Baseball Draft Kit: An Essay on Game Theory

IT'S A THURSDAY NIGHT. YOU'VE HAD A LONG WEEK. You decide you want to go to a bar and have a few drinks. The problem is, you know it's going to be crowded at the bar. Which can be annoying if it is too crowded. Maybe you should stay home instead. That could be more fun. You are so torn — what to do.

What if I told you figuring out whether to go to a bar on a Thursday night is exactly the decision-making process you need to use to figure out your approach to roster construction for your 2021 fantasy baseball drafts? You might say I have already had too much to drink (not true, yet). You might also say why would anyone go to a bar during the pandemic (very fair!)

Bear with me.

The El Farol Bar Problem is a game theory problem articulated by economist William Brian Arthur that I think has direct applicability to fantasy baseball given the landscape in 2021.

Let me start with the problem itself and then I will draw it into fantasy baseball, I promise.

Here's the scenario: every Thursday night 100 people decide independently whether to go to a bar in El Farol, Santa Fe, for a fun night out. Each person knows they will only have fun if a certain number of people show up. Specifically:

• If less than 60 go to the bar, they'll have more fun than if they stayed home; but

• If more than 60 people go to the bar, they'll have less fun than if they stayed home.

It's important to remember the 100 people are acting entirely independently — you don't know what the other 99 people will do and you have no way to text them to see if they're going to the bar. And everyone must decide at the same time — you can't sneak around the corner of the bar and see what attendance is at 9 pm on Thursday.

So how do you decide whether to go to the bar, or not?

One thing that should be immediately clear is the paradox inherent in the problem — if everyone approaches the problem with the same strategy, it is guaranteed to fail no matter what the strategy is. If the strategy suggests the bar will not be crowded tonight, everyone will go to the bar — GUARANTEEING the bar will be packed — which means everyone is miserable because of how crowded it is. On the other hand, if the strategy everyone comes up with suggests the bar will be crowded, everyone will avoid the bar on that night, guaranteeing the bar will be empty, but NOBODY is having fun because everyone stayed home.

So the worst possible outcome in this "game" is everyone uses the same strategy — regardless of what that strategy may be.

The way to maximize your odds of "success" (in this case, having the best odds of having fun on a Thursday night) is using what is known as a probabilistic mixed strategy. What are the odds of each person going to the bar? How many people have gone on average for the last 10 Thursday nights? And so on. Economists solve the problem using a lot of math — it gets complicated for a relatively simple problem — but that's sort of key. Even a simple problem like this when you dive into it has an extremely complicated probabilistic answer to maximize your odds of success.

So, what does this have to do with fantasy baseball in 2021?

It has struck me since the end of the weird, wacky 2020 season that a form of groupthink has taken over fantasy baseball. In particular, high-stakes fantasy baseball (those of us who play in the National Fantasy Baseball Championships), but even amongst analysts and players who don't play in the NFBC. It goes something like this:

Top starting pitchers are rare and hugely valuable commodities. Pitchers mostly do not go deep into games anymore and managers limit total innings for many pitchers. Coming off of 2020's abbreviated season, who knows what pitcher usage — never mind pitcher injury rate — is going to look like in 2021. Therefore, the top starting pitchers — the guys who will throw 180-plus innings, the ones we can count on — are worth their weight in gold.

Toby Guevin (aka @batflipcrazy on Twitter) just had one of the best NFBC seasons in the competition's history (and also happens to be one of the nicest and smartest guys you'll ever meet) and he preaches "pocket aces" — starting your drafts pitcher, pitcher in the first two rounds. It sure worked for him in 2020 and has become quite trendy. For good reason — when one player has success with a strategy, copying the strategy makes a lot of sense.

Not everyone advocates for starting your drafts with consecutive starting pitchers but — and this is the key — we are at a point where people who say you can "wait" on pitching mean you can draft your first starting pitcher in the third round. Seemingly every single fantasy pundit out there wants to have two or three starting pitchers by the end of the fifth round. I have yet to hear someone who has advocated for anything that diverges materially from this approach (which doesn't mean there aren't people making a different case — I just haven't heard it).

Are you starting to see the link to deciding whether to go to a bar on a Thursday night?

Before I dive deeper, let me be clear: I'm not trying to be contrarian for the sake of being contrarian. There is good logic with taking pitchers early. If you look at the top-10 teams in the NFBC's overall standings last year — and most years — you will see most top teams took some pitching early. Not necessarily in the first or second round, but certainly in the first four or five rounds.

Moreover, almost any study you can conduct on how starting pitchers from various parts of the draft perform will show while pitchers from any part of the draft lose money as a group (because they're pitchers; a lot of them will get hurt, others will perform worse than we think they will), early starting pitchers earn back a much higher percentage of their draft cost than later starting pitchers (to be clear: that doesn't mean there won't be some mid-20th round pick who earns second round value every year, there will, I'm talking as groups of pitchers by draft spot).

Here is the problem, though: the 45th-best starting pitcher does not become a better pitcher, nor does he become a safer pitcher just because you take him in the fifth round instead of the 10th round.

Back to the bar problem: if you know as a fact that the 99 other people are going to the bar tonight, you stay home every single time. That is clear. The right answer is to diverge from the group.

It is, of course, not a perfect analogy to fantasy baseball roster construction. We need pitching — it is half the points in traditional roto leagues. So, saying "skip pitching" isn't an option in most formats — certainly not in the NFBC.

Also, while it is true the 45th-best starting pitcher doesn't become any better if he's being drafted in the fifth round instead of the 10th round, if he's being drafted in the fifth round, drafting him in the 10th round isn't an option — he's long gone by then.

If you accept that "everyone" is drafting two or three pitchers in the first five rounds, there are two possible responses to that:

1. Also draft two or three pitchers in the first five rounds. You need elite pitching to compete, if you do not draft those early starters you are passing on the most likely pitchers to be elite, and therefore the odds of you competing go down quickly. You, of course, are very confident you will pick the RIGHT pitchers, unlike the 14 other guys in your league, and that's how you'll differentiate yourself from your competitors. Just pick the right guys and everything will fall into place.

2. Adopt a different strategy, i.e., zig while seemingly everyone else in the world is zagging. We'll call this Option 2.

Option 2 — adopt a different strategy from (seemingly) everyone else in the world — is scary. It is always "safer" to go with the crowd. Nobody laughs at your draft board as the draft is wrapping up if you play it safe.

Option 2 is also riskier. As mentioned, we know historically the pitchers drafted between round six and 10, never mind the later rounds, return a lower percentage of their draft cost than the pitchers drafted in rounds one to five.

But what if — and I am just thinking out loud here — 2021 isn't like other years. Innings are likely to be down even further across the board for pitchers (flattening the amount even top pitchers can earn). With lower innings means fewer wins going to starters (flattening their earnings yet further). Pitcher injuries might be up even higher than normal, making spending top-draft capital on pitchers riskier than usual. A month into the season, spending three of your top-five picks on pitchers — who are falling like flies and struggling to make it through five innings — may (MAY) seem like an idiotic way to build a roster for 2021.

Except everyone did it, right? Is there anything in that last paragraph that would shock you? If you knew it was going to be true, you would decide to divert more of your draft capital away from pitchers. If you accept that it MIGHT be true, shouldn't you at least consider doing so?

And that does not even touch on the opportunity cost of taking these three starting pitchers in the first five rounds. We all know how rare stolen bases are in today's game. Rarer still are hitters who steal bases while providing power and a decent batting average. To the extent such unicorns still exist in the modern game, they are largely gone in the first five rounds. It is binary in many cases — take that stud starting pitcher or take that usable speed. Tough to get both. With Option 2, you can get a couple of speed/power guys before they are all gone, as your opponents hoover up yet another pitcher.

But that is not the only opportunity cost those early starting pitchers bring. It has become as much a truism that "speed is rare" that "you can wait on power" — a lot of players who hit 25-plus home runs are available late in drafts. And that is, of course, true — there is a lot of late power available in drafts. Except it is mostly junk power. When 25 home runs come with a .220 batting average and limited runs and RBIs, they are as useless as the Jarrod Dyson who steals 15 bases but does nothing else for you.

Do you know how many players hit 30 HR with 100 runs and 100 RBIs and a .300 batting average in 2019? Five. In 2018? Two.

For all the talk of starting pitchers and speed, the guys who fill up the back of an old baseball card are in some ways the rarest players. They are all gone early. And no, you can not find players "almost as good as them" in the 17th round.

So, by going full-George Costanza and doing the exact opposite of everyone else, you can both get productive, usable speed early as well as a couple of foundational power hitters with high-batting averages. That is the good part.

The question is can you build a pitching staff that can compete after Round 5?

I am not going to suggest it's easy. And you will need a bit of luck. It also takes more work. You need to do deep, deep dives on every pitcher. You also can not assume you will just have your pick of any guy not taken early — it's not like other teams stop drafting pitchers after five rounds.

But if ever there was a year to try it, I would argue it is 2021.

This article appears in the 2021 RotoWire Fantasy Baseball magazine.