#### Topic: Variance and Standard Deviation Worksheet

This spreadsheet is a product of the conversation between DD, Xlledx, and others under the Magic Formula post linked here.

The spreadsheet is my attempt to build on the idea that the Magic Formula is based on.  For a complete explanation on what the Magic Formula is, please read the entirety of Joosbawx’s thread which I referenced and linked above.  Cliff notes version: The Magic Formula calculates the difference between the top player and the “last starter” at each position.  Those differences (also called ranges) are used to determine which position is deemed most valuable and therefore which position you should focus on early in the draft.

Rather than compare the ranges, DD had made the argument that comparing the players' totals to the overall mean (or average) score of their position would be a more accurate representation of each player’s value in relation to the rest of their position.

Example:  The mean of the RB position last year in my league was 101.625.  The RB1 scored 188 points, so his “replacement value”, or the value of RB1 when compared to the mean, is 188-101.625 or 86.375.  Conversely, RB20 scored 70 points, so his replacement value would be 70-101.625 or -31.625

Once these replacement values are calculated, we can use them to determine a position’s variance and standard deviation.

What the heck is variance and standard deviation?

Ok, Quick statistics recap:
Variance measures how the data is distributed within a range, or how much the data differ.  If every score were the same in the set of data, then the variance is 0, otherwise there will be some level of variance, the larger the variance the larger the disbursement. Technically speaking, variance is the sum of the squared differences between each score and the mean average of all scores or (X-Mean)^2.

Standard Deviation similarly measures the variation of the data from the average.  A low standard deviation indicates that the scores tend to be very close to the mean for the position, whereas high standard deviation indicates that the scores are spread farther out over a large range.  Technically speaking, standard deviation is the square root of the variance.

So what does that have to do with Fantasy Football?

The Variance and Standard Deviation helps us to determine the disparity among the scores of a given position.  The higher the variance and standard deviation, the more spread out the scores are along the range and the farther the scores are away from the mean of the position.  Therefore, the positions with a high variance and high standard deviation will generally be more valuable than the the positions with a low variance and low standard deviation.

Example:  Using 2010 data from my league, the RB position had a variance of approx. 1177 and a standard deviation of 34.  The WR position had a variance of approx. 501 and a standard deviation of 22.  Using those stats, RBs overall were more valuable than WRs.

I already knew RBs were more valuable than WRs.  That seems like a lot of work to figure that out.

True. But these stats can tell you so much more.  By using the standard deviation and the replacement value, you can have a baseline to compare individual players at difference positions using positional value.  Not sure when QB or WR should begin to enter the Round 1 discussion, This can help.

Going back to the above example, using the 2010 stats, here are the replacement values for the top 5 RBs and WRs (actual stats from my league)

Player  Total Pts    X-Mean    Player   Total Pts    X-Mean
RB #1    219    114.6667    WR #1    148    53.27778
RB #2    144    39.66667    WR #2    142    47.27778
RB #3    138    33.66667    WR #3    137    42.27778
RB #4    138    33.66667    WR #4    125    30.27778
RB #5    130    25.66667    WR #5    125    30.27778

Obviously, RB #1 is the most valuable of the players, but surprisingly, WR #1 is the next valuable, scoring 53 more points than the average WR. Here are the 10 players listed in order, based on replacement value. (Disclaimer: my league scoring is much more balanced among the positions than most.  I do not consider my league to have “standard scoring”)

Player   Total Pts    X-Mean
RB #1    219    114.6667
WR #1    148    53.27778
WR #2    142    47.27778
WR #3    137    42.27778
RB #2    144    39.66667
RB #3    138    33.66667
RB #4    138    33.66667
WR #4    125    30.27778
WR #5    125    30.27778
RB #5    130    25.66667

But you’re using old data, how does that help me for the 2012 draft?

Another good question!  By averaging the stats of the last 4 years, we can generate projections for the 2012 season without worrying about guessing yards or TDs.  Now considering that last year’s stats are more meaningful than stats form 3 or 4 years ago, we use the following formula to generate the 2012 projections:

2012 projections = 2011 scores(40%) + 2010 scores(30%) + 2009 scores(20%) + 2008 scores(10%).

So in 2012, I can predict that the #1 RB will scores approx. 210 points (188 * 40% + 219 *30% + 252 *20% + 185*10%)

OK, OK, I’ll bite.  How do I use the spreadsheet?

There are two spreadsheets.  One has the capabilities to do 12 QBs and TEs along with 36 RBs and WRs.  The other is for deeper leagues with the availability of 24 QBs and TEs along with 48 RBs and WRs.  To decide the number of each position to use, simply multiply the number of teams by the number of players you are able to start at each position:

Example:  12 team league with a starting lineup of 1 QB, 2 RB, 3 WR, and 1 TE would use 12 QBs, 24 RBs, 36 WRs, and 12 TEs.
Flex Example:  If your league uses a flex, I would count the flex as an extra spot for all allowed position.  This will allow you to determine which position is best to use as your flex.  So 10 team league with a lineup of 1QB, 2RB, 2WR, 1TE and 1 flex (RB/WR/TE) would use 10 QB, 30 RB, 30 WR, and 20 TE.

Once you have the number of positions, simply enter those players’ totals for years 2008-2011.  Who actually scored the points does not matter.  2011 RB#1 is the RB who scored the most points whether it was Rice, Foster or whoever. As you enter the values, the spreadsheet will automatically begin to calculate the mean, the replacement value (X-mean), the variance and the standard deviation.

Important note: Only enter data for the number of positions that you calculated above.  If you are only using data for 10 QBs, leave QB 11 and QB 12 BLANK.  If you enter any values in those rows (even 0), those values will be used in the calculations and ultimately skew the results.

At this point, the spreadsheet is designed for 4 years worth of data.  If you do not possess that much data, you would need to manually change the formula to recalculate the 2012 projections to use less than 4 years of data.  Both spreadsheets already have my league’s data included as an example.

I hope you find the spreadsheet useful.  Please feel free to offer feedback.

Last edited by Devo49 (2012-08-11 21:55:29)

Im sorry, I cant hear you over the sound of my own awesomeness...

+6

#### Re: Variance and Standard Deviation Worksheet

read through twice already...nice work.  I think we should join forces to rule the world.

#### Re: Variance and Standard Deviation Worksheet

I'd love to see a totally comprehensive effort on all of your guys' parts.

#### Re: Variance and Standard Deviation Worksheet

DD wrote:

I'd love to see a totally comprehensive effort on all of your guys' parts.

this could be included into TMF Worksheet without any difficulty whatsoever.

#### Re: Variance and Standard Deviation Worksheet

I can't wait to see it, can't get at it now.  You guys are all very talented with numbers and putting them places and stuff.

#### Re: Variance and Standard Deviation Worksheet

Really nice presentation and thorough walk-through... You present your method cleaner and more efficiently that Zarzycki does. I like your method much more!

Last edited by broskie9 (2012-08-10 07:15:00)

12 Team League - QB: Ryan RB: Lynch, Morris, Murray, Stewart, Thomas, Powell WR: Green, White, Harvin, Decker, Wright TE: Pettigrew
10 Team League - QB: Ryan, Luck RB: McFadden, Martin, Johnson, Ballard, Thomas, Green, Rodgers WR: Green, Decker, Wayne, Garcon TE: Hernandez, Rudolph

#### Re: Variance and Standard Deviation Worksheet

Awesome job, look forward to digging more into this over the weekend. Thanks for all your efforts!

Excellent work.

#### Re: Variance and Standard Deviation Worksheet

Still think you guys are over thinking all of this.

10 team ppr.  2 flex spots, 3 WR otherwise standard rosters
QB: Andrew Luck, Jay Cutler  RB: Shady McCoy, Demarco Murray, Andre Ellington, Bernard Pierce Toby Gerhart, MOJO.  WR: AJ Green, Keenan Allen, Manny Sanders,  Kendall Wright, Justin Hunter, Reuben Randle, Brandon Cooks. TE: Travis Kelce, Kicker: dude from the Eagles,  Def: Tampa Bay

#### Re: Variance and Standard Deviation Worksheet

JamesRustler wrote:

Still think you guys are over thinking all of this.

#### Re: Variance and Standard Deviation Worksheet

I love the variance, mean and standard deviation discussion, works quite well for my league, especially when I integrate it into the MF.

As a point of clarification Devo, you the X - Mean, just means you're taking the total points of RB1 and subtracting it from the mean, correct? Just want to make sure the Var or StDev aren't being integrated there as well.

Cheers

"I want me some glory hole!" J.Jones

10-team 2QB PPR keep 4: QB: P Manning, Mariota, Hoyer, Romo RB: Gurley, Hyde, Hill, Duke Johnson, Blue, Foster, Cobb WR: D Thomas, J.Jones, Jeffery, St. Johnson, Boldin TE: Olsen, Reed
hog gargler Free-PPR (6-4, most overall points): QB: Brady RB: Freeman, D Murray, Hill, D Lewis, Blount, M Gordon WR: Maclin, Jeffery, J. Jones, Diggs, R Matthews, Parker TE: Barnidge

#### Re: Variance and Standard Deviation Worksheet

I used the x-Mean and MF to map out when certain positions should be taken in first 9 rounds of the draft for my particular league's scoring. I then took my league's projections and put where that player could be drafted by others (yes I know, and agree, that these are NOT a good basis for evaluation, however I know that the others in my league will not be doing the same sort of analysis I will be, I'm sure it's the same in many other leagues and the others will be 'relying' on the projections to an extent). For example, RB1 - Foster; WR1 - Calvin; QB1 - Rodgers and so on....

If you have the time and inclination I'd recommend you do that same; the reason being is that while we as FFG regulars may understand where you 'should' draft someone, you should be aware that that will NOT happen in your draft. You should keep track of where others are drafting. For instance, if your analysis shows that you can wait for your 2nd RB until round 8th round (mine has RB18, 9-team league, going as an 8th round draft) and there's a run on RB2's you'll have to move up when you're going to draft someone. Know your league and your opponents - I know my league will have a run of QBs early and while my analysis says I can wait for Ryan as my 8th ranked QB in the mid-4th round, chances are he'll be gone by the early to mid-3rd and because of positional league importance (thank-you MF) you may need to move him up.

I say this for those of you look at MF and X-Mean as a 'Rule.' Remember it's a guideline and if you're able to use it to map out where people should be taken and then be able to use YOUR draft board as well you'll be able to get value players in some areas but also have to reach for some as well, especially if there's a run on a certain position. Don't be afraid to reach for a player or position because you know the positional importance, I guess is my tip for the day.....trust the numbers and know thy opponent.

"I want me some glory hole!" J.Jones

10-team 2QB PPR keep 4: QB: P Manning, Mariota, Hoyer, Romo RB: Gurley, Hyde, Hill, Duke Johnson, Blue, Foster, Cobb WR: D Thomas, J.Jones, Jeffery, St. Johnson, Boldin TE: Olsen, Reed
hog gargler Free-PPR (6-4, most overall points): QB: Brady RB: Freeman, D Murray, Hill, D Lewis, Blount, M Gordon WR: Maclin, Jeffery, J. Jones, Diggs, R Matthews, Parker TE: Barnidge

#### Re: Variance and Standard Deviation Worksheet

WinterIsComing wrote:

I love the variance, mean and standard deviation discussion, works quite well for my league, especially when I integrate it into the MF.

As a point of clarification Devo, you the X - Mean, just means you're taking the total points of RB1 and subtracting it from the mean, correct? Just want to make sure the Var or StDev aren't being integrated there as well.

Cheers

Yes, X-Mean simply means that player's points - the mean of the position.  That is why those on the bottom half of the list have negative X-Mean values.

Im sorry, I cant hear you over the sound of my own awesomeness...

#### Re: Variance and Standard Deviation Worksheet

JamesRustler wrote:

Still think you guys are over thinking all of this.

You. Are. Troll.

It is a fair wind that blew men to the ale.

#### Re: Variance and Standard Deviation Worksheet

I am working off spreadsheets from devo49 and joosbawx and I tweaked a little bit of my own. Here is what I came up with for my league. The summary tab shows the relative values by draft position based on the averages of the last three years statistics. Am I on the right path? Any thoughts?