Your Hidden Enemy: Accounting for Variation in Fantasy Baseball

A Cafe forum discussion from February on the subject of JD Drew versus Shawn Green got me thinking about accounting for variation in selecting players in fantasy baseball. Let me quickly recap that discussion. One particular Cafe member asked which of these two players to pick in a 6×6 league with OPS. The topic attracted my interest since these two were going to be available in round 11 of my main 16-team league (with ten keepers), and I have them ranked near the top right next to each other, Green being slightly ahead of Drew. Quite a few people disagreed, emphasizing the potential upside of Drew.

That upside, however, comes with a downside. A healthy Drew is likely to outperform Green by quite a bit (compare Drew and Green in 2004); an unhealthy Drew is likely to fall short of Green by a substantial margin (compare 2005). Many of those responding to the initial question seemed to see the upside risk and ignore the downside risk. This is actually a common phenomenon in the study of human decision-making; we tend to overestimate the chances of winning the lottery and underinsure against potential risky losses.

So, how should we account to risk—meaning variation in player performance—in fantasy baseball? My argument would be that we can look at this just as we do in the area of financial investments. We can buy a really safe investment and get a three percent return. To get a higher return, we have to take on more risk. Stocks are one of the riskier investments that pay a higher return on average, but there is also much more variation in performance—more return entails more risk.

Developing a fantasy team of 25 players or a portfolio of 25 investments is really no different. A successful financial manager tries to maximize the return while minimizing the risk. Maximizing return is easy. You want to pick the guys with the highest predicted level of production. But how do you minimize the risk?

One of the keys to getting the greatest return with the minimum risk is to choose investments that are negatively correlated. In essence, this is what fantasy footballers do when they handcuff a player. If the starter is injured (and his numbers decline), the back-up gets more time and his stats increase. In statistical terms, there’s negative correlation between the starter and the backup. Even though there may be a better player to pick than the backup—in the sense that the other player may outperform the backup on average—the backup may be the better pick because he reduces the risk of my portfolio … er, team.

Finding negative correlations in fantasy baseball is more difficult. Wasting a roster spot just because some guy might become injured is tough to do, so picking a backup is difficult to justify. To some extent most fantasy players already recognize one simple way of dealing with correlation. The flipside of “look for negatively correlated investments” is “avoid positively correlated investments.” We generally follow that rule when we are cautious about selecting players from the same team. Team-dependent stats like wins, runs, RBIs, etc. are often positively correlated for players on the same team. So, if you have two players with basically the same projection, but one of them is a teammate of two guys already on your roster, you might pick the other player, just because he is less likely to be positively correlated with your existing team members. That way, if the team underperforms as a whole, you only take two hits, rather than three.

Are there other ways to exploit potential negative correlations? Suppose I’m picking between two pitchers who have identical projections, one from the AL Central and one from the AL West. If I have several AL Central hitters on my roster, maybe I want to favor the AL Central pitcher. If my hitters underperform, that may mean my pitcher pick will be more likely to overperform, giving me the benefits of negative correlation.

Since that seems to be a stretch, let’s think about another way of incorporating risk into fantasy baseball decisions. Another important rule in balancing risk and reward is that when two investment decisions have similar returns, you should pick the less risky investment.

This gets me back to Green versus Drew. The potential return on both players is really quite similar, if you do two things:

1) Account for Drew’s injury potential
2) Treat Green as a platoon player playing only against righties

If you do that, here’s what those two players look like in a simple three-year weighted average projection (50% 2005, 33% 2004, and 17% 2003):

Cats	R	HR	RBI	SB	AVG
Drew	73	20	56	5	0.293
Green	65	17	55	3	0.296

Now, there’s a slight advantage for Drew, but it’s not a big one. Note that the original question from the thread would require comparing the two players on OPS, and Drew has a significant advantage there, though it is offset somewhat by the fact that he averaged 70 fewer ABs over these three years. So, I’ve excluded that part of the question to focus on the 5×5 comparison where things are clearer.

Let’s add one line for each player to that table:

Cats	R	HR	RBI	SB	AVG
Drew	73	20	56	5	0.293
CV(Drew)	51%	46%	56%	127%	3%
Green	65	17	55	3	0.296
CV(Green)	12%	27%	14%	23%	4%

The new lines are the coefficient of variation, showing how much the player’s performance varies as a percentage of the mean. Drew’s runs, in other words, vary by as much as 51 percent of the mean. Steady Shawn, however, varies less than 12 percent.

In all cases, except batting average, Green has a significant advantage over Drew in variation. So, if we follow the basic investment rule, we have two “investments” with basically the same expected rate of return, but investing in Drew is riskier. Most fantasy players look at Drew’s upside and prefer to grab him. Contrary to what many fantasy players seem to do, the investment rule says to pick the less risky investment (again, this analysis ignores the OPS difference, which would weight it more towards picking Drew).

So, what does this mean, practically, for fantasy baseball? My recommendation to others is to incorporate a measure of risk in your spreadsheets. You could use a coefficient of variation as I did. You might grab information from Baseball Prospectus on “breakout” versus “collapse” and create a little ratio of “breakout to collapse” with high numbers identifying strong upside potential and low numbers indicating strong downside potential. This isn’t a real variation measure, but gives you some information about the likelihood of being far above or below the main BP prediction. The Marcel numbers include a “reliability” measure that can be taken as a measure of variation.

When ranking players within tiers (that is players you think have about the same level of value), put your variation measure up with them. Within tiers, you should tend to rank players higher if they have a better variation score (a lower coefficient of variation, a greater “breakout to collapse ratio, or a greater Marcel reliability score). If you do that, you should end up with a team that has, on average the same level of performance that you expected, but much less risk that your roster will collapse on you.

Good luck!

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