Player Valuation: How to Create Cheat Sheets and Translate Projections into Dollar Values

This is the second of several installments in RotoWire's guide to winning your fantasy baseball league. The first, Draft Preparation, can be found here.

There are but three components to player valuation: (1) Assessing a player's skills and situation; (2) Creating a stat-line for him for the upcoming season; and (3) Figuring out what those stats are worth in your league's particular context.

1. Assessing Skills and Situation

A number of factors go into deciding whether a player will grow or regress and by how much:

A. Skills

(1) Stats - last year's numbers, three-year averages, BABIP/strand rate to determine how reliable those stats were, home/road splits, left.right splits, steals/caught stealings, K:BB ratio, ground ball/fly ball rates, etc.

(2) Scouting - raw power, speed, defense (affects opportunity), batting eye. For pitchers, velocity, repertoire, command, movement.

(3) Pedigree - Where a player was drafted, how he's viewed in the organization, what the team has already invested in him - this will buy him more patience when he slumps and more chances to succeed.

(4) Health

B. Historical Comps/Career Arcs

A player's personal history isn't always enough, especially with younger players like Mike Trout or Bryce Harper. One must look at how baseball players at certain ages, experience levels and skill sets perform generally.

(1) Age - Hitters typically get better until about age 27 and decline slowly into their mid-to-late 30s until they fall off a cliff. Pitchers often peak early for velocity, but in their early 30s for their overall skills and repertoire.

(2) Experience - Often hitters with 700-1000 career at-bats finally "get it," for example. Pitchers often take a few seasons before the light bulb goes on.

C. Context

(1) Teammates - RBI and runs depend on lineup. Wins depend on run support, ERA and WHIP depend on defense. Who's on the roster and in the organization helps determine playing time, batting-order slot and opportunity.

(2) Park - Stadium dimensions favor different hitters and/or pitchers significantly.

(3) League/Division NL East pitchers have it far easier than AL East ones, for example - in fact the difference is about half a run in ERA.

2. Creating a 2013 Stat-Line

Once you've gathered the relevant facts about a player's skills and context, you might want to translate that into a statistical line for the upcoming season. There are two kinds of stastical lines one can create, and each has its merits and flaws.

(A) Projections - a player is given a stat line that's the average of his many possible 2013 seasons. It's his 50th percentile season, neither exceeding nor falling short of what his skill set and situation likely portend. The virtue of doing projections for every player is the process is ostensibly unbiased - i.e., you give everyone his middle-of-the-road season based on the relevant and probative research. You're not playing favorites, giving one player his 75th percentile season and another his 25th.

The problem with this is two-fold:

(1) You may think you're giving a player his 50th percentile season, but your reading of his skills and context are more generous than someone else's. As such, your opinion of Mike Trout's 50th percentile numbers might be someone else's 75th-percentile ones. Essentially, your projections aren't much less subjective than someone's hunches or predictions; the subjectivity just occurs at the input phase rather then the output phase of the process; and

(2) If you used a formula taking three-year averages and regressing players to the mean, then you'd be more objective, but your projections would look very little like the actual distribution of stats in a given season. To take a simple example, let's say I win $1 if a coin flip comes up heads, and you win a dollar if it comes up tails. My expected return, i.e., my 50th percentile outcome, is 50 cents. I should project myself to win 50 cents. But clearly that will never happen. I'm either going to win $1 or nothing. So by projecting 50 cents as my stat line, I ensure I get it wrong no matter what happens.

Put in baseball terms, someone will probably win 20 games or hit .340 or hit 45 home runs. If we give everyone his 50th percentile season, it's likely no one will achieve those numbers. But we know that someone will have his 95th-percentile season and someone will have his 25th percentile one. As such, we'd like to have a set of numbers that reflects that. Which brings us to:

(B) Predictions - Here we assign players stat lines that mimic the real distribution of player stats in an actual season. We predict who will have his 75th-percentile season and who will have his 25th. We give someone 20 wins and someone just as good 13 wins because that's how it goes in real baseball.

The flaw in this is that it's completely subjective and arbitrary to decide what player will have a breakout and what player will be a bust when both have similar skill sets and find themselves in similar situations. Instead of giving us each 50 cents, you're saying you're going to win a dollar, and I'm going to win nothing - when it's just as likely that I win the dollar and you win nothing.

In the end, if you're going to create statlines for the entire player pool and use them as the basis for your draft/auction rankings, you'll probably have to settle for projections, but I like to mix in a few predictions based on hunches. A hunch can be considered a disproportionate emphasis on a particular skill, stat or contextual detail, one you wouldn't apply generally but that jumps out on you in a particular case. Aggregating the disparate facts - not all of them easily quantifiable - into a projection is part art as well as science, and we know that certain factors work in combination, so that a beneficial change in ballpark doesn't affect all players the same way or to the same degree, for example. Leave room for hunches, but be realistic about their fallability.

(C) Volatility and Reliability - By condensing an array of disparate numbers and facts about a player into a 50th percentile statline, you lose some important information. A projection by itself just tells you the player's average season. But not all averages comprise the same distribution of highs and lows. Although the numbers might be similar, Robinson Cano's projection is more reliable than Josh Hamilton's. Hamilton has more upside and more downside. At the top of your draft (or in an auction when you pay top dollar for a player), you'd like more reliability and less upside, so Cano - even if he weren't a second baseman - would probably go ahead of Hamilton. But in the middle and especially toward the end of your draft (and with cheaper players at auction), the projected average numbers aren't nearly as valuable. You want the player to be capable of far more in his 80th or 90th percentile season, even if the possibility that he loses his job outright, i.e., his 20th-percentile season drags down his average. For that reason, Billy Hamilton - who might not even see the majors this year but could steal 50-60 bases if he does - is worth having on your 12-team mixed league bench, while Cliff Pennington is not.

Straight projections alone are not enough to inform a cheat sheet. You must know about a player's volatility and reliability.

3. Translating Performance into Value

Once you've put together your 2013 projections for the entire player pool, you need to figure out how to turn that into a cheat sheet or list of dollar values. While it's pretty easy to see that Miguel Cabrera's projected stats put him near the top of your list, it's not obvious whether they're better than Mike Trout's, and if so, by how much. It's also not immediately evident whether a .345 batting average in 500 at-bats does more for you in batting average than 42 home runs does for you in homers. The problem of comparing players relative to the overall player pool and across categories isn't something we can solve by eyeballing it.

To address that, we need two key concepts:

A. Value Over Replacement - This is the margin by which a player is better than those who are freely available on the league's waiver wire. In other words, if you're in a 12-team mixed league that starts 14 offensive players, that means the top 168 offensive players are starting at any given time. Because the 169th player might be a steals specialist with no power, or a big power bat who hits .200, it's best to use an average of the next 10-20 players to generate a baseline for replacement value. Let's say players 169-188 average 12 HR, 60 RBI, 70 runs, 8 SB and a .265 average. Now we have our rough estimate of replacement value*.

As such, any starter's value is determined by the extent to which his stats exceed or fall below these benchmarks (again assuming these are the numbers you came up with for your league parameters). So if Ryan Braun is projected for 42 HR, he's 30 HR above replacement. You would subtract his RBI, runs, SB and average (adjusting for at-bats) accordingly. Once we subtract out replacement value stats from all of the hitters on our list, we now have their real stats insofar as they inform our values. A player like Ben Revere might be projected for 1 HR, and thus his true home run total is -11 for purposes of his value.

But this still doesn't help us answer the original question as to whether a .345 average in 500 at-bats is worth more than 42 HR, or in this case 80 points of batting average over 500 at-bats vs. 30 home runs. Essentially, we're asking which stat is a bigger outlier relative to the player pool, i.e., which stat is likely to have a bigger impact on the standings. For that we need our second concept: Standard Deviation.

* There are many nuances here I'm omitting, including but not limited to: some starting catchers will be worse than replacement value, I'm ignoring position scarcity, the size of one's bench and whether the bench or the waiver wire should be considered the starting point for calculating replacement value, that prospects who play half a season will often be more valuable than replacement value because you get the other half of a season from someone else, or that shuttling in two-start pitchers or platoon players also changes the baseline, etc.

B. Standard Deviation - this measures the average amount the data points, i.e., players' stats in a given category, differ from the mean in that category. For example, if the average number of homers in the usable player pool is 18, and the player pool consists in four players, two with 20 HR and two with 16 HR, then the standard deviation is two HR. But if the average were 18, but there were two players with 30 and two with six, then the standard deviation would be 12.

As you can see, in the former case, the data points are more clustered together, and in the latter, they're further apart. This has implications for the value of stat-lines because in a case where the data points are clustered together, e.g., in 1921, players ranked No. 2 - No. 14 in HR had between 24 and 16 HR. The standard deviation for that player pool was fairly small. But Babe Ruth led the league in HR that year with 59! You can see what Ruth would do for your fantasy team in that context - he'd win homers for you virtually all by himself. Looked at in terms of standard deviation and value above replacement, we can see why this is. If we say replacement value was roughly five homers, then Ruth had 54 homers above replacement. And if the standard deviation was about four, then Ruth was a whopping 13.5 standard deviations above replacement!

Had the players been less clustered together, and the standard deviation were 10 HR, then Ruth would have been "only" 5.4 standard deviations - still a huge number - above replacement. The more clustered together the data points are, the bigger the impact of the rare outliers.

We can do this for every player in every category, figuring out his outlier-ness (both positive and negative) in each and add up the true extent to which he helps or hurts your team.

Which brings us back to the original question: Is 30 HR above replacement worth more than 80 points of batting average in 500 at-bats (let's assume 500 at-bats is the average number of at-bats in the pool so we don't need to make a volume adjustment)?

The answer depends on what the standard deviation is for each category. Using the RotoWire projections it's about nine for HR, and about 18 points for batting average. Based on those numbers, the 30 homers is 3.3 standard deviations above replacement while the 80 points of batting average is 4.4. Clearly, given these ballpark replacement levels and the RotoWire projections, the batting average would be worth substantially more than the HR.

Sticking with Ryan Braun, for a moment, he'd be 30 HR, 55 RBI, 35 runs, 20 steals and 56 points of batting average in 604 at-bats (roughly 1.2 times the average) above replacement. So we go down the line and add up his contributions in each category.

When you add it up, Braun gets you 3.3 in HR, 2.6 in RBI, 2.1 in runs, 2.5 in steals and 3.7 in average for a total of 14.21. We can compare that number to that of every other player in the league, e.g., Mike Trout comes out to roughly 15.08 and Miguel Cabrera roughly 13 given the RotoWire Projections. Now we have a basis for our cheat sheet, i.e., we've converted the stats into values.

To generate dollar values for an auction, there are a couple further steps. You need to add up each player's total scores across the five categories for the top 168 offensive players, figure out what percentage of the league's collective budget ($260 x 12 = $3,120) is going to offense, e.g., 70% = $2,184, and divide that number ($2,184) by the sum of the scores. You'll probably end up with a result like 3.1 or so. Then you multiply each player's score by 3.1 (or whatever your number is) to get the dollar values.

C. Volatility - We discussed this earlier, and of course, it applies here. The reason Trout grades out better than Braun or Cabrera is that his projections are worth more. But Cabrera and Braun are probably safer bets to get something resembling their projections than Trout is to get his. So when you're spending $40 of your $260 budget or a top-three pick, it might be worthwhile to give up some of Trout's expected return for a safer investment. On the lower end of the pool, the consideration is just the opposite. A player might even have a negative dollar value taking into account his lack of prospective playing time, but his 90th-100th percentile seasons are so valuable you spend several dollars to acquire him.

D. Translating Performance into Value without Projected Stats

Having said all this and done all the math, I generally don't rely on projections to evaluate players. I do the research and aggregate the disparate factors into a slot on my cheat sheet. Having done enough auctions and drafts, I have a pretty good idea of what different stat lines are worth without crunching the numbers for each one, and I also know that each statline is based on a fictional rendering of the 2013 season and is usually not much more scientific than my placement of a player in a cheat-sheet slot.

Moreover, I'm not wedded to my cheat sheet order when the auction or draft starts - I might take my No. 12 SS ahead of my No. 10 one, when push comes to shove, given volatility considerations and arising hunches.

And even if you use three-year averages and regress players to the mean to create your projections, you're going to make choices based on playing time, park effects, age/experience/health related growth/regression that are less than scientific. And even if you were to automate those factors - park effects for gap-hitting lefties that are 6-2, 190 and score a 65 on the power scale, adjust it for a player's schedule, his historical comps for age-related career arc, you're making a lot of choices on the inputs that are imprecise. And even to the extent your model gained precision over time and backtested its results, there's no guarantee your conscious aggregation of the factors that comprise value will be better than the unconscious snap assessement of an experienced and open-minded evaluator - at least not without the conditions of baseball remaining static while you collect a larger sample of data of the next couple decades. (But I'm open to being proved wrong on this point.)

The bottom line - there's no substitute far gathering all the material facts you can find about a player, but how you translate those to a dollar value or cheat sheet is up to you. If you prefer to have the discipline of a cheat sheet based on projected stats, it's important to compare those stats to the replacement-value baseline and then to see what those results are worth based on their prospective categorical impact. A good way to measure that is by seeing how many standard deviations they are above the baseline.

Next up, we'll take on the topic of Draft Strategy.