Points leagues lend themselves to easy analysis. Every (relevant) action or outcome has a specific value, those values accrue, and you're left with a total number of points for the game/week/matchup/season. Moreover, points are points. It doesn't matter if those points are accumulated because a player hits a ton of doubles and walks a lot, or hits .250 with a slew of home runs, or steals bases and scores. In a roto league, they'd have different values (or at least be differently valuable). In a points league, they're all worth the same in the end.
While that is the crux of value in a points league, to stop there would result in a simplistic analysis. Players have different positions, and you have to roster according to the limits of your league. Chances are, you have to play at least one at every infield position, a handful of outfielders, maybe a DH, Utility role, corner infielder, middle infielder, etc. You can't just pick the top points scorers, you have to fill out those positions as well.
This is a guide to helping you do just that. We'll go over how to calculate value in a points league given positional limitations. To help clarify, we'll use the settings of my head-to-head points league (Bernie's Bombers over on ESPN). As mentioned before, I'll be using the ESPN 2011 projections.
Since this is relevant information, here's how the scoring system works for hitters: 1 point for a Hit, Walk, Run, RBI, or Stolen Base. On top of that, singles are 1 point (2 total), doubles are 2 points, triples 3 and home runs 4 points. Strikeouts are -1 point. Errors are -1 too, but since they're difficult to predict (and a relatively small proportion of the total points) they're left out of the analysis. For pitchers, it's 3 points per inning pitched, 1 point per K, -1 point per hit or walk issued, -2 points per earned run, 6 points for a win, -3 points for a loss, 5 for a save, 4 per complete game, 2 per shutout, 10 points per no-hitter. Your league may have a different scoring system, and you may think the values are odd, but this how we do it. Applying these to ESPN's 2011 projections (as of my draft on 3/13/11) gives you the total projected points for every player. Simple, right? Here are the top ten players in projected total points:
Albert Pujols (836), Adrian Gonzales (757), Robinson Cano (727), Miguel Cabrera (726), Matt Holliday (688), Hanley Ramirez (687), Ryan Braun (685), Evan Longoria (683), Mark Teixeira (675), Carl Crawford (674)
All of them are hitters, and four of those are first baseman. There's one each at second, third and short, three outfielders, and no catchers or pitchers of any kind.
But what about positional scarcity? Remember, you have to build a roster according to certain constraints. Moreover, some positions are better or worse than others. That's the reason many people think Troy Tulowitzki is one of the five most valuable players, even if he's not a top-5 point scorer. Everyone knows that shortstop is horrible this year. And how do you compare between positions? You generally expect more from a 1B than a C, and with good reason.
This is simple enough to address. You just have to figure out what baseline point production is for that position. Essentially, if you were the last person to draft your starting 2B (or your 2B went down and now you need to hit the waiver wire), what should you expect to get? This is going to vary depending on the roster composition and number of teams. For Bernie's Bombers, you roster one each of C, 1B, 2B, 3B, and SS, four outfielders, and a utility. You also have five starters and two relievers active each week. The league is also ten teams. So in the league there are by definition ten starting-caliber C, 1B, 2B, 3B, and SS, 40 starting-caliber OF, 50 starting-caliber starters, and 20 such relievers (we're going to ignore utility for this post, since everyone approaches that differently and requires a more complex analysis).
People are going to have different preferences that subtly affect what specific players might be available, so the best way to calculate replacement value is to take an average of the last two players who should be rostered and the first two who shouldn't be (averaging the #9, #10, #11, and #12 catchers, for example). That led to the following values:
Catcher: 398.5 points
First Base: 567 points
Second Base: 523.25 points
Third Base: 521 points
Shortstop: 484.5 points
Outfield: 488 points
SP: 379 points
RP: 282 points.
A few quick notes. First, there was a steep drop from 9 to 10 at shortstop, so I countered that by including the #13 shortstop in the average. Second, because 40 outfielders start, I used the average of three above and three below cutoff (#38-43). Similarly, I expanded the pool for SP (#48-53). Replacement RP was calculated using #19-22. But essentially, if you filled your entire roster off the waiver wire you could expect something like this.
Next, we calculate (if I may appropriate a term) VORP, or value over replacement player (who will produce at about baseline production). Essentially, how much more is player x worth than the guy I can get at any time at the same position? To do this, you simply subtract replacement points at that position (rPts) from projected points for the player in question (xPts) and divide by replacement. That is, (xPts-rPts)/rPts. This yields a decimal, which is the percent above (or below, if it's negative) replacement value. Here are the top-10 players for VORP:
Roy Halladay (.7335), Felix Hernandez (.6227), Joe Mauer (.5583), Cliff Lee (.5383), Tim Lincecum (.5303), Victor Martinez (.5031), CC Sabathia (.5013), Albert Pujols (.4744), Justin Verlander (.4406), and Jon Lester (.4380)
This is a very different list; only Albert Pujols makes both of them. This is populated largely with pitchers and catchers, which (excluding relievers, who don't get many points) are the two worst positions at replacement level.
Here's the problem with using only VORP though: it doesn't account for how many points a player actually scores. Remember, as I said above, points are points. And you need to get as many of them as possible. Roy Halladay may score 73.35% more points than a replacement level pitcher in my league, and that may be the best VORP, but those 657 points project to only 14th-most overall. What you need then is a measure that accounts for both total points and VORP.
To that end, I've developed a measure I call Adjusted Points Above Replacement (adj PAR). Strictly speaking, points above replacement is expected points minus replacement points (xPts-rPts). That's fine, and you can do some decent work with it. However, it has a few flaws that I'll explain in a moment.
Adj PAR is calculated simply by multiplying the expected points scored by a player by that player's VORP (xPts*VORP). Much like OPS, it doesn't have a great interpretation that makes sense. However, if you write it out long-form it looks like this: (xPts*(xPts-rPts))/rPts. Written another way (and forgive the way this is going to look), that's ((xPts^2)-(xPts*rPts))/rPts.
This has a few advantages I really like. First, total points is squared in the numerator. That means the more points you expect a player to accrue, the faster his adj PAR grows. This is valuable because points are harder to come by towards the very top end compared to the middle. To illustrate, in the data set I'm working with there are 105 players who should score 500 or more points. Of those, 30 players should score 600 or more, 4 of those should score 700 or more and only 1 of those four (sir Albert of St Louis) should score 800 or more. Now, 100 points is 100 points no matter how you get it. But it's more difficult to get those points on the top end, and so those points have relatively more value due to their scarcity.
The second advantage is that it scales for positional scarcity. Getting 600 points from a catcher (only Mauer qualifies) is more difficult than getting 600 points from a first baseman (there are seven such players). As such, Mauer's adj PAR is higher than almost all of the first basemen.
Last, it preserves the original order of points scored within a position. If outfielder x is projected to score more points than outfielder y, then outfielder x has a better adj PAR. It seems trivial, but it's an indication that the statistic is valid. Advantages one and two are the reason I don't use straight points above replacement- it simply does not do these things.
With all that explained, here are the top ten players in adjusted PAR:
Roy Halladay (481.92), Albert Pujols (396.62), Felix Hernandez (382.96), Joe Mauer (346.73), Cliff Lee (313.8), Tim Lincecum (307.6), Victor Martinez (301.38), Hanley Ramirez (287.14), CC Sabathia (285.25), and Robinson Cano (283.09)
How you use adjusted PAR is up to you. Personally, I wouldn't base my draft rankings strictly on that. It still overvalues positional scarcity at the expense of total points, in my opinion. I dealt with that issue the following way: I ordered players according to total points and ranked them, then ordered them by adj PAR and ranked them again that way. I then took the average of the two and and ranked them by that average, breaking ties by using total points (more total points = higher ranking). You can debate the merits of that strategy specifically, but the idea behind it is what counts. If adj PAR discounts total points too much, then add value to total points in a way that will counteract that. You can weight the averages if you choose; splitting the value between total points and adj PAR evenly is a matter of taste. Using that system, here's the top-10 for my draft:
Albert Pujols, Robinson Cano, Hanley Ramirez, Roy Halladay, Adrian Gonzales, Matt Holliday, Ryan Braun, Miguel Cabrera, Carl Crawford, Evan Longoria.
That's a top-10 I can get behind. You have the consensus #1 pick still first. You have three high-scoring 1B, the top 2B, 3B, SS, and SP, and the top three OF. Moreover, you have all four 700+ point scorers in there. I would say that it overvalues starting pitching too much for a head-to-head points league, since a starter's week-to-week contribution varies so much (assuming lineups are set weekly). However, for a league that uses daily lineup changes or straight season points (if there are any of those), that isn't an issue.
You don't have to use ESPN's 2011 Projections if you have another set you prefer, and your scoring system may vary. But using this walkthrough, you can come up with some killer draft prep for your points league by applying your league's scoring system to the projections you favor. Happy drafting!
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