Value Based Drafting in Baseball

[TheMaizeAndBlue]

Hey all, I'd like to bring some discussion to the idea of Value-Based Drafting in fantasy baseball.

A quick disclaimer: This post is long, and will involve math. The spreadsheet included is free to use for anybody, but is tailored for OBP based leagues.
If you would like to skip the text and jump right into the spreadsheet, or pull it up as you read, the link is below.

https://docs.google.com/file/d/0B3UnZme ... sp=sharing

On to the wall of text!

The Introduction

For those unfamiliar, VBD is a commonly used strategy in fantasy football. It takes into account the baseline production expected out of each position, thus correcting for different scoring expectations; i.e. QBs typically score much higher than other positions, TEs lower etc. Value based drafting, depending on the method, will tell you how many more points a player is expected to score than the next guy at his position, or a typical player at his position. Basically, VBD is a way of quantitatively adjusting for positional scarcity.

Now, to my experience, positional scarcity in fantasy baseball is often addressed in a more qualitative way. For example, Matthew Berry's latest fantasy baseball podcast on ESPN discusses how much of a bump Buster Posey gets for being a C vs. his value as purely a first baseman. They essentially settled on 1-2 rounds "feeling" right. It's easy to see why this is. In standard H2H or roto leagues, there are 5 categories for hitters, and 5 for pitchers. In comparison, in fantasy football it's much easier to compare between positions because all production goes into the same category: points. In baseball, the same analysis will get you +/- in 5 different categories; comparing apples to oranges.

The Methodology

With all that in mind, we finally get to the point. Our goal is to go from comparing apples to oranges, to comparing apples to apples. In order to do so, I took a somewhat WAR-like approach. I took ESPN's projections and put them into a spreadsheet, sorted with an overall ranking, as well as positional rankings. Using this, I calculated the average of the 2*X number of players at each position, where X is the minimum number of starters at that position in my league. This creates a baseline "replacement level" player to compare to. Next, each player has a score calculated for each category: R, HR, RBI, SB, OBP. This score is calculated using the difference between each player's projected contribution and the replacement level contribution. This number is then normalized by dividing over the league leader's contribution in said category. This lets us address differentials across categories. Instead of wondering whether you should draft player A because he provides 7 more HRs than a replacement player or player B for providing 5 more SBs, you can see what percentage of the league leader in that category each contribution is.
Each player then has a total "player value" calculated as the sum of his contribution above the replacement level at his position in each category. This leads to players having very different scores depending on where you play them. For example, Carlos Santana drops more than 6(!) rounds as 1B vs. a C. This is because the "replacement Catcher" averages 60.2 runs, 18.75 HR, 71.9 RBI, 2.65 SB and a 0.344 OBP vs. a "replacement 1B" averages of 80.87/27.43/92.03/4.3/0.360.

Where I need help

Here's where you come in. I'm not a stats major. I have a solid background in math, but if I'm being honest, most of my methodology basically can be summed up as "tinker with it till it looks right". I'm looking for any pointers on where I can improve my calculations. Specifically, I'm considering taking just the average of the X number of players around the minimum players started. I feel that top catchers have been unnecessarily boosted by being compared to guys that will not see a draft board in anything less than a 15 team league. You'll also note that in the methodology segment, I did not mention how I calculated pitcher values. This is because despite using a similar system, I have no idea how to value each category in order to get an accurate comparison across pitchers and hitters. The link to my spreadsheet is given at the top of this post, as well as again below.

https://docs.google.com/file/d/0B3UnZme ... sp=sharing

If anyone has the time and inclination to peruse the data and come up with suggestions they would be most appreciated. If not, enjoy the spreadsheet, I hope it's useful. I will be updating with any changes I make.

tl;dr: Just read the post, you're in fantasy baseball forum anyways

[Ender]

I don't think this works at all for baseball. It works in football because you don't have to balance stats as much since everything gets turned into points.

One simple example of where this fails is if you look at how much value this gives a C for a SB it is simply broken. Napoli has a positive value in SB because his 3 SB projection is 'above average' at the position while Ben Zobrist gets a negative value in SB for having 17 since it is so common. 3 SB from a C is not more valuable than 17 from a SS. It might be harder to replace those 3 SB from the C but they aren't more valuable.

Replacement level is a slippery slope to begin with btw. The deeper you go into your rankings the less reliable they get to where the 'replacement level' player is maybe 50% accurate at best. Last year 3B was shallow going into the draft and by the end of the year it was very deep. There are better ways to look at positional scarcity than replacement level. Comparing players to an average player at the position is better as an example. Positional scarcity is a sham in general in most leagues though. Between multiple position players, the utility slot, MI, CI it all tends to get spread out to where it just doesn't exist anymore. About the only scarce position is C in a 2 C league.

[TheMaizeAndBlue]

I think that while you can argue that 3 SB from a catcher is essentially a guess since predicting something to that degree of accuracy is pretty much a crapshoot, IF these predictions were guaranteed to be 100% accurate, I would argue that a +1 SB for a catcher is indeed more valuable than a -2 SB from a SS regardless of the raw numbers. To make an extreme example, (given 100% accurate predictions of course, if you're arguing that the accuracy of Catcher SB predictions is low then no arguments here), if the average SS stole 1000 bases, and my Zobrist stole 999, and the average catcher stole 5, but Napoli stole 7, then Napoli's SB contribution is in fact more useful than Zobrist's assuming that I can in fact get "replacement level" production from that spot otherwise.

[TheMaizeAndBlue]

Admittedly though, Catcher appears to be somewhere this model flies in the face of conventional wisdom. However, I don't think it's wrong to say that something like Wieters' +10 HR over the average catcher is more valuable than Prince Fielder's +8 despite the raw numbers being 29 and 35 respectively. It's simply significantly easier to replace HRs from 1B than it is from catcher. Likewise between C and SS with SB.

[Ender]

Pretend we are in a pickem league so we can have the same players

Two teams have exactly the same roster except for their SS and C who happen to be exactly the same overall value. The two teams end the season in a tie. Now add 2 SB to the SS on team A and 1 SB to the C on team B. By your stats team B has more value in players but team A still wins the league with 1 more SB. Same example but add 1 SB to the SS on one team and one to the C on the other team. The 2 teams are still tied but your numbers say the team with the C is more valuable. A SB isn't more valuable based on the position. It just doesn't work that way.

[OaktownSteve]

I am not a fan of value based drafting in baseball for a couple of reason, and particularly not where using value above replacement at a positional level.

I'll give you a quick thought experiment to illustrate. Imagine you are in a 12 team draft where each team must acquire one player each (A and B). I'll give you a value range for each of the 12 players available for A and B:

A: 12 11 10 9 8 7 6 5 4 3 2 1
B: 8 8 8 8 8 8 8 8 8 8 8 1

All players B except one have a value over replacement of 7. Players A have a range of values over replacement. But, regardless of the VAR, it's clear that the draft order would be all Players A first.

What this illustrates is that value based drafting cannot give you any information about what order you should draft players in relative to the requirement to fill a prescribed roster of particular positions. It can tell you after the fact how well you have succeeded relative to your own projections, but the calculus for draft order (which is often given the terrible misnomer position scarcity is quite complex).

Imagine you had a super computer that could analyze every possible draft scenario in a 12 team snake draft. The computer could potentially tell each player what is his optimal pick at any particular place in the draft. However, that analysis would need to be recalculated after every pick to account for the change in the player pool created by each selection. In other words, if values are fixed against either average or replacement relative to the entire player pool, they become increasingly inaccurate as the average or replacement player universe changes as player come off the board.

Finally, each drafter will be using a different set of player projections and a different draft strategy. Some players will make stupid or irrational picks. Using a value based system tends to try to put a mathematical framework on a problem that isn't strictly mathematical in this way. It's something that is better addressed by game theory in order to understand optimal drafting given the expected behavior of the other drafters.

In short, values are an excellent tool for understanding the player pool, how the values are arrayed across all players and within the positional rankings, but it is the wrong tool for the job when it comes to executing a draft.

[TheMaizeAndBlue]

I think perhaps I was unclear in my methodology. It is not divided by the league leader in that category per position but by the league leader in that category overall. You are correct that a +1 SB is not more valuable for a C than a SS. I never said it was. The entire point is that the differential between that player and the replacement level player is the important part. In your example, Ben Zobrist has a lower value at SB than Mike Napoli not because he beats the average SS by a smaller proportion but because he actually loses to the average SS in SB while Napoli wins vs. the average C. To use your example, if a C and SS had the same SB value, let's say zero, meaning they exactly match the replacement level at their position. If you added 2 SB to the SS and 1 SB to the C, the SB-score for the SS is now 2/(43) and the SB-score for the C is 1/(43). 43 being the number of SB Mike Trout, ESPN's projected league leader in SB gets. There is no contradiction. The SS ends up with a higher score.

[Ender]

Oh ok that makes sense at least. I'm still pretty against replacement level by position for the other reasons I stated. The replacement level player is really impossible to know and once you fill out a real roster the positions filter such that positional scarcity doesn't end up existing in most leagues. I use basically the same method you use to find the replacement value for C which in my 2 C leagues was $8 over a normal player. All other positions are basically equal though once you put the 1B/OF into OF and the left over 1B in the UT slot etc.

I actually used VAR for quite a number of years but the longer I play the less I worry about the projections and 'value'. I'm now a largely tier based drafter. I mean I create values but I don't obsess over them because projections all should have a +/- $5 added to them. The difference between the 120th player on your sheet and the 150th player is something like moving up 1 spot in the lineup and having 2 HR sneak over the wall. It is just so small.

[BChinly]

I sort of do something like this in my drafts. I always go for 5-tool players, then when all of the 5-tool players are gone I will look at 4-tool players and pitchers since pitchers affect 4 categories at most when saves are involved. Then I will look at 3-tool when all the 4-tool are taken and so on. However I don't really do it by position, more batters vs. pitchers.

[OaktownSteve]

I think perhaps I was unclear in my methodology. It is not divided by the league leader in that category per position but by the league leader in that category overall. You are correct that a +1 SB is not more valuable for a C than a SS. I never said it was. The entire point is that the differential between that player and the replacement level player is the important part. In your example, Ben Zobrist has a lower value at SB than Mike Napoli not because he beats the average SS by a smaller proportion but because he actually loses to the average SS in SB while Napoli wins vs. the average C. To use your example, if a C and SS had the same SB value, let's say zero, meaning they exactly match the replacement level at their position. If you added 2 SB to the SS and 1 SB to the C, the SB-score for the SS is now 2/(43) and the SB-score for the C is 1/(43). 43 being the number of SB Mike Trout, ESPN's projected league leader in SB gets. There is no contradiction. The SS ends up with a higher score.

Value against average is only nominally better than value against replacement. But once again, while it tells you how the players stack up relative to each other pre- and post- draft it cannot inform you as to how you should draft at any particular pick because of the complexity (chaos?) of 12 teams trying to fill a roster with 23 players across prescribed positions. It generates false confidence.

Not too mention the obvious point that you could assemble a roster of 13 players who derive a majority of their value from a single category like SBs and have a high "value" roster destined to finish last in 4 of 5 categories.