Measuring Week-To-Week Consistency With Standard Deviation

There's nothing worse than watching your number one pick put up single digits in any given week—owners of Frank Gore and his seven single-digit games last year can attest to this.

This raises the question: How safe is your lineup for each week?

To answer that, I found the standard deviation of 55 players—15 quarterbacks, and 20 of both running backs and wide receivers—each the best at their positions (according to ESPN's rankings).

What's standard deviation, you ask? To put it simply, standard deviation is how spread out your data is from the mean. A higher deviation means a higher volatility, a lower deviation a lower volatility.

Instead of just using last year's data, I used every game played by a player in the last three years.

Games in which a player was injured were included (games missed due to injury, however, were not), and if a player hadn't had any major playing time to that point (take Tony Romo, for example), I only included the game if a player had 15 attempts, ten touches, or three receptions (for quarterbacks, running backs, and wide receivers, respectively; touches are defined as carries plus receptions). I used this caveat for Week 17 games as well.

In the table, the last column, "Value", is calculated by dividing the fantasy PPG by the standard deviation; this is used to devalue players, for example, with low weekly outputs that range from seven to ten points each week (which would produce a standard deviation less than one who puts up only 20 and 40 points each week).

First, the quarterbacks.

Standard Deviation of ESPN top-15 QBs

Player	Team	Fantasy PPG	Standard Deviation	Value
Peyton Manning	Colts	17.8	7	2.54
David Garrard	Jaguars	14.3	5.7	2.51
Matt Hasselbeck	Seahawks	15	6	2.50
Carson Palmer	Bengals	15.9	6.5	2.45
Jay Cutler	Broncos	13.4	5.5	2.44
Derek Anderson	Browns	16	6.8	2.35
Ben Roethlisberger	Steelers	15	6.5	2.31
Tony Romo	Cowboys	17.8	8.4	2.12
Tom Brady	Patriots	18.3	8.8	2.08
Drew Brees	Saints	16.1	7.9	2.04
Eli Manning	Giants	12.8	6.4	2.00
Donovan McNabb	Eagles	17.5	9	1.94
Marc Bulger	Rams	14	8	1.75
Brett Favre	Packers	13.3	8.2	1.62
Matt Schaub	Texans	10.3	7.3	1.41

Some notes:

• When Donovan McNabb is healthy, he's a top-five quarterback. It's just too bad he's missed 14 games the past three years.
• Eli Manning still isn't a serviceable fantasy QB.

• David Garrard is an nice option, even in a ten-team league, if you want to lower your risk week to week.
• I wouldn't be worried about Tom Brady. Keep in mind last year, Brady had under 17 points once, yet his standard deviation was still 9.2, which was due to his five outings over 30 points making his outings in the teens seem like single-digit games for an average player.

Standard Deviation of ESPN top-20 RBs*

Player	Team	Fantasy PPG	Standard Deviation	Value
Ryan Grant	Packers	15.7	5.4	2.91
Marshawn Lynch	Bills	13.6	5	2.72
Edgerrin James	Cardinals	13.3	6.1	2.18
Clinton Portis	Redskins	14.8	7	2.11
Brian Westbrook	Eagles	17.1	8.2	2.09
Larry Johnson	Chiefs	20.7	10	2.07
Willis McGahee	Ravens	11.4	5.6	2.04
Steven Jackson	Rams	17.2	8.6	2.00
Marion Barber	Cowboys	13.6	6.9	1.97
Frank Gore	49ers	14.3	7.5	1.91
Brandon Jacobs	Giants	12.5	6.7	1.87
Maurice Jones-Drew	Jaguars	13.7	7.4	1.85
LaDainian Tomlinson	Chargers	22	12	1.83
Ronnie Brown	Dolphins	12.3	7.4	1.66
Laurence Maroney	Patriots	9.9	6.1	1.62
Willie Parker	Steelers	13	8.1	1.60
Joseph Addai	Colts	14.3	9.1	1.57
Jamal Lewis	Browns	11.6	7.6	1.53
Reggie Bush	Saints	11.3	8.2	1.38
Adrian Peterson	Vikings	17.1	14.3	1.20

*Michael Turner and Darren McFadden, ranked 20th and 21st, respectively, left out due to no prior game stats; Edgerrin James, ranked 22nd, took the 20th spot.

Some notes:

• Ryan Grant's stats only included nine games, so I would put very little into his number-one-ranked value.
• James' stats included his last year in Indianapolis; without it, he had a 2.55 value. The main point: Edge is actually a very good running back for safe, I-know-what-I-can-get weekly totals.
• Last year Johnson had a 7.7 standard deviation with a 12.3 PPG, for a value of 1.60. Most of his value (fantasy value, that is) comes from his seasons of two and three years ago.
• Jamal Lewis is not worth a low second-round pick, where he's going in drafts right now.
• Adrian Peterson isn't the number one pick (or a top-three pick either, but I don't want this turning into a Peterson debate, so I digress).
• Clinton Portis is a top-six running back—maybe even top five.

Standard Deviation of ESPN top-20 WRs

Player	Team	Fantasy PPG	Standard Deviation	Value
Larry Fitzgerald	Cardinals	12.2	6.1	2.00
Brandon Marshall	Broncos	10.3	5.3	1.94
T.J. Houshmandzadeh	Bengals	11.4	6	1.90
Reggie Wayne	Colts	11.3	6.2	1.82
Torry Holt	Rams	11.5	6.4	1.80
Terrell Owens	Cowboys	14	8.2	1.71
Marques Colston	Saints	12.1	7.1	1.70
Anquan Boldin	Cardinals	11.3	6.8	1.66
Roddy White	Falcons	8.7	5.5	1.58
Braylon Edwards	Browns	10.9	6.9	1.58
Andre Johnson	Texans	9.8	6.6	1.48
Plaxico Burress	Giants	10.8	7.3	1.48
Greg Jennings	Packers	9.4	6.5	1.45
Steve Smith	Panthers	12.5	8.9	1.40
Roy Williams	Lions	10.1	7.2	1.40
Santonio Holmes	Steelers	8.8	6.4	1.38
Chad Johnson	Bengals	12.1	8.8	1.38
Randy Moss	Patriots	11.9	8.7	1.37
Hines Ward	Steelers	10.1	7.5	1.35
Wes Welker	Patriots	7.4	5.8	1.28

Some notes:

• Moss' value with the Patriots was 2.00, and Welker's was 1.47.
• Fitzgerald is a top-5 wide receiver.
• Chad Johnson remains one of the most overrated wide receivers solely due to the fact that he's inconsistent, and Houshmandzadeh is the better of the two Bengals wideouts.
  
• Hines Ward is not a top-25 WR.
• Torry Holt is still a top-10 receiver, despite his age and knees.
• I'm not a fan of Jennings without Favre—he's borderline top-20, for me.

What does it all mean?

Choosing a roster with Matt Schaub, Adrian Peterson, Jamal Lewis, and Chad Johnson might win you four or five weeks by a large margin, but you'll lose all the weeks those four put up single digits. In the end, it isn't worth all the headaches.

Picking up David Garrard, Brian Westbrook, Edgerrin James, and T.J. Houshmandzadeh instead of those four will gain you three or more wins in the season, when the former group all put up stinkers and the latter group put up point totals ranging from 10-15 points.