In 1981, Donruss produced the greatest set of baseball cards imaginable. Not great for stylistic reasons, but great because it was rife with mistakes. Bizarre mistakes. Like it's possible that Oscar Gamble's head was on Lenn Sakata's body – that sort of thing. Names were misspelled, statistics were wrong, pictures were reversed, players were misidentified. It was boldly amateurish. Basically, it was the set of baseball cards that you and your friends would have produced if you'd been given a Polaroid One Step, a Baseball Encyclopedia, and 48 hours to design 600 cards.
But at some point during the set's distribution, all the errors were corrected. Ken Forsch's face stopped appearing on Vern Ruhle's card, "Paul Spitglorp" was changed to "Paul Splittorff," and – with his image no longer reversed – Buck Martinez suddenly looked like a right-handed hitting porn star instead of a left-handed hitting porn star.
The Donruss set then became just like any other set: glossy and odd-smelling, but lacking surprises. Yet the mid-season corrections led to a total frenzy among my card-collecting peers – We were 10 years old, just for the record. We wanted all the error cards. We traded our Jim Rices for Willie Norwoods, and the logic seemed solid. Willie's card was scarce. That scarcity was going to make it insanely valuable, we reasoned. Because scarcity and value have a simple relationship, right?
Well, no. As it turns out, the error version of a Willie Norwood card is still just a Willie Norwood card. Same with Luis Pujols. Value can be a tricky thing. It's often about more than scarcity.
This fact brings us to fantasy baseball. More specifically, it brings us to this quote:
"Steals are more valuable than power."
Just read that in a 2007 MLB fantasy draft guide. It doesn't matter which one; you'll find the same idea in lots of places. Often you'll actually hear that stolen bases have twice the value of home runs. The logic behind the statement is that in most leagues, there's a 2:1 ratio of HR to SB. In fact, last year in the majors there were 5,386 home runs and 2,767 steals. That's 1.95 homers for every stolen base. Thus, in fantasy:
"Steals are more valuable than power."
Half the number, twice the value. Stat scarcity rules. That's the thinking. Adherents to this belief are tough to budge. They have math on their side. They have Juan Pierre in their outfield, too. They drafted him early and gloated when they did it. Because they're thinking that Pierre's 50 steals are really like 100 home runs. And who hits 100 home runs? No one. So they'll happily take Pierre in the third round, thank you.
At this point, an old line from former Red Sox pitcher Bill Lee comes to mind: "In baseball you're supposed to sit on your ass, spit tobacco, and nod at stupid things."
We do the same in fantasy baseball. Except for some of us, there's no tobacco. But we definitely sit a lot and nod at things. Well, stop nodding at the old line about steals and power. It isn't necessarily true. The stolen base zealots are wrong. Scarcity alone isn't what dictates the value of a stat. If it did, your draft might begin this way:
There were only 1,201 saves in the majors last year. They're the scarcest of the 5x5 counting stats, but you won't find many fantasy writers telling you to load up on closers early in a draft. I'm not going to do it either. I'm also not going to disrespect, abuse, taunt, or malign the steal. It's important. There are points to be earned in steals, just as there are points in the other nine standard categories. It's just that a steal is not twice as valuable as a home run in your average Yahoo! public league, and we can say this unambiguously.
Because we looked at 5,000 Yahoo! public leagues with identical configurations.
This was really Tom Tango's idea. Tom is a widely respected sabermetrician – he's probably better known as TangoTiger – and the co-author of The Book: Playing the Percentages In Baseball. He's also significantly overqualified to answer fantasy baseball questions. Still, I sent him a convoluted email asking for thoughts on the SB/HR value dilemma. He answered in a very straightforward way: "All we care about is how much impact the extra SB and HR have on getting more points. The best way to figure that is to know the distribution of SB and HR at the team level."
It really is that easy, too. If you want to know the intrinsic value of any stat for fantasy purposes, you just need to ask this question: How many do I need in order to get more points? That's it. Points are what owners should care about. And to know how an increase in steals will affect your points, you shouldn't care about how many total steals there are in an average league, but how those steals are spread among teams. And the way to figure this out is by looking at standard deviation.
If it sounds like things are going to take an unnecessarily mathy turn, don't worry. They won't. Standard deviation is just a way to express how values – like stolen base totals – are distributed within a set of data – like, for instance, a 12-team mixed league. It's a very simple thing to calculate in Excel; you don't really need to conquer the underlying math. If the average team in a fantasy league has 100 total steals and every other team in the league is clustered tightly around the mean, then the standard deviation will be fairly small. If the standard deviation is small, then it won't take many steals to improve your category rank and increase your point total. That would make a stolen base a pretty valuable thing to fantasy owners.
As a rule, if things are distributed normally, 68 percent of the values (or 68 percent of the teams in your league) will be found within one standard deviation of a category mean – 34 percent should be one standard deviation above, and 34 percent should be one standard deviation below. Make sense?
Here's how things shook out for home runs and steals in our population of 5,000 Yahoo! public leagues:
Average HR per team: 201.9
HR standard deviation: 30.7
Average SB per team: 105.0
SB standard deviation: 34.8
So what do those numbers tell us?
Well, for starters, we don't care much about the average number of HR and SB per team at all. It's just fun to know. As Tom tells me, "The mean numbers are really irrelevant." It could be 3,000 or 300. Doesn't matter. Remember, all we care about are points. If we add 30.7 HR to a fantasy team that's at the league average, they'll move one standard deviation. Moving up one standard deviation should mean that they'll pass 34 percent of the teams in the league – that's potentially four points. Adding 34.8 steals to an average team should result in the same leap in points and category rank.
Again, that's 30.7 additional homers or 34.8 additional steals to achieve a similar increase in points. How you might choose to acquire your HR and SB is a different issue. The point is, steals are not necessarily twice as valuable.
Here's another way – maybe a more familiar way – to visualize the impact of adding HR and SB:
|TEAM||HRs||SBs||HR Rank||SB Rank|
|Plague of Corderos||261||110||12||8|
|Ian Snell and the Drells||210||153||7||12|
|The Inscrutable Dougs||217||131||9||9|
|Youre With Me, Weathers||232||106||10||7|
|Boca Burgers and Special Sauce||183||103||2||6|
|The Flaming Rons||205||40||5.5||2|
|The Acie Earl Experience||239||102||11||5|
|The Boneless Squabs||198||87||4||4|
|Nadys Swollen Appendix||184||137||3||11|
|Jennifer Love Ditka||205||79||5.5||3|
|The Lazy Outliers||34||23||1||1|
Those are the HR and SB results from one of my 12-team mixed roto leagues last season. All team names have been altered to protect the innocent (and to minimize vulgarity).
The mean for homers and steals holds up pretty well, considering that the last-place team conceded early and didn't maintain his team – Something about a disputed trade, I think. There's always an uneven trade that sends an owner off the cliff. Anyway, you'll notice that if you manage to add 30-odd HR or 30-odd SB to the squads closest to the mean, they'll jump over pretty much the same number of teams.
Here's an important caveat: moving up by two standard deviations in a category will not have the same impact as moving up one. There are diminishing returns. The second leap should only allow you to pass another 13 percent of the teams in your league. So if you're fortunate enough to draft Jose Reyes in the first round – which, just so we're clear, is still a good idea – don't pair him with Willy Taveras (who I think will pretty much be Juan Pierre this season, but with a different average draft position). Many of those additional steals Taveras gives you will be wasted, since you'll probably take the category by a mile, and it will likely come at the expense of power or pitching.
Alright, if you're still convinced that steals are way more valuable than power, I probably can't help you. I can, however, invite you to join the above roto league this season. The Outliers have quit. We're looking for someone. Also, somewhere in my parents' house I've got a stack of mint '81 Duffy Dyers that might interest you. . .
- standard deviation
- fantasy baseball