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Player Evaluation
Posted by Chris Liss at 3/28/2008 6:12:00 PM
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Someone posted a question about this in the forums, and I figured it would be useful to address it here, too:

The first thing we do when we evaluate a player is figure out what his numbers will look like. We create a projection for him. Everyone does this to an extent - you look at Adam Dunn and think - he'll probably hit 40, but his average could be around .250. (After I wrote that, I checked out Erickson's projection for him, and it turns out those are his projections exactly!).

But once we have everyone's projected (estimated) numbers, we still have the problem of translating those numbers into a ranking (or dollar value). You can just eyeball it and say you'd rather have Adam Dunn than Andruw Jones, but it gets tricky when we compare different kinds of players. Let's take Ryan Howard's stats from last year - 47 HR, 136 RBI, 94 R, 1 SB, .268 in 529 AB, and Ichiro's: 6 HR, 68 RBI, 111 R, 37 SB, .351 in 678 AB.

Which numbers are worth more? What basis do we even have for answering that? I guess you could eyeball it and decide which one was more of an outlier, but that's imprecise, and maybe you'd pick the wrong one.

To do this more precisely you need to take into account two factors: (1) Value Above Replacement and (2) Standard Deviation

The first one is easy enough to understand. If a player in a 12-team mixed league hits 12 homers, how much is that really helping you? Let's say there are 14 offensive players per team. That's 168 total offensive players. So players 169-190 or so are what we call "replacement value".

Those are the guys on your bench or on the waiver wire. Let's say the average HR total for those players is 10. So your 12 HR guy is really only getting you 2 HRs in that category. If you had a 3 HR guy, he'd be giving you -7 HRs. Remember every roster spot on your team has an opportunity cost. (Even before taking position scarcity into account).

OK, so we can do this value above replacement calculation for each category, pitching and hitting. But we still have a problem. Because let's say Ryan Howard is 37 HRs about replacement, but 12 points below replacement in batting average. Let's say he's plus 60 in RBI, plus 35 in runs, -6 in steals. And let's say Ichiro is plus-76 points in batting average (adjusted for his 678 at-bats which is about 120 percent of the average starter's). And Ichiro is plus 45 runs, minus 2 HR and minus 10 RBI. Which player is better, Howard or Ichiro?

There's no way to know without being able to compare ACROSS categories. How do we know if 47 HRs is worth more than a .351 average in 678 at-bats? The answer: Standard deviation.

Let's take last year's stats as an example: If we take into account the stats of every player in your league, we can come up with the standard deviation (the average amount by which a player differs from the mean) in each category). In other words, if there are 168 hitters drafted (14 hitters, 12 teams), then among those hitters, there's a mean (or average for each category). It might be 20 HR, 80 RBI, 85 R, .280, or something like that. Now if the average amount of home runs is 20, the standard deviation in home runs is the average amount a player differs from 20 home runs. In Howard's case, that number was 27. He hit 27 more home runs than the average. In Ichiro's case, it was 14. he hit 14 homers less than the average. But other players hit 21, just one off the average. Some hit 16, four off the average. If you average out all those differences (27, 14, 1, 4, etc.) for all 168 players, then you find the standard deviation for home runs. Let's say is was 8.

Now remember a player's stats don't start to count positively until they've done better than what's freely available on the waiver wire, i.e., until they are better than replacement value. And in a 12-team mixed league, we argued that the average replacement player was good for roughly 10 home runs. So Howard, who hit 47, was 37 home runs better than replacement. And how good is 37 better than replacement?

We can figure that out by asking the question: "How many standard deviations above replacement is it?" The answer: 37/8 or a little more than 4.5. So Howard's home runs are worth 4.5 on our scale. Ichiro batted .351 in 678 at-bats. How much better was that than replacement? First, we'd look at what the replacement batting average was - .275. So .351 -.275 = 76 points. Then we'd figure out what the average of 168 drafted players was. We came up with .280. We'd need to find the standard deviation - how much is the average difference from .280? Ichiro differs by 71, Howard differs by 12, other players differ by a few, let's say the average is 15 points. (I'm making these numbers up, but just roll with me here). It's 15 points, and Ichiro is 76 above replacement, so he gets 76/15 - roughly five points for average. But, he also has more at-bats than the average drafted player who has 500 or so. So that five points needs to be multiplied by 678/500. So Ichiro gets closer to seven points for batting average.

These numbers aren't precise (I'm making up the SD as we go for the purposes of this question) - though I do think Ichiro's contribution to batting average was probably bigger than Howard's to HRs in last year's context, but you get the idea. You need to compare players category by category in the context of the league to know which is more valuable. It's not simple, but understanding how it works can help you from underestimating average or overestimating other categories - they're all worth the same amount, and the question is really - how much of an outlier is each contribution relative to the rest of the league.

Once you get the number of standard deviations above replacement for each player for each category you can add them up. In Ichiro's case, it might be (and I'm making this up, too): +7 for average, -1 for HRs, -.5 for RBI +3 for runs, +4 for SB. You get 12.5. You can generate a total for every hitter.

To convert that into dollar values, you figure out the total amount of money spent on hitting in your $260 league - let's say $160 * 12 = 1920. That means the total dollar values of the top 168 players need to equal 1920. You add up all the totals (Ichiro's was 12.5) and get a number. Let's say it's 600. You divide 1920 by 600 which is 3.2. So you multiply each player's raw total by 3.2 to get his dollar. 12.5 * 3.2 = $40 in a 12-team mixed league. (Of course, I'm making these numbers up).

Now there are a lot of other components I'm leaving out like position scarcity and projection reliability (Derek Jeter's projections are far more reliable than Justin Upton's, for example), but this at least gives us the ability to compare and evaluate different kinds of players on one cheat sheet.


Excellent article!
Posted by Rugby12901 at 3/28/2008 6:29:00 PM
Based upon Erickson's projections (which I have unbelievable faith in) I have done a bunch of drafts which show the following players that have more value in straight drafts than they are going for:Ichiro, Smoltz, Chris Young (SD), Capps, Figgins, Helton, Ibanez, Bay, Hill, Fukodome, Lowe, Carlos Guillen, Harang, Billingsley. Players that are going for too much: Manny Ramirez, David Ortiz, Sizemore, Chipper Jones, Felix Hernandez, Reyes, Ordonez, Fielder, Beltran, Tulowitzki, Andruw Jones, Beckett, Vernon Wells. Just some observations, I have total faith in you guys.
Posted by kevinccp at 3/28/2008 7:48:00 PM
Oh and Verlander has been a hot pick, I worry he'll lose focus when he's up by 5 runs after the second inning.
Posted by kevinccp at 3/28/2008 7:50:00 PM
I have a lot of respect for both you and Jeff but I am not at all a fan of projections. I have always let history be my guide and draft based on feel and grouping players into tiers than going by predicted numbers.

I believe it is fool-hearty, and arguably arrogant, to draft or argue a player's value based on numbers that one has predicted.

Now, I might glance at a sophisticated system like PECOTA because it is interesting, but I generally pay no attention to projected numbers found in magazines and blogs. They mean absolutely nothing.

I just shake my head when I hear someone say "actually, I have him projected for..." Like this is some kind of evidence of something.
Posted by skinsnut at 3/28/2008 8:19:00 PM
Just curious, but how do you know how to value a guy if you don't have any idea as to what his stats could be?
Posted by vtadave at 3/28/2008 8:35:00 PM
I suppose then you'll have the following on your team: randy johnson, mike sweeney, mike piazza, kelvim escobar, hoffman, pettite, eric chavez, garciaparra, marcus giles.. and many others that I'm sure others will add to the list. You have to look at projections, if you think Vernon Wells will be better than Rios or Halladay will be better than Chris Young, your just kidding yourself.
Posted by kevinccp at 3/28/2008 8:51:00 PM
I am doing just fine in my one and only league (don't believe in poleagueamy) thanks. All I am saying is I think predicting specific stats is junk science. And when I said history I meant a guy's track record. I am fully aware that Randy Johnson is past his prime...again, thanks.

Posted by skinsnut at 3/28/2008 9:19:00 PM
vtadave- That's the point. I have an IDEA of what the guy is going to do and that is all I need. Instead of putting down Vladmir Guerrero down for 29 home runs and acting like that is set in stone, I assume he will be around 30, give or take a few. I base this on his track record, age, and other factors that everyone considers.

Just saying it is kind of silly to sit down and write exact numbers for someone when all you need is a broader idea of his likely performance and focus more on grouping players accurately. Just my opinion...I knew it would not be a popular one.
Posted by skinsnut at 3/28/2008 9:38:00 PM
How long have you been playing fantasy skin?
Posted by LABLUE at 3/29/2008 5:06:00 AM
Been playing for 8 years.
Posted by skinsnut at 3/29/2008 5:21:00 AM
I understand the idea of just making a list intuitively because any number you put down is just a guess. I'm not sure it isn't better to do it intuitively because you prevent a false sense of certainty that the numbers seem to provide. But this article is more about a quantifiable way to compare players across categories. You can eyeball it and just do it on feel. I know some old school guys in my home league who do that and could hang with any of the experts in the industry. It's like poker - some guys do it by the math and others play by feel.
Posted by cliss at 3/29/2008 10:35:00 AM
Skin - I take no offense at that at all. You're right about the notion of projections - they're less a science and more an art, even when it's a well thought-out system like PECOTA. And I actually agree with your general point - the idea here is to give a general idea of what a player is likely to do, rather than focus upon a specific number. I think the real value in projections is to identify a trend with a player, either on the rise or on the decline.
Posted by Erickson at 3/29/2008 12:32:00 PM
Chris and Jeff - Thanks for the feedback. I am a big fan of both of your shows and your contrasting styles.

To be fair, maybe my approach wouldn't work as well in a roto league, I play in a points system...yet again I am in the minority.

Just not many that play in a points league (roto overvalues SBs and SVs) and that chose it to be their only one (more challenging and rewarding IMO)

Posted by skinsnut at 3/29/2008 1:50:00 PM
Thanks for the article Chris-it was really enlightening. Tomorrow I'm participating in an auction draft (my first auction in forever) with 20 teams and 25 man rosters. It's H2H using points. I used Rotowire to project the points for each player like I always do (works great), then had to try and develop a method to translate the points into dollar values, so your article is of great interest.
Posted by Thomas10966 at 3/29/2008 2:07:00 PM

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