#prospecttheory

Behavioral finance arba savo galimybių pervertinimas. Tęsiame straipsnį apie investuotojų ir spekuliantų elgesį rinkoje. Psichologija yra bene svarbiausias

Contenuto elaborato da: Vittoria Perego

Nel 1979 Kahneman e Tversky hanno elaborato un modello in grado di spiegare come gli esseri umani prendono le decisioni. Si tratta di un processo molto più complesso di quanto possiamo immaginare, le persone non sono così razionali e capaci di considerare ogni singolo aspetto quando devono fare delle scelte. 

Questa teoria è applicabile anche al contesto quotidiano e alla sfera personale proprio come vien illustrato nell’articolo di Luigia Barzaghi pubblicato nell'osservatorio sul COVID-19 di aBetterPlace. In questo periodo di emergenza sanitaria e di forte incertezza abbiamo vissuto momenti di smarrimento e di angoscia, ci siamo trovati nel “terzo quadrante” quello in cui il dolore e gli effetti negativi vengono avvertiti in modo più profondo rispetto ai momenti di felicità. 

Inoltre man mano che il tempo passa questa sensazione negativa va scemando e il dolore diventa meno forte. 

Non spaventatevi, è un effetto del tutto normale, è una lettura in chiave comportamentale di un periodo che molti di noi stanno ancora affrontando. Esserne più consapevoli ci aiuta sicuramente a viverlo meglio.

From time to time I notice things in “the real world” that can be further explained with behavioral economics. Today’s topic is baseball’s save stat.

Ask any baseball stathead their thoughts on saves and the value of closers and you’re sure to get a scornful response.

Announcers and sportswriters continue to question why teams’ seemingly best relievers are only used for save situations. Teams lose games without ever putting in their best reliever, and then that same pitcher “saves” a game 4 days later that the team very likely would have won anyway.

Surely, most front offices today (sorry Phillies fans) are using better methods to evaluate relievers. And surely this new information can be used to optimize how arms in the bullpen are used.

Yet the save stat prominently lives on and bullpens are still managed around it. Why?

Humans Aren’t Computers

Humans don’t act in their own rational self-interest. They don’t make logical decisions, they make emotional ones that often come from an irrational place. There are countless cognitive biases always in effect, and the rationality of a decision is bounded by the information we have at the moment we make it.

What’s going on in the case of closers, the save stat, and the decisions around those 2 things is a result of Prospect Theory. Prospect Theory is very interesting in itself - I recommend you click that link and read about it. The two components relevant to the context of this article are:

Losses hurt more than gains feel good. The effect is about 2.25 times more powerful. For example, according to the irrational human brain, avoiding a $5 surcharge feels equal to getting a discount of $11.25.

Humans are risk-averse when there is a high probability of feeling a gain, and they are willing to overpay for certainty. For example, given a 95% chance to win $10,000 or 100% chance to obtain $9,499, they’ll take the $9,499 (and probably even less) even though the expected payout of the first scenario is $9,500.

The End of a Baseball Game is Prospect Theory at Work

When it’s the end of a game, and it doesn’t feel certain that a victory is at hand (a reasonable cutoff for that feeling being a lead of 4+ runs), managers, GMs, fans, and players alike are all willing to overpay for the certainty of not feeling a loss. So in comes the closer for the save. This is normal, risk-averse, human behavior and it’s not going to stop until teams are managed by computers or Phil Ivey.

How about close games? Why are closers saved for when a team is ahead? And why aren’t they used in the 7th inning with no outs and Mike Trout coming up with the bases loaded?

Here are the possible outcomes of a baseball game ranked on a “feeling scale” from most powerful to least powerful.

-4.5: Losing when you thought you were going to win

+3.25: Winning when you thought you were going to lose

-2.25: Losing

+1: Winning

0: Game suspended due to rain

Pitchers can’t create a win (from the mound, at least). They can only not lose. So the 2 losing scenarios govern a manager’s bullpen decision-making in those close games.

Technically, a pitcher can’t “not lose” in the 7th inning as there are still 2 more innings to play. In that moment, there are all kinds of unconscious calculations a manager’s brain makes in the background to help him quickly decide how to optimize the use of the bullpen to not lose.

Whatever those calculations are, the decision is usually the same: the closer’s butt stays glued to the bench and in comes a non-closer reliever. And the real reason why, no matter what the manager says, is that he’s optimizing to avoid the greatest loss possible: losing when you thought you were going to win.

It’s fair to reiterate that this isn’t something managers are consciously doing. They aren’t calculating odds of victory (or not losing) and choosing a reliever accordingly. This is all happening unconsciously based on thousands of years of evolution that has turned us into loss-avoiding scaredy cats.

Saves = Loss Avoidance

So why is losing when you thought you were going to win so painful? Any loss sucks. It feels crappy. But when you thought you were going to win? That feels much worse! Why? It’s because your point of reference changed. You already felt and accounted for the gain of the win. So now instead of feeling one loss, you’re feeling that loss PLUS the loss of the win you thought you had. Major bummer!

The save stat is simply a representation of loss avoidance. Closers aren’t paid to accumulate saves. They’re paid for what the save attempt represents: an opportunity to increase the certainty that a team’s stakeholders won’t feel the pain of losing what, in their mind, is already a win. In other words, they aren’t paid to get saves, they’re paid to not get blown saves. This differs from what non-closer relievers are paid to do and, as we’ve already learned, humans are willing to overpay to avoid the loss of a near-certain gain.

That’s why saves and blown saves matter. They’re the best metrics we have to describe the reality of the irrational human brain of baseball’s decision makers.

What do the numbers say?

I used Spotrac’s Free Agent Tracker to get a list of all the free agent reliever signings from 2012-2015 (2012 is as far back as it goes). I used FanGraphs to filter the list of relievers to those with a SD-MD% of over 60% in order to remove the relievers signed for middle-innings mopop work. Depth relievers aren’t signed to not lose. Last, I compared the average annual value of the remaining closer contracts to the non-closer contracts to get a ratio of how much closers are valued over regular relievers.

I averaged the 4 ratios and it comes out to 2.91. To be honest, I thought it’d be more like 2, as the value of relievers signed to not lose (2.25) is half of those signed to not lose when you thought you were going to win (4.5).

This variance might be due to small sample size, incomplete data, using the wrong data, or perhaps I just don’t know what I’m talking about.

The effort invested in 'getting it right' should be commensurate with the importance of the decision.

The prospect theory, which explains people's attitudes towards risk, continues to be a valuable resource for investors to consider