Positional weighting (aka ‘positional scarcity’ for fearmongers or fearophiles) in fantasy baseball is one of the most discussed and least understood variables when it comes to ranking players. I have heard arguments ranging the whole gamut on how much a player’s value is impacted by their position – everything from ‘it means nothing’ to ‘it means everything.’

In my yearly review of my Point Shares methodology, I decided to test the underlying assumptions on positional weighting. One advantage and burden of using a ‘methodology’ is that you have to make decisions on each variable. If you rely on gut feel for player valuation, all variables are just blended together into one experience-honed calculator. So you have both the benefit of never fretting about your underlying assumptions as well as the detriment of never testing and refining them.

For Point Shares, I’ve historically weighted hitters 75% vs. position and 25% vs. overall regardless of league format – e.g., a player’s value is based 75% on how he compares with the average drafted hitter at his position and 25% on how he compares with the average drafted hitter (regardless of position). I hadn’t revisited it in recent years so it felt like an assumption worth testing.

To test it, I ran Point Shares against my projections for a 12-team mixed league (C/1B/2B/SS/3B/5 OF/CI/MI/UTIL/9 P) using the following weights (positional/overall): 0/100, 25/75, 50/50, 75/25, 100/0. I then averaged the differences in projected dollar value, adjusting it so 1B became the base (1B=0). To translate the dollar figures into rounds, you can assume +/- $4 is a round in Rounds 1-3, +/- $3 a round in Round 4, and +/- $1 a round in Rounds 5-22.

For example, a 75/25 weight using Point Shares would value a player $10 more if he was a Catcher vs. a 1B, $7 more for a Catcher vs. an OF (10.1-3.2), etc. From a snake draft perspective, that’s saying a top catcher (say Posey or Mauer) is 2-3 rounds more valuable than a 1B/OF with the same projected stats. See below for the full chart:

Avg $ Adjustment Based on Position For 12 Team MLB | |||||

Pos | 0/100 | 25/75 | 50/50 | 75/25 | 100/0 |

C* | 0 | +3.4 | +6.7 | +10.1 | +13.4 |

1B | 0 | 0 | 0 | 0 | 0 |

2B | 0 | +1.3 | +2.7 | +4.0 | +5.4 |

SS | 0 | +2.5 | +4.9 | +7.4 | +9.8 |

3B | 0 | +1.0 | +2.0 | +3.0 | +4.0 |

OF | 0 | +1.1 | +2.1 | +3.2 | +4.3 |

DH | 0 | -0.6 | -1.3 | -1.9 | -2.6 |

* For a 2 Catcher league, the catcher adjustment would nearly double (75/25 goes to +19)

Armed with this data, Grey and I tested our ‘gut feel’ across a number of different scenarios – e.g., how much more is Youkilis worth as a 3B vs. 1B?, how much less is Posey worth if he just had 1B eligibility? Before running the data, I assumed 75/25 would prove too high of an adjustment. But after going over various mixed-league scenarios, we found that the 75/25 adjustments were most in line with our drafting experience. There were about as many cases that we exceeded the 75/25 results as cases where we fell below it. We generally agree that Youkilis is worth about $3 more (or an early round) as a 3B vs. 1B, Posey is worth about $10 more (potentially from 15th round to 5th round) as a catcher vs. a 1B, etc.. (Note: For DH, I multiply the average 1B’s counting stats by 5%)

I tested this across 10-16 team mixed leagues and found that the 75/25 proved best across each format. The dollar differences vary slightly but generally hold up since even 16 team leagues never really suffer from ‘scarcity.’ There are always free agents available who are clearing a projected 400+ ABs. The point where ‘scarcity’ plays a big role is AL/NL-only when you run out of starting players and delve into players at 300 and less ABs.

This scarcity is felt across all positions in AL/NL-only and it was therefore not surprising when I found out how little positional weights matter in these formats. There were only two real impacts of the positional weights when I tested the 0/100, 25/75, 50/50, 75/25, 100/0 scenarios: 1) 1Bs lose about $1 every 25% increment of positional value (so Votto would be worth about $47 with no positional weighting and about $42-$43 with 100% positional weighting) and 2) Catcher values changes dramatically. In the end, I decided to switch this to 25/75 as I’ve found that 1B projections are a lot more reliable than Catcher projections. In addition, even with just a 25% positional weight, Posey is valued at $36 for 12-team NL only with 2 catchers. This is already more than he’ll likely go for in most leagues (he went at $29 in our recent CBS) whereas most 1Bs seem to go closer to the 25% weight vs. 75% weight.

Please leave comments if you have a point of view regarding the ideal positional weighting. Does the 75/25 weight seem too much/little? If you prefer a different split, why?

How did you come to the initial conclusion that 75/25 seemed the correct estimation of value? Just a gut feeling?

Beautiful! I’ll have to use this to finish my top 300 projections for my 8×8 league. Glad that you spent the time hashing this out. Just based on point value alone McCann is valued about the same as Aaron Hill. But this will balance that out a little bit.

So would you say that in mixed 14-team and 16-team leagues, there is no need to inflate MI simply because more people are drafting?

I also have an unrelated question: In Yahoo!, CC is actually ranked at #57. When a commenter brought this up to Grey, he mentioned that was good value, despite CC’s negative trends.

My question: Would you take CC as a SP to supplement Weaver (my keeper), or Cole Hamels? Hamels and CC are close to each other in the ranks. I feel like Cole is on the cusp of a monster season, so I just wanted to gauge your opinion, Rudy. This is a 12-team H2H league btw.

Great article.

in your evaluation, votto is $47 with 0% and $42-43 with 100%

then would this make a trade of votto for tulo a no brainer???

Hey Rudy,

Isn’t there a more legitimate way to figure this out rather than testing those estimates? Maybe I am missing something, but let me know if this makes sense…

At any given point in the season, at each position, there is an avg expected performance for any given player, and all players’ performance ranges at some standard deviation of that expected performance. Isn’t it possible to figure out the extent to which players deviate from the mean on avg, for any given position? Some positions, 1b, will have much lower average intervals between players, because there are a lot of high performing players. Other positions, like SS, will have a much higher average intervals between players, because few players perform at a level close to Hanley.

Wouldn’t those #’s – the avg SD interval between players at a certain position – give you a more reliable multiplier to factor in positional scarcity to rankings?

Rudy-interesting stuff. What is Pujols value in a 12 team NL-only league?

Am I missing something, or did you randomly decide to use 25/75 at the end of the article, even though most of your evidence supports 75/25?

“In addition, even with just a 25% positional weight, Posey is valued at $36 for 12-team NL only with 2 catchers.”

So, a first baseman with Posey’s projected stats would go for about $29, then? That seems high. I don’t think Derrick Lee costs $29.

thank you rudy-san.

great stuff, and very interesting that 75/25 panned out, I too would have gone in thinking that wouldn’t be verified by the results.

@ Matt S.: Rudy said

“There were only two real impacts of the positional weights when I tested the 0/100, 25/75, 50/50, 75/25, 100/0 scenarios: 1) 1Bs lose about $1 every 25% increment of positional value (so Votto would be worth about $47 with no positional weighting and about $42-$43 with 100% positional weighting) and 2) Catcher values changes dramatically. In the end, I decided to switch this to 25/75 as I’ve found that 1B projections are a lot more reliable than Catcher projections. In addition, even with just a 25% positional weight, Posey is valued at $36 for 12-team NL only with 2 catchers. This is already more than he’ll likely go for in most leagues (he went at $29 in our recent CBS) whereas most 1Bs seem to go closer to the 25% weight vs. 75% weight.”

Nicely done. So if I’m understanding this correctly, the order of position scarcity goes as follows…

C, SS, 2B, OF, 3B, 1B

If that’s true, I didn’t think 3B was that deep…

Good topic…. so that brings me to this…

Im in a 10 team keeper league that uses R, HR, RBI. SB. AVG and OPS

Here is my roster

C VMart

1B MIggy

2B EMPTY

SS Tulo

3B JBautista

OF CarGO

OF Ichiro

OF Crawford

UTIL Tex

UTIL Krispie Young

Bench

Rasmus

Stewart

E Young

D.Espinosa

Do I make this proposed deal to me?

Tex for Uggla?

Thanks

Dan

So this leads to the question, how do you handle a scarce position? Overvalue the top tier (eg Tulo) or punt the position (as Grey seems to be doing with catcher, eg Posey)?

So I’ve got a 20-team 40-man roster league where there’s only a handful of free agents projected to receive more than 200 ABs. In that case, what’s your feel for how positional scarcity should be weighted?

You hurt my brain.

I know its annoying but would appreciate some fantasy help here

16 team Head to Head dynasty standard 5 X 5 with OPS instead of average and quality starts instead of wins

Someone’s offering me Adrian Gonzalez for Travis Snider and John Danks. Is this really a no brainer ? i happen to like Snider a lot, he’s gonna put up monster numbers very soon and my outfield core is pretty weak with Choo, Lind( who could lose his OF eligiblity), Pagan, Pierre, Berkman(who could gain OF eligiblity) and then a bunch of bodies like Carlos Gomez, Jack Cust, Michael Brantley and Matt Joyce

Okay – maybe I’m just slow.

I understand that you’re saying that a batter’s value in relation to the average player at his position is worth 2x as much as his value in relation to the average hitter regardless of his position. But I don’t understand how you determined what the average player at a position is, or what the average hitter is. I also don’t understand how you determine how 10 more points of batting average compares to 2 more home runs, or how either of those compare to 8 RBI.

I also don’t understand how you came up with that numbers you did for comparisons across positions. Assuming I’m reading things right, you were looking at within position VS all batters, then suddenly you had numbers of some sort for comparing catchers to outfielders.

One last thing – you listed (C/1B/2B/SS/3B/5 OF/UTIL/9 P) as your positions, but later mentioned 1st base sharing a slot with 3rd base. I assume you were using ESPN default settings, and meant to include CI and MI as positions?

@Rudy: Nice work. It is good to test your assumptions from time to time. I also think that what you have is a pretty good rule of thumb that at least allows you to try and compare apples to oranges across the different positions. The fact that it matches is up with your basic assumptions about how to draft tells you that you’re at least not totally out of the ballpark. I do wonder about a couple of things.

Let me give you a grid:

A B C

101 68 35

100 67 32

99 65 31

Imagine that you have three players and they are going to draft one at a time. Each has to get one value from each column. The maximum score a player could achieve is 204, the minimum is 195. The total values in each column are 300, 200 and 100. The averages (rounded) are 100, 67, 33. No player The average player across all grids is 66.666 and no “player” is more than 2 units from the average in it’s category. So if you apply a 75/25 rule, you’re going to come up with all values in column A being more than column B and all in B being worth more than C. So if you drafted in order value from highest to lowest, snaking, with each player taking the highest value off the board you’d get final scores of A: 201, B: 200 and C: 199. It kind of looks like you’ve fairly valued the players and ended up with a fair draft. But if you look pretty close, you’ll see that 35 was actually the best pick. However, because the standard deviation was low, you kind of got a false positive on your valuations…it sort of looks like a good enough system. Let me show you what I mean.

Now let’s change the grid slightly.

A B C

101 68 50

100 67 49

99 65 1

The total value in each column is still the same (300, 200, 100) but now the max score is 218 and the minimum is 165. Big difference.

That’s what Alex was on about below when he was talking about standard deviation (the diversity of the values in the set). In the first grid the STDEVs are 1, 1.52, and 1. In the second grid you have STDEVs of 1, 1.52 and 28! Something is going on there, right? And anybody would know intuitively that the first two picks off the board should be 50 and 49. The average player has not changed either across all players nor within each category, and yet we have a very different result.

I think what this points out about your system is that it tells you how to get the highest rated pick at any point, but it doesn’t tell you anything about the downside of getting more lowly rated picks at a category.

However, how can you know how to weight value against deviation? Now you’re really talking about apples and oranges. I haven’t been able to figure out the math, but I put the word out to some mathy folks and I’ll let you know what I came up with.

Meantime, I calculated the STDEV of each position using last dollar picked and Marcel projections for 1-12 plus 36 outfielders. Here are the results.

C: 8.8, 1B 9.5, 2B 4.3, 3B 6.6, SS 9.6, OF1 5.1, OF2 1.9, OF3 .83

I have some thoughts about what the stdev’s mean as well as why I think your findings correlate with Grey’s gut instinct, but I think I’ll hold off and see if anybody makes it through my mess above first.

@Rudy: Reminds me of an old joke. Bill Gates walks into a bar and makes everybody a billionaire…on average.

I agree that what you have is a pretty good tool, especially in a draft where you have a lot of information, you have to think fast and sometimes rely on your intuition. However, I think there might be room for some refinement to you calculations. I do think that there is enough variance in stdev that your system might be slightly overvaluing or undervaluing players.

I’ve also been tinkering around with Mauer (the classic outlier). Unfortunately I have to run, but I’d like to continue the conversation. If you check back on this same comment thread tomorrow, I’ll put my thoughts up there.

Thanks again for your excellent thoughts.

Keeper league without limits on keeping, 6×5 (+OPS).

Heyward and Hamilton for Hanley?

@Rudy Gamble:

Preparing for my draft in a 16 team H2H dynasty league. I’ve got the 16th pick in the snake draft. Normally I’d be happy to have that draft slot for the back-to-back picks, but my the only other Razzballer in the league (who is probably going to read this post) landed the 15th pick. I’m concerned about him poaching my draft targets (especially in the later rounds) and have found two owners (non-Razzballers) that are willing to trade draft positions (swap positions for all 20+ rounds).

Should I swap for the guy picking 10th, the guy picking 12th, or stand pat at 16 and risk having my friend (@ #15) mess with my game plan?

Thanks for the perspective!

But is a fearophobe a walking oxymoron?

@Rudy: First of all, the more I think about it, the more I think that the 75/25 weighting system is pretty clever. It doesn’t make pure mathematical sense, but what would make sense is so complicated that I can’t figure it out. You’d need a pretty complex algorithm to factor in overall talent available versus available talent at a position versus your roster construction, versus the roster construction of the other teams (factoring optimized future teams as well). You could do it, but you’d need some heavy math and maybe Deep Blue. So your solution is pretty good…it works for you in the real world. Still, some of the point shares rankings seem out of place with conventional thinking (Mauer, Posey, Cabrera, Howard, all low, AROD being so high). Either you were really on to something or the point shares could use some refining.

I wanted to start thinking of standard deviation instead of scarcity. I put the top 12 point shares at each position and checked the stdev at each and as I expected I found the highest deviation at catcher, shortstop and first base. The lowest deviation was at 2B, 3B and OF.

I think the reason why point shares tend to be slightly more wonky at positions with a high deviation is that in the calculation, each player is both contributing to and being measured against the positional mean. Mauer brings the mean way up and then gets a positional adjustment based on his relation to that average, essentially being punished for his good performance. Doumit, on the other hand, benefits from his own lowering of the mean by having a lower average to compare against. This is true across all positions, of course, but it’s particularly true where stdev is high. The further a player is from the mean, the more he benefits from or is penalized by this effect.

I would be really interested if you basically took the same methodology but compared each player to the positional average not including himself. I think this gets you a lot closer.

Finally, relevant to yesterday’s comment, I do still think that point shares, while a potentially excellent tool for comparing apples to apples value, still does not tell you enough about the relative advantages of owning a good player or punishment of owning a bad one where stdev is high (think of the matricies above). One thing you might consider toying with is instead of doing a flat 75/25 break out, weighting positional effects proportionally even higher where stdev of point shares at a position is high and reducing that proportion where it’s low.

Lastly, a word on why point shares as is are a good fit with Grey’s gut. I think almost everybody who plays fantasy misunderstands scarcity. We’re all equipped with a belief that scarcity = value. But you know there’s not a lot of elephant crap where I live, but that doesn’t make it valuable. But because drafters misunderstand scarcity, players at high stdev positions generally go way to early. So if point shares rank Mauer lower than he truly belongs, it doesn’t matter because you guys aren’t going to draft him anyway. Somebody else will take him too early. On the flip side, 1B is perceived as having low scarcity because the 12th ranked player is still high relative to the overall mean. But stdev is still high at that position because of the strength of the top tier. That’s also factored into Grey’s drafting strategy as he says he’s going to get a top rated 1st baseman no matter what, which is basically a good intuitive read on the position.

Thanks again for introducing me to point shares! Lot of hard work on your part and a good way to think about valuing players.

I’m in a 10 team 5×5 keeper league, non auction. I am struggling to weigh positional scarcity in my keeper selections. I get to keep 5 and I am struggling with OF vs 1B vs SS. Who to keep?

Choices: Cano, CarGo, Zimmerman, Fielder, J. Upton, Reyes, McCutchen, Choo. Any thoughts???

I won the league last year, so I get the 10th pick. We have a rule in the league that you can only keep a player for 3 years. Last year I kept Cano, J. Upton, Zimmerman, Fielder and Braun. I traded Braun last year to help me win the league knowing that I had Choo, McCutchen and CarGo who I could keep. So if I keep Upton, Zimmerman or Fielder I can only keep them through the 2012 season, but McCutchen, Choo and Reyes I could keep through 2013 along with Cargo.

Also, I know that there will be a few teams that choose to keep less than 5 players and draft in the 5th round.

Thanks for the help!

Also, we have 2 UTIL spots and 4 OF spots, with NO CI or MI spots

So let Zimmerman, Upton and McCutchen go? I struggle with letting Zimmerman go at a weak 3B spot.

@Rudy: Lemme splain what I was looking at with standard deviation. I took the dollar values (I took mine from the website last player picked, but could just as easily use point shares instead of $s…the concept remains the same) of all the players at a position 1-12 and I calculated the mean of those dollar values and also the standard deviation from the mean for each position. For instance: 1st base goes from Pujols @ $43 down to Konerko @ $11 and the mean dollar value across the top 12 1st basemen is just over $22 bucks. I then calculated the standard deviation in values for the 12 first basemen and got 9.5. For the many who I am sure are following along with my rambling, standard deviation is a measure of how diverse the values in a data set. Low deviation means values are clustered around the mean, high means more diverse. The sets (1, 51, 101) and (50, 51, 52) have the same average but very different deviations. The values in the second are all much closer to the mean.

When I calculated the deviation for all positions I found that 1st base actually has the second highest deviation, which also suprised me a bit. It’s somewhat counter intuitive because the lower rated 1st basemen are still relatively high value compared to other positions. It just speaks to how far superior the top 1st baseman are.

Here are the standard deviations for all positions from highest to lowest: SS 9.6, 1B 9.5, C 8.7, 3B 6.5, OF1 5.1, 2B 4.3, OF2 1.9, OF3 .83

I basically took two things away from looking at standard deviation for each positions and I’ll resummarize them here.

First, with regards to point shares, the further a player is from the mean at his position, the more he is either rewarded or penalized by being included in the mean and then benchmarked against it. In your example above you say your not sure how much of a difference it makes but it seems like an extra 8 runs and another .004 in average above the mean for the position might move the needle a little. It’s tough to tell just how much it would move it because you’d need to calculate all the point shares that way to see and as you said, that’s a tougher bit of work.

Of course every player who was not statistically identical to the average player would have an adjustment, but the point is, this adjustment becomes larger and larger the further a player is from the mean. The point share rankings are pretty tight so even a small adjustment to the outliers at the top and bottom of each category might potentially make a material impact on the rankings. I kind of think it would make more of a difference than you think. What makes me think it’s a possibility is that the positions where I see your rankings disagreeing more with conventional wisdom happen to be primarily at the positions where you have more deviation from the mean, c and 1B in particular.

The last thing is the reason I think you might want to adjust the 75/25 split, or at least tinker around with it, to account for deviation is that after you’ve normalized values by calculating point shares (getting to apples to apples) two players with the same dollar price at different positions aren’t necessarily of equal value. That’s because where dollar prices are clustered around the mean, you can’t separate yourself from the pack as much or be penalized as much relative to the players the other teams will be starting at those positions because the deviation is low. On the other hand, at high deviation positions, you get a lot more pleasure/pain at the extreme ends of the rankings.

Thanks for your detailed response, Rudy! Really appreciate the conversation.

Okay, I was able to re-run Point Shares where the player is removed from the positional average.

These were the results for the top 6 in each position:

(Total Rank Change,Total Point Shares Change)

C 14, 0.9

1B 4, 1.1

2B 6, 0.6

SS 6, 0.9

3B 9, 0.8

OF 0, 0.5

The biggest rank change was in Joe Mauer who shot up from #39 to #31 – with almost all of this driven by an increase in AVG contribution. No other hitter in the top 150 had their rank change by more than +/- 3.

Net-net, this would lead to an improvement in the data but it’s one that’s very subtle. It also leads to a number of other issues for producing the data – e.g., the query for calculating a different positional average for every player is more complicated and is problematic for players who won’t be drafted or are DH. So I’m still debating whether it’s really worth the trouble.

I think it’s probably not worth the trouble to change the way you compile your data, but a good thing to understand about your data. If you look at the changes by position, they do in fact correlate with the standard deviation and of course the Mauer thing was predictable as he’s the biggest outlier. Also, although Pujols, Tulo, Hanley probably didn’t shoot up much in the rankings, that’s probably because they are already very high. I bet there was some adjustment to their point shares and their dollar value though. I think the overall takeaway is that players who are far better or far worse than the players at their position are probably slightly under/over valued by point shares so you can kind of keep that in the back of your mind.

For me personally, I’m also going to continue adjusting slightly upward and downward based on the standard deviation at each positon as I look at the draft. I’ll also use change in standard deviation to put my tiers together too. Great stuff, Rudy. I look forward to chatting with you more on the message boards over the course of the year.

@Rudy: well, an extra buck fitty is not nothing, but it’s not a ton either. Good news for you…seems like point shares hold up pretty well as is!

@Rudy: Would you change your keeper recommendations with Choo’s recent elbow problems, since he has had elbow issues in the past? You said keep Choo and Reyes, throw back Zimmerman, J. Upton and McCutchen.