Friday, August 29, 2014

Matt Forte is Your #2 Pick in Standard or PPR Leagues

Hello and Welcome to Market Fantasy!

When I started Market Fantasy last year, the objective was to take fantasy sports analysis and go completely mathematical about it. I wanted to try to have as little bias as possible creep in. So far, I think I’ve done a fairly decent job and have yielded some hits (Alshon Jeffery) and misses (Marques Colston).  I read a lot of fantasy analysts and the recurring theme with the “numbers” guys is I get the feeling reading some of their columns that they’re just throwing out stats to sound smart and really have no idea what they’re talking about. The numbers have absolutely no correlation to each other. I read a column recently where the analyst stated that John Lackey had a high K/BB rate in Boston despite Fenway increasing runs scored by whatever percentage. A high strikeout rate has absolutely nothing to do with how much a park increases runs scored. Nothing. But I digress. Hopefully, by reading this blog, you’ve learned a little about statistical analysis, where to spot nonsense, and impartial observation.

Today, I’m taking a left turn and going full homer on you. I’m sure you can tell by my profile picture that I’m a huge Bears fan. I’m completely, 100%, unabashedly all-in on the Bears offense this year. Brandon Marshall and Alshon Jeffery shouldn’t last past the second round. Jay Cutler should be in for a career year. While watching this Bears team, what with their video game offense and sieve of a defense, is like living in a bizarro NFL world, I’ll gladly take it. All this Bears bullishness leads me to the point of this post. Matt Forte is your number two pick this year in standard and PPR leagues. There’s a clear cut top four or five RB (depending how you feel about Lacy), and if you pick either of them first, no one is going to fault you. In my mind, however, there is Jamaal Charles at #1 and Matt Forte at #2. After that, do whatever you like. Most sites I read have a 1 – 2 punch of Charles and Shady McCoy, but I can’t get behind McCoy over Forte at all. Below is my case for Matt Forte as your #2 overall pick. Hell, when I’m done, I’ll probably end up drafting him #1 overall.

Competition and Team Setup
At first blush, it seems silly to talk about competition for two of the top players at their position. The Eagles have made some interesting moves lately, however, in regard to this and I think they could have an impact. First, we’ll start with Forte. He has no competition. None. Shaun Draughn isn’t good and Ka’Deem Carey is a rookie who shouldn’t have much of an impact. It’s also important to note what the Bears figured out about bothering to give Forte competition last year. At the beginning of the year, Michael Bush was supposed to be the goal line back and poach all the touchdowns as well as provide a change of pace. That’s not really how it ended up working out. Bush received 63 carries despite appearing in every game. He never received more than 8 carries in a game and poached three TDs.

Going into the year, the thought was that Matt Forte was ineffective at the goal line, but last year, his 60 touches inside the red zone led all of football. This led to a career high 9 rushing TDs and 12 TDs overall. With this increased emphasis the Bears gave Forte at the goal line, there should be no reason to expect that anything will change. In fact, his biggest competition for TDs is probably the Bears’ awesome WR duo of Marshall and Jeffery, but the Bears will still have plenty of Forte in the red zone. I expect another 9-10 rushing TDs from Forte with another 3 receiving thrown in.
As for the rest of the Bears’ offense, it’s pretty good. Last year, in the first year of Marc Trestman’s offense, the Bears threw for 4450 yards and 32 TDs and rushed for 1828 yards and 13 TDs. With improvements on the offensive line, and the duo of Marshall and Jeffery stretching the field, Forte should easily justify the #2 pick.

On the other hand, Philadelphia just added pass catching specialist Darren Sproles to the backfield. This will no doubt limit McCoy’s catches, which were a big part of his value last year when he caught 52 balls for 539 yards and two touchdowns. The last three years, Sproles has caught no less than 71 passes for 604 yards. Don’t underestimate the impact those receptions going to McCoy will have on his value.  He’ll still be involved in the passing game, but not nearly as much as in the past.

The other side of the coin is carries. Last year, Shady had a career high 314 totes, leading the league. Word out of Philly is that Sproles will garner some carries, and don’t forget about the intriguing addition of Kenjon Barner from Carolina. I know last year, Bryce Brown had 75 carries and McCoy still led the league. That’s not the point. The point is he now has two backs that the Phillies actively went out and got to steal carries. Prior to last year, McCoy’s previous high in carries was 273.  Last year, McCoy only outscored Forte by 17 fantasy points. Even a slight dip in usage would be enough to tip the scales Forte’s way.

Like the Bears, this Philly offense will hang some points on people. A lot of points.  I’m a believer in Nick Foles and the passing game as well. Jeremy Maclin is very good and TE Zach Ertz looks primed for a breakout.  Chip Kelly likes to run a high tempo offense that runs a lot of plays, but the Eagles only ranked 12th in the league last year in offensive plays. McCoy will still be a big part of that, but I think he has more competition

Injuries
Both of these players might get a bit of a reputation, deserved or not, as injury prone thanks to a couple big injuries for each. Since 2010, however, McCoy has missed 6 games while Forte has missed 5. That’s pretty good. I wouldn’t call either of these backs an injury risk, any more than all NFL players are injury risks. What I will say, however, is that McCoy is already dealing with some worrisome nagging injuries. He’s reportedly been dealing with a thumb injury that’s not thought to be a big deal, and turf toe. Turf toe tends to be an injury that lingers and can be especially harmful to running backs. Turf toe is a strain of a ligament in the toe, making it very painful to cut or even run. It’s things like this that could limit McCoy’s workload or even force him to miss games. Forte, on the other hand is completely healthy.

Conclusion
From where we are looking right now, it’s going to be hard to mess up the number two pick. You’re going to get an RB that is great. For my money, I just think that Forte will be a little better than McCoy. And when it comes down to it, that’s all we’re looking for, who will score the most points.


Tuesday, August 26, 2014

Six Sigma Drafting - Using Standard Deviation to Predict Your Team's Results

Hello and Welcome to Market Fantasy!

Six Sigma Drafting:

I love standard deviation and the principals of six sigma when looking at a player’s scoring. One of the most helpful things these two things can do for us is to show us a players’ floor.  By finding a player’s average weekly score and standard deviation, and using the idea of six sigma, we can determine a value for 84% of a player’s scores throughout the year. Looking at the normal distribution below, we get to 84 percent because 68.2% of all weekly scores will fall within 1 standard deviation on either side of the mean. Another 13.6% will fall two standard deviations above the mean, and another 2.1% will fall three standard deviations above the mean, and lastly, .1% of a player’s scores will fall over three standard deviations above the mean. This is what six sigma quality is based on, the idea that 99.9% of results will fall within three standard deviations of the mean. It is used for things like determining an expiration date of food. Take milk, you would get 100 different gallons of milk, let them go bad, log the amount of days each takes to go bad. Then you determine the average and standard deviation from that data set. Say the average is 20 days, with a standard deviation of 3. Since we know that 99.9% of all outcomes will fall right of three standard deviations left of the mean, we can say three standard deviations of three is nine. Subtract that from 20 is 11. So by putting an expiration date of 11 days after a gallon of milk is produced, we can know that on the 11th day, 99.9% will still be good, but will now start to go bad. That way there is an incredibly small chance that any will go bad before the expiration date.

So how does this all relate to fantasy football? I’ll tell you. A lot of us are used to looking at full season values and drafting players projected to score the most points throughout the season. Unfortunately, this isn’t roto and all that matters is what a player scores in a given week. So while it’s great that player X is projected to outscore player Y at the end of the year, that doesn’t really tell us how a player will do week to week, which is what we’re really concerned about. Case in point, would you rather have a running back who scores 20 points in back to back weeks, or one who scores 39 one week and 1 the other? They are both averaging 20 points over those two weeks, but in all likelihood, the second player killed you in the 1 point week, while the first player most likely helped you win both weeks. This is where establishing a floor comes in extremely handy. Say you have two QBs who both average 20 points per game, player A has a standard deviation of 4, while player B has a standard deviation of 7. Using the idea of the normal distribution like I outlined above, player a will score at least (or have a floor of) 16 points in 84% (or 13 in a 16 game season) of their games. Player B will score at least (or have a floor of) 13 points in at 84% (or 13 in a 16 game season) of their games. Player A will have a three point floor advantage over Player B. Three points might not seem like much, but now take that over an entire roster (say 1QB, 2RB, 2WR, 1TE, 1FLEX, 1K and 1DST). If your team has a three point floor advantage at each position, that is a 27 point (three points times nine players) higher floor than your opponent. While that is an extreme example, you can see the point here. If the idea is to score more points than your opponent each week, then it is imperative to SCORE MORE POINTS EACH WEEK! Having a roster of players projected to score more points over the course of a season is great, but if they have wide variations in their weekly scoring, they will leave you with a lower floor, or greater chance for disaster.

What is the flip side then? Well the flip side is in upside. Take the above scenario. If we can determine that 84% of player A’s  weekly point totals will be above 16 points, we can also take the reverse for player B. In this case, we can look at upside. Take the average of 20 points and add one standard deviation, or 7 points. What we can say now is that 14% of the time, player B will score above 27 points. Conversely, Player A will only exceed 24 points 16% of the time. This means player B has greater upside.

This will be imperfect (since it relies on last years’ data and projections to an extent), but so are all predictive models in fantasy sports. To make this work, you will need two sets of data. You will need weekly scoring from the previous year, and projected scoring from the upcoming year (to get a per game average). Better yet, take upcoming year projections, and try to apply them to projecting each game in the upcoming schedule. This will give you a current standard deviation to use. Take the average points per game and subtract one standard deviation. This will give you the player’s floor. In a couple of my leagues last year, the average points per team per week was around 95 using standard scoring, non-PPR. Using this drafting strategy, your draft should basically be a race to 96 points as your team’s average. We’re looking at floor, however. To get that, let’s take one standard deviation from each position on a standard roster away from the average score to get the floor we need to shoot for.  To do that, let’s just use the average positional standard deviation. (QB – 9.7, RB – 6.54, WR – 7.06, TE – 4.88, FLEX – 6.75 K – we’ll use 4, DST – we’ll use 5) Remember, since there are 2 RB and WR, we have to use that number twice. Doing this, we get 58.53. Now we subtract 58.53 from 96 to get 37.47. This is the floor we need to shoot for in our draft. You can’t control your schedule, but you should be able to put together a team that has a good shot week in and week out.  You will probably be hard pressed to field a team with a projected 96 points as their floor, but remember, the floor is the expected WORST case scenario. Just get a couple players to perform at their mean or above and you’re quickly at or past your league’s mean score.

So now that we know how to draft a team with a good shot at winning week in and week out, there are a couple caveats to this approach. First off, standard deviation by definition is greatly affected by outlier performances. Stars are going to have larger standard deviations because they are more likely to go off, thus inflating their average and therefore, standard deviation. Don’t let this shy you away from them. The other side of this coin is that they have a huge ceiling. Remember, the player will outscore their floor 84% of the time, their average 50% of the time and their ceiling 14% of the time. The other thing to keep in mind is this strategy will leave you with a lot of boring old very good 
players. They tend to have the least amount of fluctuation in their game. These are the running backs who just go out and score 10 fantasy points per week one way or another. While they are unsexy, there is a lot to be said for this kind of player. As the numbers show, this is the kind of player who will rarely kill you. They are also less likely to give you the crazy week, but they will almost always help you win.

Below, I've posted the average projected score per game per player for this year along with their standard deviation from last year. For rookies, I’ll just use last year’s average standard deviation. Along with those numbers, I’ll post the +/- 1 standard deviation score to help you in your drafting. Take a look at the numbers, and work with them to find the best combination of safety vs. upside. Doing this will help take a lot of the guesswork out of your team and should win you a lot of games. Remember, the floor represents the players' floor for 84% of the games, and the ceiling is what they will exceed 16% of the time.

As always, thanks for reading and good luck!


 QB:

Rank
Player
St Dev
Avg
Floor
Ceiling
1
Peyton Manning QB DEN
12.78
27.10
14.32
39.88
2
Drew Brees QB NO
12.20
24.97
12.77
37.18
3
Aaron Rodgers QB GB
12.20
24.01
11.81
36.21
4
Nick Foles QB PHI
15.20
23.05
7.85
38.25
5
Matthew Stafford QB DET
9.12
22.12
13.01
31.24
6
Colin Kaepernick QB SF
10.15
22.00
11.84
32.15
7
Matt Ryan QB ATL
6.92
21.40
14.47
28.32
8
Tony Romo QB DAL
10.73
21.06
10.33
31.79
9
Andrew Luck QB IND
8.94
20.97
12.03
29.91
10
Cam Newton QB CAR
9.06
20.94
11.89
30.00
11
Robert Griffin III QB WAS
9.70
20.79
11.09
30.49
12
Russell Wilson QB SEA
7.75
20.73
12.98
28.48
13
Tom Brady QB NE
10.78
20.55
9.77
31.33
14
Philip Rivers QB SD
9.19
20.49
11.30
29.68
15
Ben Roethlisberger QB PIT
9.82
20.02
10.19
29.84
16
Jay Cutler QB CHI
8.10
19.66
11.57
27.76
17
Ryan Tannehill QB MIA
7.33
18.56
11.23
25.89
18
Andy Dalton QB CIN
11.73
18.49
6.77
30.22
19
Sam Bradford QB STL
9.70
18.35
8.65
28.05
20
Alex Smith QB KC
21.11
18.05
-3.06
39.15
21
Josh McCown QB TB
14.09
18.04
3.95
32.14
22
Carson Palmer QB ARI
8.74
17.23
8.49
25.98
23
Johnny Manziel QB CLE
9.70
16.80
7.10
26.50
24
Teddy Bridgewater QB MIN
9.70
15.87
6.17
25.57
25
Jake Locker QB TEN
9.70
15.73
6.03
25.43
26
Joe Flacco QB BAL
6.52
15.66
9.13
22.18
27
Eli Manning QB NYG
9.27
14.74
5.47
24.01
28
EJ Manuel QB BUF
7.64
14.68
7.04
22.31
29
Ryan Fitzpatrick QB HOU
11.22
11.66
0.44
22.88
30
Matt Schaub QB OAK
10.44
11.63
1.18
22.07





 RB:

Rank
Player
Std Dev
Avg
Floor
Ceiling
1
Jamaal Charles RB KC
11.49
16.46
4.97
27.95
2
Matt Forte RB CHI
8.41
15.75
7.34
24.16
3
LeSean McCoy RB PHI
9.44
15.73
6.29
25.18
4
Adrian Peterson RB MIN
9.49
14.39
4.90
23.87
5
Eddie Lacy RB GB
7.33
13.55
6.22
20.88
6
DeMarco Murray RB DAL
8.03
13.41
5.38
21.44
7
Montee Ball RB DEN
5.27
13.22
7.95
18.49
8
Arian Foster RB HOU
6.54
13.15
6.61
19.69
9
Giovani Bernard RB CIN
5.76
12.92
7.17
18.68
10
Marshawn Lynch RB SEA
8.28
12.51
4.23
20.79
11
Le'Veon Bell RB PIT
4.74
12.43
7.69
17.17
12
Andre Ellington RB ARI
6.71
11.89
5.19
18.60
13
Alfred Morris RB WAS
4.75
11.83
7.08
16.57
14
Toby Gerhart RB JAC
6.54
11.74
5.20
18.28
15
Bishop Sankey RB TEN
6.54
11.52
4.98
18.06
16
Zac Stacy RB STL
8.25
11.46
3.21
19.70
17
Doug Martin RB TB
6.54
11.09
4.55
17.63
18
Joique Bell RB DET
7.10
10.86
3.75
17.96
19
Ryan Mathews RB SD
6.42
10.82
4.39
17.24
20
Reggie Bush RB DET
8.03
10.58
2.55
18.61
21
Rashad Jennings RB NYG
8.94
10.21
1.26
19.15
22
Chris Johnson RB NYJ
7.74
10.19
2.45
17.93
23
Shane Vereen RB NE
7.40
10.13
2.73
17.52
24
Stevan Ridley RB NE
7.31
9.81
2.50
17.12
25
C.J. Spiller RB BUF
6.88
9.69
2.81
16.56
26
Frank Gore RB SF
6.39
9.68
3.29
16.07
27
Trent Richardson RB IND
3.83
8.95
5.12
12.78
28
Ben Tate RB CLE
6.99
8.91
1.92
15.90
29
Fred Jackson RB BUF
5.61
8.84
3.23
14.44
30
Steven Jackson RB ATL
5.33
8.76
3.43
14.09
31
Bernard Pierce RB BAL
6.54
8.72
2.18
15.26
32
Knowshon Moreno RB MIA
8.36
8.54
0.18
16.90
33
Maurice Jones-Drew RB OAK
4.92
8.39
3.48
13.31
34
Terrance West RB CLE
6.54
8.31
1.77
14.85
35
Pierre Thomas RB NO
5.96
8.25
2.29
14.20
36
Ray Rice RB BAL
6.15
8.22
2.06
14.37
37
DeAngelo Williams RB CAR
4.82
7.96
3.15
12.78
38
Danny Woodhead RB SD
5.41
7.65
2.24
13.05
39
Devonta Freeman RB ATL
6.54
7.56
1.02
14.10
40
Jeremy Hill RB CIN
6.54
7.05
0.52
13.59
41
Lamar Miller RB MIA
4.42
6.93
2.51
11.34
42
Tre Mason RB STL
6.54
6.92
0.38
13.46
43
LeGarrette Blount RB PIT
8.92
6.87
-2.05
15.79
44
Khiry Robinson RB NO
6.54
6.81
0.27
13.34
45
Darren Sproles RB PHI
6.96
6.70
-0.26
13.66
46
Christine Michael RB SEA
6.54
6.54
0.00
13.08
47
Stepfan Taylor RB ARI
6.54
6.52
-0.02
13.06
48
Charles Sims RB TB
6.54
6.06
-0.48
12.60
49
Chris Ivory RB NYJ
6.61
5.97
-0.64
12.59
50
Darren McFadden RB OAK
6.41
5.89
-0.52
12.29
51
Dexter McCluster RB TEN
6.54
5.71
-0.82
12.25
52
James White RB NE
6.54
5.43
-1.11
11.97
53
Carlos Hyde RB SF
6.54
5.36
-1.18
11.90
54
Ahmad Bradshaw RB IND
6.54
5.34
-1.20
11.88
55
Roy Helu RB WAS
6.54
5.27
-1.27
11.80




 WR:

Rank
Player
Std Dev
Avg
Floor
Ceiling
1
Calvin Johnson WR DET
12.50
14.90
2.41
27.40
2
Demaryius Thomas WR DEN
8.70
14.15
5.45
22.84
3
Brandon Marshall WR CHI
7.00
12.79
5.79
19.79
4
Dez Bryant WR DAL
7.75
12.54
4.78
20.29
5
Randall Cobb WR GB
6.75
12.13
5.38
18.88
6
A.J. Green WR CIN
8.70
12.12
3.42
20.82
7
Antonio Brown WR PIT
8.70
11.50
2.80
20.21
8
Julio Jones WR ATL
6.34
11.23
4.90
17.57
9
Jordy Nelson WR GB
7.28
11.17
3.89
18.45
10
Alshon Jeffery WR CHI
11.23
11.11
-0.12
22.34
11
Larry Fitzgerald WR ARI
6.25
10.27
4.02
16.53
12
Vincent Jackson WR TB
9.10
10.02
0.92
19.12
13
Michael Crabtree WR SF
3.88
9.92
6.03
13.80
14
Michael Floyd WR ARI
6.68
9.87
3.19
16.54
15
Andre Johnson WR HOU
10.77
9.71
-1.06
20.49
16
Keenan Allen WR SD
6.31
9.48
3.18
15.79
17
Wes Welker WR DEN
5.10
9.32
4.22
14.41
18
Pierre Garcon WR WAS
7.66
9.08
1.42
16.74
19
Cordarrelle Patterson WR MIN
6.64
9.04
2.40
15.68
20
Victor Cruz WR NYG
7.06
8.90
1.84
15.96
21
Terrance Williams WR DAL
6.78
8.89
2.11
15.67
22
Percy Harvin WR SEA
7.06
8.84
1.77
15.90
23
Golden Tate WR DET
6.93
8.67
1.74
15.60
24
DeSean Jackson WR WAS
9.77
8.67
-1.11
18.44
25
Eric Decker WR NYJ
11.93
8.58
-3.36
20.51
26
Torrey Smith WR BAL
8.93
8.55
-0.38
17.48
27
Roddy White WR ATL
6.70
8.45
1.75
15.15
28
Riley Cooper WR PHI
9.85
8.42
-1.43
18.28
29
Rueben Randle WR NYG
5.86
8.31
2.45
14.17
30
Emmanuel Sanders WR DEN
4.59
8.29
3.70
12.89
31
Julian Edelman WR NE
7.57
8.13
0.56
15.70
32
Mike Wallace WR MIA
7.08
8.02
0.95
15.10
33
Marvin Jones WR CIN
6.34
7.98
1.64
14.32
34
Marques Colston WR NO
7.16
7.98
0.82
15.13
35
Kenny Stills WR NO
7.46
7.68
0.22
15.14
36
Kendall Wright WR TEN
5.16
7.61
2.45
12.77
37
Sammy Watkins WR BUF
7.06
7.52
0.46
14.59
38
Justin Hunter WR TEN
7.06
7.46
0.40
14.53
39
T.Y. Hilton WR IND
9.78
7.35
-2.44
17.13
40
Mike Evans WR TB
7.06
7.33
0.27
14.39
41
Jeremy Maclin WR PHI
7.06
7.29
0.23
14.35
42
Tavon Austin WR STL
7.06
7.21
0.14
14.27
43
Dwayne Bowe WR KC
4.18
7.15
2.98
11.33
44
Kelvin Benjamin WR CAR
7.06
7.08
0.01
14.14
45
Reggie Wayne WR IND
7.06
7.07
0.01
14.14
46
Doug Baldwin WR SEA
4.47
7.02
2.55
11.49
47
Brandin Cooks WR NO
7.06
6.93
-0.13
13.99
48
Brian Hartline WR MIA
5.36
6.78
1.42
12.14
49
Anquan Boldin WR SF
8.95
6.66
-2.29
15.61
50
Jerricho Cotchery WR CAR
7.00
6.58
-0.41
13.58
51
Rod Streater WR OAK
5.45
6.54
1.09
11.99
52
DeAndre Hopkins WR HOU
5.03
6.38
1.35
11.42
53
Hakeem Nicks WR IND
5.05
6.35
1.30
11.39
54
Malcom Floyd WR SD
6.68
6.27
-0.41
12.94
55
Jarrett Boykin WR GB
5.51
6.21
0.69
11.72
56
James Jones WR OAK
6.34
6.04
-0.29
12.38
57
Robert Woods WR BUF
4.42
6.01
1.59
10.43
58
Harry Douglas WR ATL
6.90
5.91
-0.98
12.81
59
Cecil Shorts WR JAC
7.06
5.86
-1.20
12.92
60
Danny Amendola WR NE
6.41
5.68
-0.73
12.09





 TE:

Rank
Player
Std Dev
Avg
Floor
Ceiling
1
Jimmy Graham TE NO
8.29
13.24
4.95
21.53
2
Julius Thomas TE DEN
7.23
10.48
3.25
17.71
3
Vernon Davis TE SF
8.27
9.46
1.19
17.73
4
Rob Gronkowski TE NE
4.88
8.81
3.93
13.69
5
Jason Witten TE DAL
7.01
8.61
1.60
15.62
6
Jordan Cameron TE CLE
7.31
7.59
0.28
14.90
7
Ladarius Green TE SD
4.88
7.35
2.47
12.23
8
Greg Olsen TE CAR
3.65
7.30
3.65
10.96
9
Zach Ertz TE PHI
4.98
7.05
2.07
12.03
10
Dennis Pitta TE BAL
3.26
6.79
3.53
10.05
11
Kyle Rudolph TE MIN
4.88
6.78
1.90
11.66
12
Eric Ebron TE DET
4.88
6.78
1.90
11.66
13
Jordan Reed TE WAS
4.88
6.72
1.84
11.60
14
Dwayne Allen TE IND
4.88
6.23
1.35
11.11
15
Martellus Bennett TE CHI
4.66
6.21
1.56
10.87
16
Antonio Gates TE SD
5.30
6.05
0.75
11.35
17
Delanie Walker TE TEN
4.22
5.77
1.55
9.98
18
Jared Cook TE STL
6.37
5.44
-0.93
11.81
19
Charles Clay TE MIA
6.18
5.35
-0.83
11.52
20
Heath Miller TE PIT
6.95
5.33
-1.61
12.28
21
Brent Celek TE PHI
4.26
5.24
0.98
9.50
22
Jace Amaro TE NYJ
4.88
5.13
0.25
10.01
23
Garrett Graham TE HOU
5.67
5.11
-0.56
10.77
24
Marcedes Lewis TE JAC
4.22
5.09
0.87
9.31
25
Mychal Rivera TE OAK
3.46
4.63
1.17
8.10