Standard Deviation
What is it? and why do I care?
June 29th, 2001
I
guess the place to start is to give you the definition.
Standard deviation is the square root of
the average squared deviation from the mean.
Say
what? Come again? In English this time please? I remember when I had someone
call me a deviant, but get real dude. Yeah, I guess it would be better to try
that again, but first we should set some guide lines here.
·
The average
football guy should probably move on. This is only for the hardcore shark that
absolutely must have every advantage.
(But if you are clicking on a link called “standard deviation”, you must
be a fantasy football addict!)
·
There may
be some terms thrown out that you don’t know, but this will be the easy part.
My job is to take something that is supposed to be real confusing and put it
into words that make sense to a ten-year-old. At least that’s how I approach my
teaching job, don’t dumb it down, just use words and pictures that make sense
to people.
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The
examples I use to illustrate concepts will only use football statistics.
·
The
statistics I am going to use only cover the 2000 season. These are going to be
for illustration purposes only. I could use lots of seasons and wads of game
data, but working with just one season will get us off to a decent start.
Question #1:
Why do I give a rip about this?
Answer #1:
Because your math teacher says you’ll fail if you don’t do your homework. Oh
wait, that’s my other classroom. Ummm. OK. Got it. Using standard deviation you
can analyze the following questions better:
·
How can I
tell for sure whether a player is a boom/bust type of player or more of a
steady eddie? Is it possible to assign a number or value to these players so I
can compare them?
·
Are RB’s
really more consistent than WR’s?
·
Can I expect
the QB’s in my draft to be spread out all over the place (same amount of good,
average and poor), or possibly have a whole mess of QB’s that are about the
same ability level (good, average or poor)?
·
Several
teams draft with the concept of “buckets” or “tiers”. When placing players into
these buckets before my draft, is there anyway of knowing how many players
should go in each tier on an average year? Each year is different, but should
there be some sort of guideline that tells me if my projections are way off
base?
·
Which
position is the most predictable from year to year?
Question #2:
What is standard deviation? Be gentle...
Answer #2:
Standard Deviation is one number that we use to describe a bunch of numbers. It
tells us how “spread out” a group of numbers is. With respect to football
players, it describes how far away from their average you can expect them to be
on any given Sunday. In essence, it’s all about consistency from week to week.
Let’s
take a look at some examples from the 2000 season. We’ll compare the games from
the top 10 rushing leaders. The rushing totals from each game are listed from
smallest to greatest, not by week number. The number at the bottom of each
column is the Standard Deviation (S.D.) for each set of numbers.
If
we list the Standard Deviation for each RB above in a tidy list we get the
following:
What
can we get out of this list? Corey Dillon was the most erratic of the top 10
RB’s in 2000. Dillon tended to be farther away from his average of 89.7 yards
more often than the others were. Stephen Davis was the most consistent during
the 2000 campaign. Davis tended to be closer to his average of 87.9 yards more
often than the others were. These numbers don’t tell us who was better, they
only indicate who was more CONSISTENT
and who was more ERRATIC.
Question #3:
What exactly does standard deviation tell us?
Answer #3:
Standard deviation is a value that tells us how far above or below his average
you can expect a player to be around 68% of the time.
Corey
Dillon:
68%
of the time we expect between 16.5
(89.7 - 73.2) & 162.9 (89.7 +
73.2) yards.
Stephen
Davis:
68%
of the time we expect between 53.8
(87.9 - 34.1) & 122.0 (87.9 +
34.1) yards.
The
graphs below show how often we expect Davis and Dillon to get any given amount
of yards. Davis will be close to his average more often, hence the graph is
higher at his average. Dillon will get his average less often, but will have
more games where he is getting small amounts and huge amounts of yards. The
thing to notice here is that Davis has a
higher and narrower graph while Dillon has a flatter and wider graph. These
graphs demonstrate a Normal Distribution
or what is commonly called a “bell curve”. To see a great demonstration of how
a normal distribution can be created check out this Ball Drop
web site.
One
standard deviation away from the average** in either direction on the
horizontal axis (the red area on the above graph) accounts for somewhere around
68 percent of the games by either player. Two standard deviations away from the
average (the red and green areas) account for roughly 95 percent of their
games. And three standard deviations (the red, green and blue areas) account
for about 99 percent of their games.
**
NOTE: Most mathematicians call average the “mean” when referring to average in
this sense of the word. If we are talking about adding up a bunch of numbers
and dividing by the population, we call it the mean. If we are talking about
the number that shows up most often, it’s the “mode”. If we are talking about
the number that would show up in the middle if we lined them up smallest to
largest, it’s the “median”. Three types of average, three different terms. We
will stick to “mean” for today just to try and keep things a bit easier.
Question #4:
Where on earth does the standard deviation number come from? How is it
calculated?
Answer #4:
As an example I plan to use Marshall Faulk’s receiving yards from 2000 because
I think Faulk is too cool for words. Dude is an awesome team player and a
winner. If you remember the play where Faulk picked up Torry Holt and planted
him on the line of scrimmage so that Warner could spike the ball and save a
timeout you know what I’m talking about. There are so many players worried
about getting theirs that we don’t see enough of this. Players that make
extraordinary plays just to gain one yard or save 2 seconds off the clock.
What? What’s that? Oh. Sorry. Back to the question. This table shows all of
Faulk’s receiving yardage from 2000 and a whole mess of other stuff that I’ll
explain below.
1.
The first
shows which games Faulk played in during the 2000 season. Well duh.
2.
The second column
shows how many receiving yards Faulk had in each of those games. Well double
duh.
3.
The third
column shows how far Faulk was away from his average (59.3) in each week.
4.
The fourth
column is the value from column three squared.
5.
To find
standard deviation, you must take the average of the numbers in column four,
then take the square root. This example is actually “population standard
deviation”. To find “sample standard deviation you would divide by 13 when
finding the average in column four instead of 14 (number of games he played).
If you are looking for a better explanation of the difference between the two
types try this
site that has some decent explanations of statistics.
Question #5:
Hey! What about the WR’s? I just have to know...
Answer #5:
Okey Dokey. When compiling the numbers for the top ten WR’s we get the
following table.
Here
is a side by side comparison of the top RB and WR yardage standard deviations.
The
average SD for the RB’s = 50.8
The
average SD for the WR’s = 45.9
Hey!
Just a garsh darn minute here fella. Aren’t the top RB’s supposed to be more
consistent than the top WR’s? I sure thought so. Hmmm. Sumpin strange here. I
know it doesn’t have anything to do with the amount of yardage. They were a
virtual match. Take a look above at the season totals for each position. In
fact, the difference between the season yardage numbers for the average top 10
RB and average top 10 WR was only 7 yards! That’s pretty close Hoss.
OK.
Reality check time. Anybody score their fantasy teams based solely on yardage?
Thought not. AND, don’t RB’s get
tons of receiving yardage? Yep. AND,
don’t RB’s generally score more TD’s? Yep. So what sort of comparison might
yield better fruit? Let take a look at Fantasy Points / Game and standard
deviation.
Question #6:
Yo. Dave. What about applying this standard deviation stuff to Fantasy Points /
Game?
Answer #6:
Can do amigo. Here are some tables that list the top 10 RB’s and WR’s based on
fantasy points per game. You’ll quickly notice that some of these guys were not
top 10 yardage fellas.
Scoring
system used here is for a basic performance league: 1 yard = 0.1 pts and TD =
6pts. (How many times have you had to do a double take at that 26.5 under
Marshall Faulk’s name? Geesh.) When listing them out in order of standard
deviation you get these two tables.
When
looking at these numbers, the players on the bottom appeal to me big time. They
are consistent. Notice how E. James was the second most consistent RB AND the second highest scorer in points
/ game? This is why I am moving James ahead of Faulk on my cheatsheets. Even
though I like Faulk more as a player, I’m not blind. I just can’t see Faulk
repeating last year. That run of games at the end of the season was amazing.
So
who’s more consistent? The WR’s have a lower standard deviation, but there’s a
catch. The RB’s score more points than the WR’s do. If we talk about the
average top 10 RB and top 10 WR, we need to consider how many points they are
scoring to see an appropriate SPREAD
of these points. Remember that the standard deviation is giving us a range
above and below a player’s average. These are values that we expect to see
about 68 percent of the time. Check out this graphic.
Neither
position is way more consistent than the other is. The graphic above displays
that the range for RB’s and WR’s are almost the same, but every now and then
your top flight WR will score 5 points while your RB at least got you 10
points. It happens. It doesn’t mean that
RB’s are more consistent. It means they score more points!
Conclusions, Questions, and Thoughts:
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Way back at
the start of this article I was hoping to give you some ideas about standard
deviation. Did we get that accomplished? I’m thinking so if you are still
reading this.
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I was also
hoping to address consistency of the RB and WR position from week to week
through the season. Yep. Taken care of.
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How many
guys in the NFL would play for free? Hey. It’s just a thought.
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If
consistency is something you look for in a player, standard deviation is
something you will want to look into. The same can be said for boom/bust
players as well.
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I’m curious
to know what the QB numbers look like now. Sounds like some more number crunching.
At this moment, (Aw crap, its 1:20 AM, why am I still slammin the keys? Love of
the hobby!) I’m guessing that QB’s are fairly consistent with the yards, but
not the TD’s.
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How about
TE’s, PK’s, DF’s? Got any guesses? I’m clueless right now. Maybe a shot of
caffeine? Better not go there.
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If you are
serious about examine these numbers on your own, you can download the
individual games file from Doug
Drinen’s site.
another Footballguys.com exclusive from David Shick
Mail comments to: shick@footballguys.com