ROTISSERIE: Recency bias and the belief in the law of small numbers

A main theme this year at BaseballHQ.com is to raise awareness of a recency bias often prevalent when we attempt to forecast future performance. In essence, "recency bias" means we use the most recent past to guide our choices. Thoughts and information that come to mind first are quite salient and often seen as most important.

In everyday life, judgments based on recency can be an adaptive and efficient way to make choices. However, such judgments can sometimes lead us astray. This article will examine how recency-based thinking can potentially lead to imprudent early season managerial decisions.

Perceptions of chance and the law of small numbers

In general, people tend to expect a sample drawn from a particular population to be more similar to the population than sampling theory predicts, at least for small samples. All over the fantasy baseball world, especially here at BHQ, you'll hear the admonition, “Don’t read too much into small samples.”  Even knowing this caveat, though, individuals still overweigh small samples.

A basic rule, the law of large numbers, states that very large samples will be highly representative of the population from which they are drawn. However, people's intuitions about random sampling often extend this concept to by asserting that the law of large numbers applies to small numbers as well (law of small numbers). Psychologist Amos Tversky and economist Daniel Kahneman (1971) suggest the believer in the law of small numbers faces several particular dangers relating to biased judgments.

Applying their warnings to fantasy managers, the believer of the law of small (fantasy) numbers:

  • Gambles his fantasy lineup on small samples without realizing that the odds against him are unreasonably high.
  • Lets early trends and hot (or cold) streaks carry excessive weight in the perceived stability of observed patterns.  
  • Evaluates future performance with unreasonably high expectations about the replicability of past performance (in other words, he underestimates the breadth of confidence intervals from projections).
  • Rarely attributes deviations from expectations to sampling variability, because a causal "explanation" for any discrepancy can be generated. For instance, he attributes variation to a potential hidden injury, PEDs, or ballpark effects, rather than the sampling variance that is the most likely cause.

Preliminary analysis of most dropped and added players

Based on the most added and dropped list from a popular online fantasy baseball site, we can see evidence of over-weighting small samples. Of the Top 25 hitters dropped as of Saturday, April 21, some notable names appear. Some players, like Brandon Belt (1B/OF, SF; -14%) and Mark Trumbo (1B/3B, ANA; -8.8%), have not received regular ABs yet, but both could produce double-digit value by season end.

Some pre-draft sleepers, like Lucas Duda (1B/OF, NYM; -7.2%) and Paul Goldschmidt (1B, ARI; -6.9%), have also been relieved of regular fantasy duty. Duda’s BA has been struggling but has displayed the power for which he was likely drafted (.200 BA/3HR/130PX), rather than his .311 BA in the 2nd half of 2011. Goldschmidt, who arguably has greater upside, has also struggled out the gate (1HR/ 97 PX). Although not projected to hit for high BA, a 53% GB rate to date is limiting his power output.

Bounceback candidates Adam Dunn (DH, CHW; -12%) and Jason Kubel (OF, ARI, -10.6%) are being dropped despite solid early-season peripherals. Dunn’s BA has regressed closer to its mean, and his 273 PX is staggering, albeit unsustainable. Kubel, on the other hand, has produced pedestrian surface stats (.250 BA/ 1 HR), but his .298 xBA suggests that higher BA may be arriving, and his 23% fly ball rate (20% lower than his 3-year average) potentially indicates more power may be coming.  

The most added batters also show evidence of small sample size bias.  For instance, the hot start (.275/3/14) by Luke Scott (DH, TAM; + 19.2%) has caught the attention of owners, but his 20% HR/F rate is likely to regress and his DCD reliability grade reinforces elevated playing time and injury risk. Jordan Schafer’s (CF, HOU; +28.2%) 6 SBs and regular playing time confirms his value as a source of speed, but his .182 xBA and 39% hit rate point to BA downside. Likewise, Chase Headley’s (3B, SD; +11.9%) 4 HR and 12 RBI may suggest that his power stroke has returned, but 29% HR/F rate is bound to regress.

Causal attribution in small samples

We naturally try to make sense of what we see in the world. As a result, we tend to discount the impact of small sample sizes by making causal attributions for why the data seem inconsistent with expectations. For instance, there has been a great deal of speculation about the health of Tim Lincecum, whose 8 + ERA and 1.80 WHIP after four starts stirred concern in the minds of some managers.  Some have even suggested that a drop in velocity may be a harbinger of a forthcoming meltdown.  A drop in velocity is certainly symptomatic of arm failure. However,. Lincecum’s peripheral statistics (11.6 Dom and 46% GB rate) suggest that the surface stats arising from this small sample will positively regress towards Lincecum's mean statistics.

Related, Ryan Braun’s slow start might have sparked some early concern in managers. Representative thinking may lead us to think that suspected PED use may have affected past statistics. We believe that PEDs increase performance, and therefore that not using them should reduce performance. This thinking may lead one to believe that Braun is “just another ‘roids case,” and career lows may be expected — even though he was officially cleared by the league office. Again, 50 ABs should not form the basis of the judgments. Even with regression to the mean from Braun’s 2011, you would be hard-pressed to find a more reliable bat long-term.

Day-to-day transaction watching

Avid fantasy managers likely check their team and watch live scoring on a daily basis. Although technology has improved access to our teams and this flexibility allows us to keep close tabs on breaking developments, it may also come at a cost.  Day-to-day performance is inherently more variable than performance over longer intervals.

A classic behavioral economics study, (Kahneman et al., 1997) found that individuals were more likely to accept risk (which is positively correlated in the real-world, but inversely related in our minds) if they evaluated their investments less often. By placing too much stock in daily statistics, managers may be more prone to act on small sample size data because short-term performance is highly prone to variability which includes losses and gains.

This by no means should be taken as advocacy for ignoring teams and daily news, especially in daily transaction leagues. Instead, it is meant to raise awareness that more effective player evaluation may be made if the evaluation window is longer. Fantasy baseball is a marathon, not a sprint. Sometimes, this point is discounted. 

 

CITES:
--Kahneman, D., Schwartz, A, Thaler, R.H, Tversky, A. (1997). "The Effect of myopia and loss aversion on risk taking: An experimental test." Quarterly Journal of Economics 112, 647-661.

--Tversky, A., & Kahneman, D. (1971) Belief in the law of small numbers. Psychological Bulletin, 76, 105-110.


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  For more information about the terms used in this article, see our Glossary Primer.