Where Greedy Optimization Shows Up In Sports

Underneath the athletic facade, sports is all about optimization. And perhaps the most commonly employed tactic is greedy optimization. Some might call the strategy “win now” while others might call it short-sighted. But greedy optimization is a viable technique in math as well as sports.

In this article we’ll look at the different ways in which greedy optimization creeps into sports and sports analytics. We consider three different cases: one where greedy optimization is optimal, one where it is close to optimal, and one where it is the furthest thing from optimal.

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What is Greedy Optimization?

It’s baked into the name. Greedy optimization is making decisions and choices based on what is optimal at the current moment. The other approach – global optimization – makes choices based on looking multiple steps into the future. By looking further into the future, global optimization can yield more accurate results. However, the complexity of global optimization can be prohibitive.

Let’s look at Chess as an accessible example. Often when beginners play, they talk about how many moves into the future they’re looking. The good players are those who can look many, many moves into the future. The further they can look into the future, the closer the player gets to finding the “globally optimal move”. True beginners only look at the current move: is this a good trade? Am I checking the King on this move? Etc.

Sometimes greedy optimization works really well – Chess is not such a case. Kruskal’s algorithm is an example where the greedy optimization method actually gives you a globally optimal solution! This means there is no benefit to looking into the future to help make decisions at the current step.

Let’s look at some examples of how greedy optimization factors into the sports world.

Greedy Optimization in Fantasy Drafts

Hands down, the best part of a fantasy football season is the draft itself. In a typical snake draft, most people go in with a strategy of which position they’re going to take in the first two to three rounds. “I’m going to go RB-RB” or “I’m reaching for TE1 then loading up on WRs” are strategies you might hear before the draft.

But an equally common strategy is simply described as “best player available”. This strategy involves taking whoever the best player remaining is with each of your picks, regardless of their position. The idea is that reaching for specific positions results in decreased net value. Best player available is something that shows up in the real NFL draft as well.

But is it optimal? Almost certainly not. There is the chance that you end up missing out on talent at one particular position. Or two positions. Or you end up with 3 quarterbacks when you only start one.

Take a look at some of the past articles I’ve done showing the optimal strategy for when to take which positions at which pick: Optimal 2022 fantasy draft strategy. It can be valuable to plan multiple picks ahead and wait on certain positions. Taking the best player available at each pick isn’t necessarily optimal. For a more dramatic example of how global optimization does better than greedy optimization, take a look at our articles about auction optimization.

In the fantasy football draft setting, greedy optimization is close to the optimal solution. Next, let’s look at an example where greedy optimization is the optimal solution.

Deciding Batting Order in Baseball

A second place where greedy optimization shows up in sports is in picking a batting order. Conventional wisdom in baseball has your best hitter go fourth, batting cleanup. More modern strategies place your best batter first so they get the most at bats. Before the universal designated hitter, some teams got fancy and made their 9-hole hitter a good one so that the best players at the top of the lineup had more RBI chances.

But what is best? Well, we’ve actually studied this before. In “Batting Order Doesn’t Really Matter”, we showed that there is very little difference in terms of runs scored between different batting orders. The difference between s team’s opening day lineups and random batting orders is only about 3%. This means over the course of an entire season, the difference between doing random lineups and what the manager thinks is their best lineup is only about 1 run every 8 games.

However, while there isn’t much difference between batting orders, it seems like the greedy solution is best! In this context, the greedy solution is putting your best hitter first, then your second best hitter, all the way down to your worst hitter last.

This strategy works on two levels:

• Your best hitters get the most at bats
  
• Your best hitters are clumped together so they have lots of at-bats with runners in scoring position.
  

In optimizing your baseball batting order, the greedy strategy works pretty well.

Football Play Selection

The biggest way coaches can impact success in the NFL is by deciding on play calls. Both on offense or on defense, finding the right play at the right time can lead to increased success. So how can we determine what play to call in which scenario?

This is actually an example where greedy optimization fails spectacularly. In the normal flow of an NFL game, runs and passes are mixed to ensure that the defense has a harder time knowing what to expect. Teams try to force defenses to either respect the run or respect the deep threat to increase the likelihood of success for all other plays.

But if an NFL team was just concerned with maximizing the yards per play, then the greedy optimization approach says to pass the ball every time. The plot below shows yards per play on rushing and passing attempts for a selection of teams from the 2023 NFL season.

The same relationship holds true for every team: passing plays average more yards than running plays. Greedy optimization says to pass the ball every time. In the real world this never happens. (And if the coach did pass every play, they might be fired the very next day).

This is an example where the result from greedy optimization bears very little relationship with the real world strategy.

Why Greedy Optimization is Always Helpful

In the three examples above, we showed where

• Greedy optimization is the optimal strategy (baseball)
  
• Greedy optimization is close to the optimal strategy (fantasy drafting)
  
• Greedy optimization is a terrible strategy (NFL play selection)
  

Sometimes greedy strategies work and sometimes they don’t. What they do always provide, though, is a good tool to start thinking about a problem. They are a good method to gain intuition.

Take the optimal fantasy draft strategy problem. If I asked you: “what is the mathematically optimal way to draft in fantasy”, you would certainly struggle to come up with a solution off the top of your head. But if you say “I’m going to start with the greedy approach and work from there” suddenly things start to make sense. You’ll quickly realize that when drafting best player available:

• It is important to look at production relative to position average
  
• It is important to project which players will be available at your next pick
  
• It is important to project the strategies other teams take to predict availability further into the future
  

Starting with the greedy solution helps to uncover the structure of the problem. Finding out what is right and what is wrong with the greedy solution reveals insights that help find the true solution.