The Great Valuation System Test: The Divisive Players
The aftermath of The Great Valuation System Test continues! Before reading further, be sure you know what was being tested and our process, along with the results:
At the end of the results article, I mentioned that although we now have a good idea of which valuation system proved best at converting a player’s statistical line into a dollar value, that doesn’t necessarily mean that the system does the best job for every individual player or player type. So today I’ll look into different player groups and individual players and see if we could find any patterns.
I will be excluding ESPN because their rating number is on a different scale and only using the Razzball – 0% Pos Adjustment & 100% versions. I also don’t have room to fit all the systems in so had to cut down in some manner.
Catchers
Easily the most divisive position is catcher. This is especially true in two catcher leagues, because depending on the league size and format, players qualifying at the position could get a significant boost in dollar value solely because they are catchers. Many fantasy owners are uncomfortable with this, preferring to punt the position and be satisfied drafting the bottom tier catchers.
I’m obviously a proponent of the positional boost, if warranted, because when generating dollar values, enough players at each position to fill every active roster slot must be worth at least a buck. Without some sort of positional adjustment, it’s very likely your last few catchers will be worth in the negative (though that won’t always be the case, at which point no positional adjustment is necessary). You’re certainly not going to be given extra auction dollars to add to your budget for taking these guys, so they must be boosted to a buck, which removes money from other players.
So let’s begin by taking a look at the top 12 catchers, using the names from Zach’s z-scores simply because that’s the position designations I have on my file. These aren’t necessarily the same top 12 from the other systems, but it doesn’t matter.
Note that Carlos Santana was listed at 1B in Zach’s values, which I assume means he was valued there, rather than at catcher, so if Zach had him at catcher, he would likely be worth more. I also assume all other systems valued him at catcher.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms |
|---|---|---|---|---|---|---|---|---|
| Buster Posey | 22.26 | 22.60 | 25.00 | 17.60 | 15.30 | 23.04 | 21.60 | 22.03 |
| Jonathan Lucroy | 16.15 | 15.25 | 16.00 | 11.30 | 17.10 | 15.24 | 14.98 | 14.94 |
| Devin Mesoraco | 13.95 | 12.96 | 14.00 | 11.70 | 10.10 | 13.95 | 13.39 | 13.55 |
| Yan Gomes | 13.24 | 12.01 | 13.00 | 10.30 | 7.40 | 12.00 | 11.99 | 12.63 |
| Carlos Santana | 10.89 | 13.39 | 12.00 | 12.90 | 19.50 | 11.85 | 13.58 | 14.28 |
| Salvador Perez | 8.56 | 6.15 | 9.00 | 6.00 | 4.90 | 5.41 | 6.58 | 7.33 |
| Brian McCann | 8.32 | 6.19 | 7.00 | 7.00 | 3.60 | 4.76 | 6.43 | 7.73 |
| Russell Martin | 7.35 | 4.92 | 7.00 | 4.30 | 8.70 | 6.61 | 6.25 | 5.52 |
| Dioner Navarro | 5.60 | 2.67 | 5.00 | 3.00 | 5.20 | 4.21 | 4.19 | 3.66 |
| Evan Gattis | 4.78 | 1.88 | 4.00 | 3.20 | -0.70 | 3.62 | 3.51 | 3.49 |
| Wilin Rosario | 3.38 | 0.25 | 3.00 | 1.00 | -0.40 | 0.88 | 1.44 | 1.61 |
| Derek Norris | 2.99 | -0.22 | 3.00 | 0.40 | 1.00 | 0.38 | 1.00 | 1.01 |
| Total | 117.47 | 98.06 | 118.00 | 88.70 | 91.70 | 101.96 | 104.95 | 107.78 |
Surprise, surprise, Razzball’s 0% Pos Adjustment valued the catchers the least amount. What is surprising, however, is that the 100% adjustment valued this group only $3 higher and was still far below the rest of the systems! I’m rather shocked that the REP system fell in the middle. In every auction and draft I’ve ever been in, catchers either go cheaper than my values or get drafted after I have them ranked. Perhaps fantasy owners know their inherent values, but still refuse to pay full price given the perception of added risk?
Jason told me that he was surprised by the fact that when running his z-scores, there was no position adjustment necessary. So his values are not adjusted, because all starting positions made it into the positive dollar pool. So it’s no surprise his z-scores value this group third lowest. But, it’s still $9 more than the Razzball system, also without any position adjustment. Zach’s z-scores and LPP are easily the highest and have nearly identical totals. It’s odd that Razzball’s 100% Pos Adjustment values Santana significantly higher than every other system, and he’s their top catcher, whereas Buster Posey is tops for everyone else. A breakdown of category dollars earned would have been helpful.
Speed
With my pride riding on Billy Hamilton this season, stolen bases is a category in which its primary contributors are viewed very differently. Many fantasy owners will shy away from drafting one-category speedsters given the potential hits they will take in homers and runs batted in. On the other hand, some owners realize the value of contributing such a high percentage of a category. Let’s see how the valuation systems handle this. I’ll choose a majority of the top base stealers from last year to compare values for.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms |
|---|---|---|---|---|---|---|---|---|
| Dee Gordon | 25.71 | 26.06 | 26.00 | 20.70 | 14.70 | 33.71 | 32.45 | 22.11 |
| Denard Span | 19.58 | 19.69 | 18.00 | 14.70 | 12.40 | 21.68 | 21.47 | 17.84 |
| Ben Revere | 18.24 | 17.73 | 17.00 | 13.90 | 10.40 | 25.18 | 23.45 | 15.04 |
| Billy Hamilton | 17.72 | 17.33 | 16.00 | 15.50 | 11.70 | 23.26 | 23.63 | 14.97 |
| Alcides Escobar | 15.57 | 13.86 | 18.00 | 11.00 | 9.00 | 17.01 | 16.50 | 12.57 |
| Rajai Davis | 15.47 | 14.80 | 14.00 | 12.70 | 10.20 | 19.58 | 18.77 | 13.35 |
| Leonys Martin | 11.96 | 10.59 | 10.00 | 9.20 | 6.80 | 13.78 | 13.93 | 9.86 |
| Jarrod Dyson | 1.32 | -2.00 | -1.00 | -0.10 | -3.20 | 4.97 | 4.12 | -2.24 |
| Total w/o Altuve | 125.57 | 118.07 | 118.00 | 97.60 | 72.00 | 159.17 | 154.33 | 103.51 |
| Jose Altuve | 35.86 | 37.89 | 37.00 | 28.90 | 27.80 | 48.06 | 42.95 | 32.67 |
| Total w Altuve | 161.43 | 155.95 | 155.00 | 126.50 | 99.80 | 207.24 | 197.28 | 136.18 |
I separated Jose Altuve from the group because of his huge batting average contribution as I wanted to try isolating just the stolen base component.
WOW! And there it is. The REP system values this group highest, with the winning SGP system close behind. After that is an enormous gap where the two sets of z-scores and LPP sit. Check out the low values for Razzball’s 100% Pos Adjustment system! Even the 0% Pos Adjustment is relatively low. I’m curious what Rudy has to say about why stolen bases are seemingly devalued so significantly.
You’ll notice that REP values Altuve highest by a wide margin. This is likely for two reasons — obviously for the stolen bases, of which we see the system values more than all the other systems from the non-Altuve group, and because of his league leading batting average. In my experience with the system, it seemingly calculates a larger range for batting average contributions than other systems. So, Altuve will get more positive value for his average than another system will dole out, while a low batting average guy will get a greater negative value.
On an island by their lonesome, is REP and SGP correct with their valuation of stolen bases or are they being overvalued? Well, when I run the REP system, I allocated the same dollars to each of the five hitting categories. So in a 12-team league with a $260 budget, that means that each category is allocated $430.56, assuming a 69/31 hitting/pitching split. For that very reason, an argument that the system overvalues stolen bases cannot be made. It values steals exactly the same as the other four categories! You may choose to strategically devalue steals when entering your draft, but that decision doesn’t actually change these hitters’ inherent values.
Power
If I believe that stolen bases are undervalued by the majority of valuation systems, then it follows that power must be overvalued. In order to try isolating just the power stats of homers and runs batted in, I will try to put together a group of hitters who were strong in those two categories, but relatively neutral in the other three.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms |
|---|---|---|---|---|---|---|---|---|
| Nelson Cruz | 30.57 | 33.12 | 34.00 | 28.70 | 29.50 | 32.01 | 31.00 | 32.79 |
| Adrian Gonzalez | 23.10 | 27.90 | 26.00 | 23.40 | 18.20 | 26.32 | 25.03 | 27.59 |
| Anthony Rizzo | 22.11 | 26.89 | 25.00 | 22.60 | 21.50 | 26.85 | 25.22 | 26.68 |
| Edwin Encarnacion | 20.46 | 24.94 | 23.00 | 22.00 | 17.40 | 24.90 | 23.24 | 25.15 |
| David Ortiz | 17.62 | 21.25 | 19.00 | 19.80 | 18.70 | 22.13 | 20.15 | 21.96 |
| Marcell Ozuna | 17.29 | 17.27 | 16.00 | 15.20 | 15.40 | 15.90 | 15.96 | 17.79 |
| Marlon Byrd | 17.18 | 17.08 | 16.00 | 15.40 | 15.60 | 15.74 | 15.92 | 17.77 |
| Lucas Duda | 16.42 | 20.03 | 18.00 | 18.20 | 18.60 | 19.20 | 18.58 | 20.63 |
| Adam LaRoche | 15.50 | 18.97 | 16.00 | 16.90 | 14.00 | 18.15 | 17.45 | 19.45 |
| Chris Carter | 14.83 | 18.11 | 16.00 | 18.10 | 18.30 | 17.83 | 17.58 | 19.25 |
| Brandon Moss | 12.51 | 11.77 | 13.00 | 11.70 | 11.90 | 9.79 | 10.40 | 13.17 |
| Total | 207.59 | 237.33 | 222.00 | 212.00 | 199.10 | 228.81 | 220.54 | 242.24 |
Well this was unexpected! The REP system actually values this group third highest! Five of the eight systems value this group between $220 and $242. Another headscratcher is those Razzball systems again. They were lowest or near lowest for the catchers, again for speed and now again for power! Where are those dollars allocated to?!
Let’s take a look at where each system ranked in dollar values allocated for power and speed. The speed ranks exclude Altuve.
| Speed Value | Power Value | Total Value | Speed Rank | Power Rank | |
|---|---|---|---|---|---|
| Todd Zola REP | 159.17 | 228.81 | 387.99 | 1 | 3 |
| SGP – Winning Fantasy Baseball Denoms | 154.33 | 220.54 | 374.87 | 2 | 5 |
| Jason’s Z-scores | 118.07 | 237.33 | 355.40 | 4 | 2 |
| SGP – Tony Fox Denoms | 103.51 | 242.24 | 345.75 | 6 | 1 |
| Last Player Picked | 118.00 | 222.00 | 340.00 | 5 | 4 |
| Zach’s Z-scores | 125.57 | 207.59 | 333.16 | 3 | 7 |
| Razzball – 0% Pos Adjustment | 97.60 | 212.00 | 309.60 | 7 | 6 |
| Razzball – 100% Pos Adjustment | 72.00 | 199.10 | 271.10 | 8 | 8 |
One might expect to find the systems to be relatively close in total value between speed and power. You would assume that if a system is valuing one highly, it would value the other less so to balance things out, as after all, every system is working with the same $260 per team budget to allocate those dollars. But this is certainly not what we see here. Maybe it’s just a matter of assuming different hitting/pitching splits. That could very well be at least part of the explanation, as my valuations were based on a 69/31 split.
Batting Average
As mentioned in the Speed section when discussing Altuve, I believe the REP system weights batting average more heavily than other systems. It might be argued that it is doing things correctly, whereas the other systems aren’t. And since my batting average dollars are the same as the other categories, it’s difficult to argue the math is wrong. Let’s check out a group of high average hitters.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms |
|---|---|---|---|---|---|---|---|---|
| Melky Cabrera | 19.42 | 19.77 | 19.00 | 15.60 | 15.40 | 19.10 | 18.39 | 19.42 |
| Adrian Beltre | 17.91 | 22.92 | 22.00 | 17.70 | 18.80 | 23.68 | 20.95 | 22.42 |
| Justin Morneau | 14.40 | 17.34 | 17.00 | 13.90 | 9.40 | 18.86 | 16.10 | 17.37 |
| Jon Jay | 3.90 | 1.21 | 5.00 | 0.90 | 0.00 | 2.04 | 1.84 | 2.10 |
| Justin Turner | 1.00 | 2.85 | 3.00 | 2.40 | 3.50 | 6.15 | 4.07 | 3.69 |
| Juan Uribe | -1.00 | 0.24 | 1.00 | 0.90 | 0.70 | 3.07 | 1.00 | 0.90 |
| Adam Lind | -3.19 | -3.45 | -2.00 | -2.30 | -5.20 | -1.00 | -2.57 | -1.76 |
| Total | 52.44 | 60.88 | 65.00 | 49.10 | 42.60 | 71.91 | 59.78 | 64.14 |
BOOM. I was correct. The REP method values these players by $7 more than the next highest system, LPP. Bringing up the rear are the Razzballers once again, which makes me think Rudy must have allocated significantly fewer dollars to hitters than the other systems.
Now let’s check the low batting average guys. I would expect REP to value the group the lowest. Let’s find out.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms |
|---|---|---|---|---|---|---|---|---|
| Chris Carter | 14.83 | 18.11 | 16.00 | 18.10 | 18.30 | 17.83 | 17.58 | 19.25 |
| Brandon Moss | 12.51 | 11.77 | 13.00 | 11.70 | 11.90 | 9.79 | 10.40 | 13.17 |
| Khris Davis | 11.44 | 10.38 | 10.00 | 10.30 | 10.00 | 8.38 | 9.62 | 11.62 |
| Ryan Howard | 7.83 | 9.76 | 9.00 | 10.60 | 4.90 | 6.94 | 8.28 | 11.50 |
| Dayan Viciedo | 5.61 | 3.52 | 3.00 | 5.10 | 4.90 | 0.69 | 2.79 | 5.68 |
| Chris Davis | 4.25 | 5.64 | 5.00 | 7.70 | 8.30 | 3.19 | 4.82 | 7.72 |
| Oswaldo Arcia | 3.01 | 0.41 | 1.00 | 2.80 | 2.50 | 0.08 | 0.74 | 2.46 |
| Luis Valbuena | 1.68 | 3.74 | 5.00 | 4.30 | 6.30 | 2.09 | 2.94 | 5.47 |
| Mark Teixeira | 1.33 | 2.08 | 2.00 | 4.40 | 0.40 | 0.88 | 1.81 | 4.26 |
| Shin-Soo Choo | 1.00 | -2.08 | -2.00 | -0.10 | -0.90 | -3.62 | -1.86 | -0.01 |
| Mike Napoli | 0.88 | 1.44 | 2.00 | 3.20 | 1.60 | 2.15 | 1.91 | 3.20 |
| Adam Dunn | 0.74 | 1.33 | 1.00 | 4.00 | -0.20 | 0.96 | 1.42 | 3.52 |
| Mark Trumbo | 0.70 | -2.42 | -2.00 | 0.30 | -0.20 | -1.28 | -1.72 | -0.49 |
| Carlos Beltran | 0.39 | -2.77 | -2.00 | 0.00 | -0.70 | -3.21 | -2.08 | -0.65 |
| Garrett Jones | 0.30 | 0.73 | 1.00 | 2.20 | 1.80 | -0.52 | 0.29 | 2.77 |
| Total | 66.50 | 61.63 | 62.00 | 84.60 | 68.90 | 44.35 | 56.94 | 89.48 |
Right again, as REP sits a whopping $12.58 below the champion SGP system. There’s the Razzball money! The two systems now sit second and third, finally! Let’s now combine the values from the high and low average hitters for each system.
| High Average Dollars | Low Average Dollars | Total Dollars | |
|---|---|---|---|
| SGP – Tony Fox Denoms | 64.14 | 89.48 | 153.62 |
| Razzball – 0% Pos Adjustment | 49.10 | 84.60 | 133.70 |
| Last Player Picked | 65.00 | 62.00 | 127.00 |
| Jason’s Z-scores | 60.88 | 61.63 | 122.51 |
| Zach’s Z-scores | 52.44 | 66.50 | 118.94 |
| SGP – Winning Fantasy Baseball Denoms | 59.78 | 56.94 | 116.72 |
| Todd Zola REP | 71.91 | 44.35 | 116.26 |
| Razzball – 100% Pos Adjustment | 42.60 | 68.90 | 111.50 |
We know Tony’s SGP used denoms for a different league format. That’s fine, it worked kind of like a control system as we figured it would test poorly, just as it did. And we see here one of the reasons why as it somehow allocated far more to this group of players than the other systems. I’m not sure what these hitters had in common that led to such valuations as it combined both low and high average players. Interesting that in total REP was second lowest, but that’s probably because my low average group included double the number of players as the high average group. If the number was the same, REP likely would have fallen right in the middle.
Individual Players
Finally, let’s look at some individual players with the widest range of values.
| Name | Zach’s Z-scores | Jason’s Z-scores | Last Player Picked | Razzball – 0% Pos Adjustment | Razzball – 100% Pos Adjustment | Todd Zola REP | SGP – Winning Fantasy Baseball Denoms | SGP – Tony Fox Denoms | Std Dev |
|---|---|---|---|---|---|---|---|---|---|
| Jose Altuve | 35.86 | 37.89 | 37.00 | 28.90 | 27.80 | 48.06 | 42.95 | 32.67 | 6.38 |
| Dee Gordon | 25.71 | 26.06 | 26.00 | 20.70 | 14.70 | 33.71 | 32.45 | 22.11 | 5.77 |
| Ben Revere | 18.24 | 17.73 | 17.00 | 13.90 | 10.40 | 25.18 | 23.45 | 15.04 | 4.53 |
| Victor Martinez | 31.47 | 37.82 | 37.00 | 30.10 | 26.80 | 39.77 | 35.36 | 36.20 | 4.13 |
| Michael Brantley | 35.84 | 39.19 | 36.00 | 30.40 | 30.00 | 41.96 | 38.79 | 36.07 | 3.89 |
| Billy Hamilton | 17.72 | 17.33 | 16.00 | 15.50 | 11.70 | 23.26 | 23.63 | 14.97 | 3.83 |
| Jose Abreu | 29.94 | 35.90 | 33.00 | 29.60 | 25.70 | 37.95 | 33.89 | 34.76 | 3.70 |
| Carlos Gomez | 30.37 | 32.70 | 30.00 | 27.00 | 25.40 | 35.57 | 34.49 | 30.31 | 3.25 |
| Todd Frazier | 22.90 | 28.79 | 26.00 | 24.60 | 33.60 | 30.59 | 29.13 | 27.73 | 3.19 |
| Jacoby Ellsbury | 22.55 | 23.16 | 21.00 | 20.10 | 17.90 | 27.92 | 26.96 | 21.22 | 3.17 |
| Lorenzo Cain | 12.77 | 11.57 | 17.00 | 9.60 | 7.60 | 16.27 | 14.89 | 10.54 | 3.11 |
| Denard Span | 19.58 | 19.69 | 18.00 | 14.70 | 12.40 | 21.68 | 21.47 | 17.84 | 3.02 |
| Alcides Escobar | 15.57 | 13.86 | 18.00 | 11.00 | 9.00 | 17.01 | 16.50 | 12.57 | 2.95 |
| Total | 318.52 | 341.68 | 332.00 | 276.10 | 253.00 | 398.93 | 373.96 | 312.03 |
I highlighted the system with the highest value in green and the lowest value in red. The majority of the greens are REP and majority of reds are Razzball 100% Pos Adjustment. You could see from the totals that REP is most aggressive on these names, with SGP not too far behind. Perhaps the two systems could be described as using a stars and scrubs type process, whereas the others have a narrower range of values between players, akin to a spread the risk strategy.
In looking at the player names, it’s clear speed plays a large role, as the top three guys were near league leaders in stolen bases. Batting average also drives the discrepancies judging by the V-Mart, Brantley and Abreu appearances, while Gomez, Frazier and Ellsbury posted all-around contributions, so it’s hard to say where the valuation differences are coming from. Speed again?
What’s Next
Well this was a fun little exercise. Unfortunately, we can’t test which systems are right about all the players listed above. Though maybe I’m wrong and all you smarty pants could devise a method. Looking at the individual players, it’s clear that valuation plays a big role. If I came into my auction with a value of $48 for Jose Altuve, we surely know who is and isn’t winning the bidding on his services! And yet, we’re all using the exact same stats to generate his value.
As I finish typing this, I just realized that I should have probably added up the total dollars each system allocated to its top 156 hitters, which would make up the active rosters of each team. So here they are:
| Todd Zola REP | 2196.43 |
| SGP – Tony Fox Denoms | 2152.81 |
| SGP – Winning Fantasy Baseball Denoms | 2152.80 |
| Last Player Picked | 2150.00 |
| Jason’s Z-scores | 2125.70 |
| Zach’s Z-scores | 2090.24 |
| Razzball – 100% Pos Adjustment | 1843.90 |
| Razzball – 0% Pos Adjustment | 1839.40 |
It looks like I did indeed allocate the most money to hitting! That’s something I should have considered when discussing the player groups and individual players above. However, it’s still a rather small difference compared to the two sets of SGP values and LPP. Aha! The Razzball systems did allocate far less money to hitters than the rest of the systems. The discrepancy in dollars allocated to hitting did not affect the correlation test results, but just makes the analysis of the above player groups and individual players a little less meaningful.
So where do we go from here? We could continue to devise better ways to test which system does the best job of converting a player’s statistical line into dollar values, as at the very least, an improved test would require that all systems value players at the same positions and allocate the same money to hitting. We could also test the same system, with and without considering position.
We could take what we have learned and try improving upon the current valuation systems and fix the acknowledged flaws. Or we could develop a completely new system from scratch.
If nothing else, I leave you with this — entering your snake draft or auction without a set of dollar values (or rankings derived from dollar values) is like showing up to your office job naked. You will not have a very successful day, so don’t do it.
Mike Podhorzer is the founder of ProjectingX IQ, an advanced fantasy baseball analytics platform that transforms projection data and in-season performance signals into actionable intelligence. He is the 2015 Fantasy Sports Writers Association Baseball Writer of the Year and three-time Tout Wars champion. He is the author of the eBook Projecting X 2.0: How to Forecast Baseball Player Performance, which teaches you how to project players yourself. Follow Mike on X@MikePodhorzer and contact him via email.
I think the thing to do would be to weight the values of every system to add up to $2150, then see which players had big differences in value. It looks like you’d see the same things, but Razzball wouldn’t be lagging quite so far behind.
perhaps you should have adjusted the values so all the systems allocated the same money to hitters, so you could actually see the differences in weight between all the categories.
As you mentioned, value systems disagree how to value ratios and extremes. I remember back in the day Yahoo! used to rank high end relievers (non-closers) in top 100 because their low ratios skewed the results.
Do you think the discrepancy in steal value could be due to steals being a standalone stat or these systems valuing a player’s 1st steal more than his 40th?
Secondly, I have the 1st pick in a 5×5 10 team league with NW instead of wins.
Am I crazy to consider taking Kershaw? If I knew both players would perform as last year I would take Kershaw.
I’ve spent a fair bit of time trying to figure out the reasons for the discrepancy in steal value. The reason REP puts a high value on SB is that it allocates value based on what portion of the available SB a player contributes. Since SB are concentrated in a few players compared to the other stats, but as much total money is allocated to SB as to the other categories, those few players get a large portion of that SB money.
The reason z-scores put a low value on SB is that the denominator is the standard deviation within that category. Since SB are very widely and unevenly distributed compared to other stats, the standard deviation is comparatively larger, so the system ends up allocating less money to SB than to other categories. I wish I had thought of that before we ran the test – I would have come up with a version of z-scores that forced an even distribution of value to see what effect that had on the correlations.
I’m hoping that somebody has a suggestion for how we could test the correct answer to this SB question, though. The complete failure to answer whether Billy Hamilton is a 2nd round pick was the biggest disappointment of this test.
Intuitively, REP feels like the right process and z-scores does it wrong, undervaluing steals. But I’d love to figure out how to prove it mathematically.
I actually agree with you, I think. But before we did this test I would have said z-scores did a lot of things wrong. Now I’m wondering whether z-scores do things right in ways that aren’t intuitively obvious.
Why is Razzball 100% Pos Adjustment is the lowest on everyone else but the highest on Todd Frazier? Is it because he plays 3rd?
I separated Jose Altuve from the group because of his huge batting average contribution as I wanted to try isolating just the stolen base component.
Why wouldn’t you just compare how each system scored steals?
Because I dont have a breakdown of category dollars from each system. I have it from REP since I calculated it (though it’s the same for each category) myself, but that’s it.
I hadn’t noticed it before, but there’s something screwy with those Razzball positional adjustments for the catchers. Some of them are worth significantly less with the adjustment than they are without it, others are worth much more. I imagine it’s because they adjust by using position-specific baselines for the individual categories, but that’s still a very strange adjustment.
It looks to me like the 100 percent adjustment is OBP, while the 0 percent is BA.
swiss cheese
Personally, I think that valuing average less makes sense, as I’m willing to spend more for skills that are more consistent (like power).
This approach is, I think, unable to translate to a final conclusion in terms of what system is actually best on draft day. There’s a disconnect between this “draft+hold” imaginary world and actual in-season management. As an example… one of the main arguments in favor of the hit/pitch split is that a large portion of end-of-season pitcher value is going to be on the waiver wire to start the season, while for hitters that’s not the case. The draft day $ spent on pitching don’t correlate all that well with final standings points in pitching.
The same could be said of certain categories, like saves or steals, which will have a larger proportion of freely available stats on the wire. So devaluing these categories relative to the others could actually be appropriate.
I admittedly can’t quantify these effects in a useful way, but if some of these systems are doing a better job of capturing that, they’ll perform worse under your evaluation method.
Yeah, this is strictly a test of postseason valuation – what was the season worth, not what should you pay for the player. There’s some obvious overlap with preseason values, but there are certainly good reasons you might want to draft with different values, or not stick closely to your values on draft day.
I go back to the original post where you mention that you expected the correlation to be higher and wondered how you could get closer to 100%. The missing ingredient is the context within the team.
As a very basic example, if you have Dee Gordon, Billy Hamilton, Altuve, Ben Revere, Denard Span and Leonys Martin on your team, you are not winning your league. The value of a stolen base, a homer, an rbi etc is directly tied to both the performance of the individual team and the array of the entire league. It’s impossible to mathematically value players in a general, systemic way and expect correlations much higher than you have here.
That’s my take on it as well. I think there’s still some room for improvement, but not much.
That said, one of the reasons correlations were so high is that many of the leagues weren’t very closely contested. When one owner drafted Victor Martinez, Michael Brantley, and Jose Altuve, and another drafted Prince Fielder, Jurickson Profar, and Josh Hamilton, it doesn’t take a great valuation system to get it right. That’s an extreme example, but I do think we would have seen lower correlations and more of a spread between the systems if there was more parity within the leagues.
“As a very basic example, if you have Dee Gordon, Billy Hamilton, Altuve, Ben Revere, Denard Span and Leonys Martin on your team, you are not winning your league. The value of a stolen base, a homer, an rbi etc is directly tied to both the performance of the individual team and the array of the entire league.”
Not exactly. You’ve chosen the SB guys. Choose the guys who contribute in the other four categories and you get a different answer.
Can you provide a spreadsheet of all of the players and their values in each system?
email me
Re: the Catcher adjustments….
The argument is that because by absolute value, some catchers earn negative value, we need to boost their value to match the reality of needing to spend $1 for each roster spot.
The more I think about this, the less sense it makes to me. The price you have to pay in an auction is NOT the same thing as the true value a set of projections is worth. Whether you pay $1 or $5 for your last catcher, his (projected) stats have the same true value to your team. If rostering the last Catcher means your team is actually reducing it’s overall value, that’s just the math. To me, that’s an argument for buying a catcher higher-up the rankings, so you’re not stuck with a negative earner.
If the rest of the league overpays for catchers based on their True Value, let ’em! The two options I see are:
1) Artificially increase the value of catchers so that you can spend $1 for a -$3 guy (-$4 profit)
2) Let the values = the values, and try to find the best bargain you can. If the rest of the league pushes C too high, take the value hit on a guy actually earning positive value (so spend $9 for a $5-valued hitter, the same -$4 profit but actually earning you positive stats)
You’re misunderstanding how the math works. For every negatively valued catcher purchased for at least a buck, that’s less money that’s going to be spent on other players. Whether you spend $9 on a true value $5 catcher or $1 on a true value -$3 is the same thing. You’re still overpaying by $4 and your team is no better off either way.
Knew I was forgetting something…
The Hitter/Pitcher allocation is a big issue with these results for Razzball. Consider the percentage allocated to hitters based on your numbers above (out of $3120; 12 teams x $260):
70%–Todd Zola REP
69%–SGP, Tony Fox Denoms
69%–SGP, Winning Fantasy Baseball Denoms
69%–Last Player Picked
68%–Jason’s Z-scores
67%–Zach’s Z-scores
59%–Razzball-100% Pos Adjustment
59&–Razzball-0% Pos Adjustment
Yes, I noted that at the end. It doesn’t affect the results of the correlation test, just comparing individual players above.
I think the real issue with this whole discussion is that we are using one term, “valuation system” to blanket what I see as three distinct activities with distinct goals and inputs.
#1: Ranking System
The goal of the ranking system is to inform decisions on when or for how much to acquire a player at draft or auction. It is appropriate to adjust values for positions. We recognize intuitively that given an OF and C with identical projections, we should choose the catcher first. The challenges to any ranking system are determining the correct amount of positional adjustment to values, the fact that values change with each pick or player auctioned and the complexity of the game theory involved in a draft or auction (irrational behavior, vast permutations, etc.).
#2: Production
The goal of a production measure is simply to place players side by side against their peers mathematically to see how much of the share of the total number of HR, RBIs etc. or W, K etc. a player or pitcher is contributing. This function should not have positional adjustments because it is not subject to any supply/demand considerations. A home run hit by a C and an OF are of identical value once the season begins. The issues with this methodology is that it does not allow you to measure pitchers versus hitters in any meaningful way because they are playing in different statistical pools. It also runs into the problem of generally overvaluing extreme outlier contributions to SBs.
#3: Standing Gain
The goal of the standing gain is to look at the value of a player production towards a particular stat target or benchmark. It differs in context from the pure production measure in that it is pegged to team goals rather than individual stats. The difficulty with standings gain is trying to account for the context of a team’s position. If a team is going to get only 10 saves in a season, then the value of a player who produces those 10 saves is very little or zero whereas a production measure would place a value on those saves.
So I propose that there is no Higgs boson of “valuation systems” that can unify the three activities above. It may be that replacement is a good model for #1, z-scores for #2 and SGP for #3. Maybe. None of the issues facing each of the 3 has yet been satisfactorily resolved by any model or system I have seen. Maybe a good start is to stop conflating the 3 and focus on finding the right mathematical model for each specific objective so that we can then work toward the refinements that address the inherent difficulties with each.
Ultimately we should recognize that a good fantasy player would probably want to have all three sets of values at different times and would be well informed about how to apply the information packed into each number.
Z-scores are not a sound way to create a ranking. The supposed virtue of them is that they standardize the distributions, which allows them to be compared…which is true. Unfortunately, the statistically naïve take the next step and think “Ok, we can now add these standardized numbers together for a ranking!”
Nope.
Z-scores are standard deviations. Standard deviations may not be added. Period. If you want to use a Z-score approach you must first create a common metric and then calculate standard deviations of that common metric. But since the point of the Z-score transformation in the first place was the creation of a common metric that makes the entire exercise useless.