# Fantasy valuation systems: adding more context

On Friday, we discussed three different fantasy baseball valuation systems. I promised positional rankings for the rest of the season, but today we’re going to get a little more familiar with the numbers before delving into those rankings tomorrow.

When playing in a rotisserie fantasy baseball league, you want to accumulate the most roto points. Simple concept, right? Well, now we have a couple of systems that try to quantify each player’s roto point values. This should be helpful in valuing players, especially when preparing for a draft or when making a trade.

But, even as straightforward of a concept roto point values is, it can still seem a little abstract before we familiarize ourselves with some of the nuances, like what is league average for leagues of various sizes? What does the positional scarcity spectrum look like? Are two top-40 players really worth a top-5 player? If not, what is? And so on. So, without any more foreshadowing, let’s build a little framework for reference.

(For the sake of simplicity, I am only going to use one formula—my roto points above average formula (rPAA)—instead of all three. This shouldn’t change much, as all three formulas showed strong correlations with one another in their valuation of players, both hitters and pitchers.)

### League Average

League average, in this case, is simply the average roto point score for all players that would be inserted into any starting lineup in a league, with hitters and pitchers having separate calculations. A typical 10-team league has 13 starting hitters and nine starting pitchers, so in this case, league average is the average score from the top-130 hitters and top-90 pitchers. For 12-team leagues, it is 156 hitters and 108 pitchers.

Bench utilization, pitcher streaming, daily lineup adjustments and individual league rules can muddy the water a little bit with regards to a true league average, but for now we are going to continue the theme of simplicity and use this non-flexible definition of starters.

The league-average amount of raw (non-adjusted) roto points for hitting over the past three full seasons (2009-2011):

{exp:list_maker}10-team leagues: 9.61

12-team leagues: 9.03

14-team leagues: 8.53

16-team leagues: 8.08 {/exp:list_maker}This graph is displaying the top 156 hitters in terms of their roto point production in relation to league average in a 12-team league in 2011.

Only 71 hitters (45.5 percent) scored above zero. This is because there is so much roto value created by the top few players. Most seasoned players already know this. The total roto point value of those 71 players scoring in the positives was 161.12 rPAA. The top-20 accounted for 101.03 (62.7 percent) of those marginal points. So yeah, it pays to have stars on your team.

On the pitching side, league average is a little lower, again these numbers are averaged from 2009-2011:

{exp:list_maker}10-team league: 7.48

12-team league: 6.98

14-team league: 6.56

16-team league: 6.18 {/exp:list_maker}This graph shows the rPAA of the top 108 pitchers in a 12-team league for 2011.

As with hitters, pitching scores at the top are disproportionately more valuable than scores throughout the rest of the curve are, but, with pitchers, the dropoff is much steeper. Only 37 players (34.3 percent) recorded a roto point value of above average. And of the 104.38 points produced by those top-37 players, the top-10 earners raked in 65.49 (62.7 percent) of them.

__2011 rPAA Percentiles for Hitters (12-team leagues; Non-Positional Adjusted)__

Percentile | Hitter | rPAA |
---|---|---|

1 | Matt Kemp | 9.95 |

10 | Melky Cabrera | 3.54 |

25 | Jay Bruce | 1.59 |

50 | Alex Avila | -0.28 |

75 | Logan Morrison | -2.09 |

90 | Casey Kotchman | -2.91 |

100 | Ryan Ludwick | -3.31 |

__2011 rPAA Percentiles for Pitchers (12-team leagues)__

Percentile | Pitcher | rPAA |
---|---|---|

1 | Justin Verlander | 10.73 |

10 | C.J. Wilson | 3.36 |

25 | Jon Lester | 0.94 |

50 | Fernando Salas | -0.83 |

75 | Aaron Harang | -1.67 |

90 | Jason Motte | -2.36 |

100 | Edwin Jackson | -2.66 |

### Positional Adjustments

It is easier to find production at some positions than others. This is no secret. Thus, we need to adjust for positional value. To do this we simply find the number of players at each position likely to be owned for a particular league size. Let’s call this number X. Now, we take the average scores of the top-X players at each position (X will vary by position). After we find the average for each position, we measure each positional average against the others, giving extra credit to the positions with lower positional averages and giving less credit to positions where production is more abundant.

Let’s use a 12-team league as an example. There are 12 starting shortstops and 12 middle infielders. Without knowing the player pool for a particular year, it would be safe to assume that roughly 18 shortstops will be owned in a 12-team league.

Obviously, the utility slot will create some difficulties when looking at positions of abundance, but since the distribution of positions used at utility throughout a league will vary from year-to-year and league-to-league, we will ignore this variable for this summary. When actually calculating an overall list at any specific point in time using a static player pool, this can be accounted for with much better accuracy.

Moving on, now that we have a number, 18, we take the average value of the top-18 shortstops in relation to the average at other positions. Let’s say it is -1.0. Once we have averages for all other positions, we can use the most abundant position as the benchmark for what all other positional averages should be raised to after positional adjustments. Lets say that first base is the most abundant position, with an average score of +2.0. In this case we will give a +3.0 bump to each shortstop. Now we can value them on the same scale.

Here are the positional averages for 12-team leagues for each position. These are raw scores and have not been set to league average.

First base is clearly the most productive position, with outfield a distant second. Contrary to traditional beliefs, shortstop is not substantially scarcer than third base or second base, as all three positions have scored about equally in recent years. Bringing up the rear is catcher, which has a raw score of an average of 3.8 points lower than first base over the past three years.

Again, how middle and corner infielders are distributed, and what positions are commonly play in the utility slot will alter the data some, but this should give us a decent idea of what positions to pay the extra buck for.

### How much is the No. 1 player worth?

Fantasy players often wonder whether they should sell the best, or one of the best, fantasy baseball players to try to shore up weak spots in another areas or if they should just hold tight? It is always a good idea to sell a player if you are being overwhelmed with value, but what is the tipping point between accepting and rejecting a proposal?

The top offensive player in 2011 was Kemp, who provided nearly 18.6 raw roto points and just under 10.0 marginal roto points over a league-average player. To figure out what type of two-for-one trade would have worked out in retrospect—say if you made the deal at the beginning of 2011—we can add up Kemp’s 18.6 to a replacement level player worth around 5.4 roto points. (Factoring in a replacement-level player is just a quick way to estimate the value of the player you would have to drop from your roster to make room for two incoming players, as chances are this player will be close to replacement level.)

To trade away Kemp last season, you would have needed at least 24.0 roto points of value in return just to theoretically break even. A couple of combinations that would have just broke even are Joey Votto and Hunter Pence, Prince Fielder and Mark Teixeira, or Jose Bautista and Jay Bruce. And that’s without figuring in that you are probably eventually going to find a player who will produce more than replacement level value.

All of those hypothetical deals would have broken even, but Kemp nearly went 40/40 and competed for a Triple Crown. His 2011 season was easily the best (fantasy) offensive season of the last three years. So this is by no means the actual break-even point when selling the game’s best player.

Entering a season, the top-ranked player is typically valued at an expected 14-15 raw roto points, depending on the degree of aggression the projection exhibits. In this case, two top-40 hitters should be a “fair deal,” but again, that assumes that everything will happen in a vacuum. Chances are that the attentive owner will end up with a player better than replacement level to supplement that top-tier talent, and any player capable of being selected No. 1 overall is almost surely going to be more reliable than two random top-40 hitters. If it was my team and I owned the game’s best hitter in a 12-team league, I would need a bit more than just hypothetical “break-even” value, so something around two top-25 hitters might be the minimum package I’d be looking for.

Whether or not you are trading for the best player in the game, one can use this valuation system to get a general sense of where he or she stands in the deal. The more players that are involved in a deal, the more complex that deal becomes. With a simple calculation of expected roto value, an eight-player trade transforms from a complete uncertainty to a positive or negative number that should eliminate most of the guesswork. Categorical needs will have to be considered, as well, but absent of obscure, league-specific context, this method of trade evaluation should save a lot of time.

### Year-to-Year Roto Point Correlations

Pitching correlations:

From 2009 to 2010, roto point totals by pitchers correlated at 0.6154 (r^2 = .3787), and from 2010 to 2011 the correlation was 0.6331 (r^2 = .4107). I also isolated the top-20 pitchers to see if the best pitchers were more reliable year to year. The correlations were 0.2165 (2009-2010) and -0.0989 (2010-2011).

So, while pitchers like Zack Greinke in 2009 and Justin Verlander in 2011 have produced like a top-5 overall player, there is far too much variance with regards to the spectrum of reasonable, expected outcomes to justify taking a pitcher that early. This is why axioms like “wait on pitching” exist. We obviously can dissect the underlying numbers to get a little closer in our projections than these correlations might suggest, but even consistently good pitchers have a high volatility range.

Hitting correlations:

From 2009 to 2010, the roto point totals for hitters showed a correlation of 0.7739 (r^2 = 0.5990). From 2010 to 2011, the correlation was 0.7706 (r^2 = 0.5939). This correlation is much higher than pitchers. It’s not ideal, but at least there is more signal than noise with hitters. The top-20 hitters also showed much better year-to-year correlations of 0.4314 (2009-2010) and 0.4543 (2010-2011). These correlations are by no means precise, but hitters are way more reliable than pitchers, which is a predominant factor in why pitchers are infrequently selected in the first few round of fantasy drafts.

### Concluding Thoughts

Hopefully, all of this has enhanced your understanding of my methodology. Jeff Gross’ E.Y.E.S. method and Mike Silver’s FantasyPlayerRater formula, as we discussed Friday, showed strong correlations both to each other and to my method, so once we start getting into some Oliver-driven objective rankings, which are slated to begin Tuesday, following along with their valuations shouldn’t be much trouble, either.

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Fantastic article – thanks