formula help

[United_I_Stand]

Well I basically decided to do some work on this for my own interest, to find a fairly simple but effective way of calculating player values in different systems.

So I used the calculation I suggested above above, ie.;

value created in a stat = (score in stat – mean of that stat)/(standard deviation of stat)

Obviously you need to get a hold of mean and standard deviation values. A point on that, subtracting the mean is not strictly necessary, in doing so you get an indication of value created or lost in that stat over a replacement player, but when comparing two players the difference would cancel out. It basically gives a datum (zero-line) at average value, that theoretically could make it possible to compare apples and pears (or in our case hitters and pitchers).

I created my list of values of mean and standard deviation from this years stats, which I took from J35J / Jason’s excellence spreadsheet recently posted on this forum (http://www.fantasybaseballcafe.com/foru ... p?t=240400). It’s an excellent resource which I really appreciate if you see this Jason.

I limited the stats to standard 5x5 to get a baseline to see if the maths work out. I limited the field to all hitters with 450+ ab’s (300+ for catchers). Starters with 100 IP’s and all relief pitchers in the spreadsheet (as it was already limited to the only 60 commonly fantasy relevant pitchers)

Furthermore I haven’t treated each stat exactly the same.

For hitting I have simply used the formula above for Runs, Hr’s RBI’s and SB’s, however as AVG is not a cumulative stat I believe it should be treated slightly different. For instance, Cano and Jeter had AVG’s of .342 and .343 respectively, but as Jeter had 141 extra at bats, his contribution would have a greater impact, making him more valuable. Therefore for AVG I have used the above formula, but then adjusted it by multiplying by the ratio of (players at bats) / (mean at bats).

For pitching it can be seen that ERA and WHIP are both similar cases to AVG and have been treated as such (adjusted for Innings pitched), with the exception that the value has been reversed (ei. a decrease is better!). However as many leagues are limited innings, and a good manager would normally use the entire quota (or near too) I have also treated K’s SV’s and Win’s the same way. My explanation of why is as follows, a starting pitcher who gets 100k’s in 200 ip’s has lost you value, because he has limited your ability to succeed in strikeouts, whereas a reliever who gets 100k’s in 60ip has gained you value, therefore using just the cumulative number would not give a fair reflection of the value added or lost. To take this into account I have simply replaced the K SV and Win stats and replaced them with K/9 SV/9 and Win/9.

For clarity here is a full summary of the calculations used

Hitting:
Runs Value = (runs – mean)/ standard deviation
HR Value = (HR’s – mean)/ standard deviation
RBI Value = (RBI’s – mean)/ standard deviation
SB Value = (SB’s – mean)/ standard deviation
AVG Value = (AB’s / “AB mean”) * (AVG – mean)/ standard deviation

Pitching
ERA Value = (IP / “IP mean”) * (mean - ERA)/ standard deviation
WHIP Value = (IP / “IP mean”) * (mean - WHIP)/ standard deviation
K/9 Value = (IP / “IP mean”) * (K/9 – mean)/ standard deviation
Wins/9 Value = (IP / “IP mean”) * (Wins/9 – mean)/ standard deviation
SV/9 Value = (IP / “IP mean”) * (SV/9 – mean)/ standard deviation

Total Value = Sum of individual components for that player

And the various values used in this format:
Catergory = mean, standard deviation

Runs = 77.4, 21.9
HR’s = 18.4, 11.3
RBI’s = 75.0, 24.9
SB’s = 9.5, 12.6
AVG = .2829, .0247

AB’s = 516.7

ERA = 4.003, 1.104
WHIP = 1.317, 0.188
K/9 = 7.266, 2.105
SV/9 = 0.778, 1.633
Wins/9 = 0.541, 0.189

IP = 140.3

Now for the interesting part, verification, I now used these formulas on this years stats to see how it would rank the players, here’s the top 101:

Rank Value Position Player
1 8.92 1B Albert Pujols
2 8.31 1B Ryan Howard
3 7.51 SS Jose Reyes
4 7.35 2B Alfonso Soriano
5 7.28 SP Johan Santana
6 7.22 SS Derek Jeter
7 6.92 OF Matt Holliday
8 6.87 1B David Ortiz
9 6.52 2B Chase Utley
10 6.44 OF Lance Berkman
11 6.40 OF Jermaine Dye
12 6.31 OF Miguel Cabrera
13 6.29 3B Garrett Atkins
14 6.27 OF Carlos Beltran
15 6.23 OF Vladimir Guerrero
16 6.01 OF Carlos Lee
17 5.81 RP Joe Nathan
18 5.74 1B Justin Morneau
19 5.70 3B Alex Rodriguez
20 5.50 SP Francisco Liriano
21 5.45 OF Carl Crawford
22 5.28 3B David Wright
23 4.95 SS Jimmy Rollins
24 4.95 DH Travis Hafner
25 4.87 SS Hanley Ramirez
26 4.83 OF Grady Sizemore
27 4.64 RP Takashi Saito
28 4.63 OF Vernon Wells
29 4.60 SS Miguel Tejada
30 4.55 1B Paul Konerko
31 4.55 OF Ichiro Suzuki
32 4.47 RP Jonathan Papelbon
33 4.30 1B Jim Thome
34 4.19 RP J.J. Putz
35 4.17 OF Jason Bay
36 4.16 OF Andruw Jones
37 4.15 OF Bobby Abreu
38 4.09 OF Raul Ibanez
39 4.00 3B Aramis Ramirez
40 3.90 SS Rafael Furcal
41 3.90 SS Carlos Guillen
42 3.78 RP B.J. Ryan
43 3.74 OF Johnny Damon
44 3.66 RP Francisco Rodriguez
45 3.45 SP Jered Weaver
46 3.35 RP Billy Wagner
47 3.34 SP Chris Carpenter
48 3.25 RP Francisco Cordero
49 3.22 OF Manny Ramirez
50 3.16 RP Mariano Rivera
51 3.05 1B Mark Teixeira
52 3.04 RP Chad Cordero
53 2.95 SP Mike Mussina
54 2.93 RP Michael Young
55 2.84 OF Gary Matthews Jr.
56 2.77 CA Joe Mauer
57 2.75 2B Michael Cuddyer
58 2.60 OF Chipper Jones
59 2.55 RP Joel Zumaya
60 2.52 SP John Smoltz
61 2.50 SP Brandon Webb
62 2.49 RP Cla Meredith
63 2.47 SP Carlos Zambrano
64 2.42 SP Roger Clemens
65 2.42 OF Torii Hunter
66 2.39 RP Dennys Reyes
67 2.36 RP Huston Street
68 2.34 1B Carlos Delgado
69 2.34 SS Troy Glaus
70 2.30 2B Dan Uggla
71 2.30 SP Scott Kazmir
72 2.29 SS Bill Hall
73 2.22 3B Scott Rolen
74 2.22 RP Scot Shields
75 2.20 1B Jason Giambi
76 2.18 1B Lyle Overbay
77 2.16 3B Ryan Zimmerman
78 2.15 DH Frank Thomas
79 2.14 SP Roy Oswalt
80 2.12 RP Chris Ray
81 2.01 OF Juan Pierre
82 1.99 SP C.C. Sabathia
83 1.97 2B Chone Figgins
84 1.93 RP Tom Gordon
85 1.93 SP Chris Young
86 1.92 2B Freddy Sanchez
87 1.90 OF Magglio Ordonez
88 1.88 RP Brian Fuentes
89 1.87 RP Trevor Hoffman
90 1.87 RP Mike Gonzalez
91 1.84 1B Nick Johnson
92 1.77 SP Roy Halladay
93 1.76 RP Akinori Otsuka
94 1.74 RP Fernando Rodney
95 1.71 OF Mike Cameron
96 1.67 1B Adam LaRoche
97 1.66 2B Ray Durham
98 1.66 2B Felipe Lopez
99 1.65 OF Nick Swisher
100 1.62 SP Curt Schilling
101 1.61 CA Brian McCann

Not perfect. I notice a potential bias towards closers, and a definite one against starting pitching, but at least within a single position, saying hitting or starting pitching I think it makes a fair comparison of this seasons performance.

Obviously it also doesn’t take into any account positional scarcity either.

For all my complication through over explanation it is actually a quick and simple thing to do. It should be easy to apply to other non-standard stats, and gives a fair weighting.

I mainly did this for my own interest, but if there are any comments or things people notice, suggestions even, I’d be pleased to hear them.

Also I have given a little consideration to positional scarcity for hitting, and roster spot premium for pitching (i.e. 17 relivers each giving 70 innings would give you your 1250 high quality innings. it is the lack of roster spots that decreases their value and increases a starters value).

Any ideas on how to deal with these factors would be very interesting.

Iain (UIS)

p.s. (yes i know i am hopelessly geeky - and sorry if this recovers previous topics, i'm new, i did it mostly for my own interest, and if it bores you, you can skip it)

[markj11]

Thanks. Heres my top 60 hitters after adding all categories.

Code: Select all

18.174   Jose Reyes
17.773   Albert Pujols
15.069   Derek Jeter
14.902   Miguel Cabrera
14.636   Garrett Atkins
14.126   Carl Crawford
14.076   Matt Holliday
13.801   Grady Sizemore
13.591   David Ortiz
13.370   Ryan Howard
12.966   Jimmy Rollins
12.859   Hanley Ramirez
12.730   Vladimir Guerrero
12.620   Ichiro Suzuki
12.540   Lance Berkman
12.522   Chase Utley
11.980   Carlos Lee
11.970   Rafael Furcal
11.935   David Wright
11.783   Joe Mauer
11.695   Carlos Guillen
11.592   Carlos Beltran
11.426   Vernon Wells
11.415   Alfonso Soriano
11.226   Juan Pierre
11.121   Jermaine Dye
11.081   Justin Morneau
10.894   Bobby Abreu
10.677   Travis Hafner
10.368   Miguel Tejada
10.275   Aramis Ramirez
10.267   Gary Matthews Jr.
9.742   Johnny Damon
9.641   Michael Young
9.402   Todd Helton
9.341   Alex Rodriguez
9.244   Freddy Sanchez
9.166   Raul Ibanez
9.148   Manny Ramirez
8.854   Jason Bay
8.586   Paul Konerko
8.549   Nick Johnson
8.362   Mark Teixeira
8.147   Dave Roberts
7.878   Ray Durham
7.882   Jim Thome
7.758   Chipper Jones
7.666   Scott Rolen
7.376   Omar Vizquel
7.208   Michael Cuddyer
7.045   Victor Martinez
7.032   Orlando Hudson
6.991   Ryan Zimmerman
6.901   Mike Cameron
6.665   Chone Figgins
6.577   Kenny Lofton
6.506   Andruw Jones
6.478   Edgar Renteria
6.306   Brian McCann
6.087   Nomar Garciaparra

[United_I_Stand]

Glad it helped!

theres some definite eye openers in that list of values.

crawford (21 to 6), carlos guillen (41 to 21), suzuki (31 to 14), pierre (81 to 25) and dave roberts, lofton and renteria ranking in the top 60 hitters for the year!

nice to see pujols still at the top though (EDIT: i somehow missed reyes at the top of the list, d'oh - another eye opener i guess)

[markj11]

Glad it helped!

theres some definite eye openers in that list of values.

crawford (21 to 6), carlos guillen (41 to 21), suzuki (31 to 14), pierre (81 to 25) and dave roberts, lofton and renteria ranking in the top 60 hitters for the year!

nice to see pujols still at the top though (EDIT: i somehow missed reyes at the top of the list, d'oh - another eye opener i guess)

How could I make SB a little less valuable?

[United_I_Stand]

well if you are applying the formula for all 11 stats sb's shouldn't be having a large effect anyhow....

...but you could just give it a factor, put a *0.5 in there or something like that on the sb calc. My guess is it doesn't make a huge difference.

I don't think that list of players i mentioned have increased value soley because of steals though...

more a case of the stats you're using, 3B and 1B are a big boost ti speesters/lead off hitters, and they also tend to do better then sluggers in strikeouts aswell, with doubles being a wash.

Baically you're system just gives a big bonus to these players over 5x5

[markj11]

Thats were I messed up this past season. I didn't value speedsters but now I see why I didn't do very well.

[bigwords]

For the true quants out there:

After crunching the numbers, I have an idea of player value in my league. I've used a coefficient to approximate the dollar value of each of these players.

Looking back at the auction values for the players last year, and factoring in the 2006 season performance, I can make an educated guess about each of these players 2007 auction values.

My question is, now that I have their value and their cost, is there a way—a formula—to determine how I can most efficiently allocate my spending? Is there a way to determine whether it's worth getting say, Pujols and Renteria or Konerko and Rollins? Obviously, because the choice is limited in this scenario, I can do the mental arithmetic. But when I open it up to 9 different positions/cost choices, I go a little bit insane.

Am I being a little too ambitious here?

[Tavish]

For the true quants out there:

After crunching the numbers, I have an idea of player value in my league. I've used a coefficient to approximate the dollar value of each of these players.

Looking back at the auction values for the players last year, and factoring in the 2006 season performance, I can make an educated guess about each of these players 2007 auction values.

My question is, now that I have their value and their cost, is there a way—a formula—to determine how I can most efficiently allocate my spending? Is there a way to determine whether it's worth getting say, Pujols and Renteria or Konerko and Rollins? Obviously, because the choice is limited in this scenario, I can do the mental arithmetic. But when I open it up to 9 different positions/cost choices, I go a little bit insane.

Am I being a little too ambitious here?

This is when straight-up dollar values can be somewhat misleading. One of the easiest ways to overcome it is to break it down a little further and determine what each player's value is in the different categories. Then you can start to determine where your money is going a little more accurately. It can keep you from overspending is specific areas.

[bigwords]

[quote="Tavish"][quote="bigwords"]This is when straight-up dollar values can be somewhat misleading. One of the easiest ways to overcome it is to break it down a little further and determine what each player's value is in the different categories. Then you can start to determine where your money is going a little more accurately. It can keep you from overspending is specific areas.[/quote]

I agree that straight-up dollar values can be misleading. For one thing, if everyone starts undervaluing a certain category in my league—like steals—it's likely I'd wind up with a roster strong in speed and struggling in the other categories.

But I'm a little skeptical about the narrowing-in-on-category approach too. I think it has two major flaws.

1) Say you were to buy two players. One is extremely strong in HRs (+1) and weak in SBs (0) and the other is very strong in SBs (+1) and weak in HRs (0). From a value standpoint, you've accumulated two players good in each of the category (.5, .5). Problem is, however, you've opened yourself up to great degree of risk. If either of these players gets hurt, suddenly, you have a huge hole in one of these categories (.5, 0). There's something to be said for getting well-rounded players, especially at the start of the season. You can much easier acquire one-dimensional players stars (the Chris Duffy's of the world) later when you're targeting a specific category. But my big point is on the RISK factor.

2) I haven't seen as much research about this as I would like, but I suspect that HRs and SBs are a player's most consistent categories year-to-year. RBIs and Runs, on the other hand, seem to me to be dependent on some factors not wholy correlated to a player's natural talent -- e.g. strength of team batting lineup, manager's choice of lineup position. Certainly, Juan Pierre will always hit first, but as we've seen, you can't always project that D-Lee gets hurt and the Cubs can't knock him home anymore. I'm not arguing that we should throw RBI and Run statistics out the window; I'm just saying that if you want to avoid busts in a draft or auction setting, it's good to place just a small bit of emphasis on those counting categories that don't fluctuate on factors outside of your control.

I think it's important to keep everything in mind—your team needs with the most efficient use of your dollars. I'm just looking for a tool that will help me figure out the latter. In my dream scenario, I have a computer that lets me enter a player I've won at auction and then spits out a new efficiency spending matrix based on value on the board and team needs.

Unfortunately, the only guy I know good with numbers with an MBA to boot, plays in my league.

...Also, not to make this message any longer, but I figured out an easy way to spend just 25% of my budget on pitching and secure 72 of a possible 84 pitching points. Which is one of the reasons I'm especially interested in batting efficiencies. I'm pretty sure I can outbid any other team for the hitters I want. My only question is who do I want.

[bigwords]

Just discovered this good article, which talks about the factors contributing to RBI/Run production:

http://www.protrade.com/content/Display ... 8c73e9&x=x