames for each position together into a final data frame (called “players”). I write this out to CSV. I have saved the complete rankings so you can see the results.

Click here to download player ratings [NFL 2011 Ratings.csv]

It was a lot easier for me to write this code in SAS because it’s much more familiar to me. Even taking my prejudice into account, for this task I prefer SAS to R because the use of DATA steps leads to very simple, easy to understand code. R has great libraries, better extensibility, and is free, but the language itself feels a bit clunky.

Fantasy Football Player Forecasting in less than 200 lines of SAS

In my last post I provided data for NFL players and teams for the 2011 season. In this post I develop a simple, pretty darn decent forecasting engine in less than 200 lines of SAS.

Click here to download the SAS source [estimate.sas].

For the uninitiated: fantasy football involves a bunch of 30-something males selecting players from real NFL teams and competing against each other for increasingly high stakes. The score for a fantasy team is computed by applying a set of scoring rules to the real-life performance of each player during each week of NFL season. For example, if touchdowns are valued at 6 points, and throwing an interception is penalized 2 points, if Drew Brees throws 4 TDs and 2 INTs his score for the week is 4 * 6 – 2 * 2 = 20. There are typically additional scoring rules that involve the number of yards gained by players, as well as the performances of kickers and defensive units based on more esoteric considerations. A fantasy football participant drafts a set of players (and defensive units) and selects a portion of them to “play” on his team each week. Typically you can play only a certain number of players of each position per week: for example 1 quarterback, 2 running backs, etc. Fantasy teams are matched against each other each week – the team with the highest combined team score wins.

So a smart fantasy football player tries to draft a combination of players that will result in the highest projected points per week. The forecasting engine described in this post computes a rating for each player that can be used to prioritize draft selection. The basic assumption behind the forecasting engine is that a player (or team’s) performance for the 2012 season will be exactly the same as 2011. This is obviously incorrect:

• Players improve or decline in ability over time.
• Players suffer injuries.
• Rookies have no performance in 2011 since they didn’t play.
• and so on.

All of these things can be accounted for, but I won’t here. That makes things simpler: all we really want to do is apply the rules of the league to compute the number of fantasy points for each player. Let’s take running backs as an example. In my league, running backs accumulate points as follows:

• 1 point for every 10 rushing yards.
• 1 point for every 10 receiving yards.
• 6 points per touchdown.
• 2 points deducted per fumble.

So the first step is to read the running back data into a SAS dataset. Here’s a macro to do that:

** Read a CSV file into a SAS dataset.       **;
%macro ReadCSV(position);
  proc import datafile="C:\data\Football\NFL 2011 &position..csv" dbms=csv
    out=&position replace;
    getnames=yes;
  run;
%mend;

The next step is to score each player. That’s easily done using a SAS data step:

** Compute RB ratings. **;
%macro ScoreRB;
  %ReadCsv(RB);
  data rb;
    set rb;
    FFPts = (Rush_TD + Rec_TD) * &PtsTD + FumL * &PtsFum + Rush_Yds / &RushYdsPt + Rec_Yds / &RecYdsPt;
  run;
%mend;

Now the SAS table RB will have an additional column called FFPts that has the forecasted fantasy points for each player over the course of the season. I have introduced macro variables to represent, e.g. the number of points per touchdown. As you will see in the full code, you can customize those according to the rules for your league.

It’s pretty easy to write similar macros for quarterbacks, kickers, and so on. If you combined all of the resulting datasets and sorted them by FFPts, you’d have a “draft board” that could be used to select players. But this would stink. Why?

The reason is that simply sorting players by expected number of points does not take into account that when drafting players we also care about the variance between players of the same position. Here’s what I mean. By virtue of the scoring rules, quarterbacks usually score more fantasy points than tight ends on average. Consider a league where the average quarterback scores 400 points per year. Now suppose that tight ends score 200 points on average, but the best tight end in the league scores 280 (call him John Doe). Given the choice, it is smarter to draft John Doe over a quarterback that scores 400 because John will outscore his competition at that position by 80 points. 400 point QBs are easy to come by, but 280 point TEs are not.

Therefore I “center” the scores for each position by finding the score for the “worst starter” for each position. In other words, if my league has 12 teams then I find the score of the 12th best quarterback. Then I subtract that value from the scores of all quarterbacks. I know have a “position invariant” metric that I can use to compare players across positions. Computing centered scored is very easy using PROC MEANS:

** Create cross-position value estimates by subtracting the value of the projected  **;
** worst starter at that position. The number of league-wide starters for the       **;
** position are given by obscount. This value will depend on your league.           **;
%macro Normalize(position, obscount);
  proc sort data=&position;
    by descending FFPts;
  run;

  proc means data=&position.(obs=&obscount) min noprint;
    var FFPts;
    output out=&position._summ;
  run;

  data _null_;
    set &position._summ;
    if _STAT_='MIN';
    call symput('FFPtsMin', FFPts);
  run;

  data &position;
    length Pos $ 8;
    set &position;
    Pos = upcase("&Position");
    FFPtsN = FFPts - &FFPtsMin;
  run;
%mend;

We just need to call Normalize after we do the initial scoring. Again, here is the link to the full source.

Once this is done then we can combine all of the results and sort. What we get is a perfectly plausible draft board! Here are the first 25 players with both “raw” and “centered” points. Run the code to get ratings for all 640 players and teams. Poor Billy Volek is a the bottom, through no fault of his own.

Pos	Name	FFPts	FFPtsN
QB	Aaron Rodgers	487.42	216.2388
QB	Drew Brees	449.6625	178.4813
RB	Ray Rice	292.8	173.8
RB	LeSean McCoy	280.4	161.4
WR	Calvin Johnson	262.1	146.5
QB	Tom Brady	416.5313	145.35
TE	Rob Gronkowski	240.9	145.3
RB	Maurice Jones-Drew	262	143
RB	Arian Foster	250.1	131.1
QB	Matthew Stafford	394.9875	123.8063
QB	Cam Newton	379.35	108.1688
WR	Jordy Nelson	216.3	100.7
TE	Jimmy Graham	195	99.4
RB	Marshawn Lynch	215.6	96.6
WR	Wes Welker	210.9	95.3
RB	Michael Turner	212.8	93.8
WR	Victor Cruz	205.6	90
WR	Larry Fitzgerald	189.1	73.5
RB	Adrian Peterson	188.9	69.9
RB	Ryan Mathews	186.6	67.6
RB	Michael Bush	185.5	66.5
RB	Darren Sproles	185.3	66.3
RB	Steven Jackson	181.8	62.8
WR	Roddy White	177.6	62
WR	Steve Smith	177.4	61.8