The Doug Funnie Approach to Roster Construction

Previously on Dragon Ball Z, we discussed whether it’s better to run hot and cold like a reheated frozen burrito or show up at the plate with the comforting and consistent warmth of a hearty helping of mac and cheese. Specifically, when you’re a hitter trying to microwave some offense in the playoffs. The tl;dr of that article: When comparing streaky hitters to their more consistent colleagues, the streaky hitters came closer to replicating their regular season numbers in the postseason. Despite the fluky nature of playoff series and their bite-sized samples that leave no space for slumps, hitters prone to slumping still bring enough electricity when they do get hot to maintain a charge in their individual numbers.

But individuals don’t win the World Series, teams do. In the context of a team playing a sport where the superstars don’t necessarily factor into every plate appearance, individual performances don’t carry the same weight that they do in other sports. Not only do teams need contributions from multiple hitters in the lineup, but the sequence of those contributions matters too.

In my last article, I used wOBA, which is derived from the run values associated with specific events (i.e. walks, doubles, home runs), to measure individual output. In turn, run values are historical averages of the number of runs scored following the given event. Those historical averages assume that what follows a given plate appearance is a league-average hitter doing whatever is most statistically likely. But that’s not how it works irl. The player on deck might be better or worse than league average, might have distinct tendencies toward hitting the ball on the ground or in the air, might be 0-fer their last eleventy-billion, or might be hotter than soup in the summertime.

Knowing that streaky hitters perform well on an individual level in October doesn’t offer many satisfying insights on team outcomes. My last piece referred to streaky hitters as burritos and consistent hitters as MACs, and continuing that metaphor here would mean asking if it’s better to construct a lineup (or diet) of nothing but burritos or go top to bottom with MACs. No matter the answer, this ends with me making some questionable gastronomical recommendations. And even in a you-must-choose-one framing of the question, I still can’t cobble together a nutritional argument for one over the other. So rather than continue to force that metaphor, try this one on for size. The plan here is to consider the relative merits of a lineup full of consistent hitters versus a lineup full of streaky ones. A lineup made up of nine iterations of the same type of hitter naturally summoned this image to mind.

For those who didn’t grow up watching ’90s era Nickelodeon, Doug was a cartoon whose titular character, Doug Funnie, is an awkward doofus. Doug, like all cartoon characters, wears the same outfit every day, and the show makes a visual joke of the practice with this shot of his closet. The uniformity of Doug’s closet mirrors the uniformity of the lineups we intend to construct, and because Doug consistently shows up as the same endearing dork in every episode, the crew of consistent hitters will be known as the Dougs.

The streaky hitters, on the other hand, are more erratic. They oscillate between a couple versions of themselves that exist in opposition to one another. No, not Jekyll and Hyde. That would be hack. Plumbing the depths of this situation requires an expert. Thus, the streaky hitters are the Marios, who can’t ever seem to completely do away with their Warios. Wario is Mario’s archrival in the Super Mario universe, and for streaky hitters and humans alike, our greatest nemeses tend to be the internal weaknesses we struggle to overcome every day, the characteristics that lead to slumping and getting tormented by Goombas.

So given an all-Dougs batting order and an all-Marios squad, which would actually fare better in the playoffs? As it turns out, we can’t actually clone a lineup full of Aaron Judges to play against a lineup full of Steven Kwans, so it’s to the simulator we go!

I MacGyvered together a very basic simulation algorithm to handle this hyper-specific scenario, with the goal being to sim through a bunch of best-of-five series samples (a proxy designed to split the difference between the varying lengths of postseason series) with our cartoonishly exaggerated lineups taking on league-average teams. Obviously, most playoff teams are league average or better, but because we really only care about the relative performance of the lineups we manufactured in a lab, we just need their opponent to serve as a consistent control group.

The simulator does its work one half-inning at a time by logically traversing base-out states until the three-out state is reached. (A quick reminder: Base-out state is a shorthand method for expressing one of the 25 possible combinations of outs and runners on base.) The move from one base-out state to another base-out state has a historical likelihood and a typical amount of run scoring that comes with it. A different set of probabilities and run values were calculated and applied based on the type of hitter at the plate – a league-average hitter, a streaky hitter, or a consistent one.

To get each set of probabilities and run values, I used my prior analysis to pull a subset of 50 or so of the highest variance (read: streaky) hitters and 50ish of the lowest variance (read: consistent) hitters, all of whom had enough weeks with 20 or more plate appearances to confidently classify them as either high or low variance. And to lock in on the players most likely to meaningfully impact a playoff series, a minimum .330 career wOBA was also a requirement. This also works around two scenarios with potential to skew the archetypes in undesirable ways: First, the easiest path to consistency as a hitter is to consistently hit quite poorly, but that’s not really in the spirit of the what we’re doing here; second, players with a higher ceiling have a much larger capacity for variance given the broader range of outcomes available, so it helps to narrow that range by raising the floor.

Next, I went all the way back to 2013 and pulled every plate appearance, noting the base-out state immediately before and immediately after each one, as well as the number of runs scored as a result of the PA (adjusted to account for fluctuations in the run environment from season to season). Then, for every possible combination of base-out states, I calculated the probability of transitioning between the two states and the average run scoring associated with the transition. I repeated this process five times using PAs from different subsets of hitters – once with all hitters to get the league-average numbers and once with the pre-selected group of consistent hitters (the Dougs). But the streaky hitters (the Marios) required a different approach.

While Dougs are characterized by their tendency to hang close to their overall average performance, Marios have distinct, dueling profiles that blur together in the process of averaging. To capture each player’s Mario and Wario, their opposing profiles must remain distinct. Using the previously calculated seven-day rolling wOBAs for each player in the Mario group, I was able to identify which days on the calendar each player was Mario or Wario. The remaining days went into a third category that captures the messy middle, the transitions from Mario to Wario and vice versa. Now, with each PA for the Marios categorized into one of three phases, I could use each grouping to compile a set of probabilities and run values associated with each phase of a Mario’s season.

With probabilities and run scoring distributions in hand, the simulator takes a lineup composed of hitter archetypes and runs through the lineup one plate appearance at a time, using the probabilities and run values associated with the type of hitter at the plate to randomly sample the outcome of the PA. (For Marios, it’s also using a probability distribution to randomly determine his current phase in the Mario/Wario dichotomy.) More specifically, it randomly selects the next base-out state from a list of possible options and their corresponding likelihood. Then it uses the average runs scored off of that transition and the corresponding standard deviation to generate the specific number of runs scored during the PA in question. When the sim hits a three-out state, the inning ends and it’s onto the next one. Once nine innings are in the books, each team’s total runs scored are compared and a winner is crowned.

The simulator took three distinct lineup constructions and pitted them against a league-average team. Each pair of lineups faced off in 1,000 simulated best-of-five series. First up, The Fighting Marios (and Warios) won 623 series against their league-average opponents. Next, Team All Dougs and Nothing But Dougs racked up 705 series wins against the league-average squad. And finally, to offer something of a closer approximation to reality, a randomly arranged lineup composed of a 45/55 split of Dougs and Marios or Marios and Dougs took 640 series against the average joes. Though Team Mario expectedly performs well, the impact of sequencing and the difficulty in getting a group of streaky hitters to perform in concert with one another is felt when compared to Team Doug’s .705 winning percentage.

Knowing how these hyper-extreme lineups performed on a baseball holodeck provides a new looking glass through which to view the performance of postseason teams over the last decade or so. Does examining the ratio of Dougs to Marios on a team’s roster offer any useful insight on the team’s playoff success and ability to maintain playoff success across multiple seasons? Do these cartoon outcomes have any bearing on the real world?

The top 10 teams in terms of the proportion of total playoff PA allocated to Doug hitters are:

While the top 10 teams with the highest ratio of PAs allotted to Mario hitters are:

The percentage of plate appearances devoted to Dougs is considerably smaller because good, consistent hitters are a rarer commodity. If some team actually wanted to swap out its current uniforms for Doug’s sweater vests and shorts and create a full lineup of dudes with French bulldogs named Porkchop, I’m not sure even the most aggressive GMs could pull it off. There aren’t enough quality Dougs who are also free agents or available via trade to make it happen.

But even so, a few things stand out in the rankings. The Dodgers occupy six of the top 10 spots on the Mario PA Leaderboard, peaking in their 2020 World Series season. Los Angeles’ frequent postseason appearances allow it to eat up such a huge chunk of the list, which in turn, highlights how many times the Dodgers have made early playoff exits despite their “World Series or bust” expectations. They deserve praise for their consistent postseason presence and the deeper runs they sprinkle in every few years. Nevertheless, the Dodgers playoff performances often leave a disappointing taste in fans’ mouths because the level of talent stacked on those teams makes otherwise strong showings feel like underperformance. Perhaps relying too heavily on the grace of the sequencing gods and expecting the Marios to defeat their Warios contributed to a team that was talented enough to dominate the regular season and make the postseason for 11 years straight, but emerged with only one title because they were too dependent on highly variable outcomes breaking their way.

Conversely, St. Louis appears three times at the top of the Doug leaderboard at the peak of the Cardinals Devil Magic era. Fans were so perplexed by the Cardinals’ persistent ability to overperform the perceived level of talent on their roster that the only logical explanation was to chalk it up to dark forces. And maybe Matt Holliday and David Freese did sell off part of their souls, hoping to hit 50 homers a year, and instead Satan aimed a shrink ray at their slump genes, but this allowed them to get hits in the right place at the right time at a higher clip, increasing the impact of their teammates’ abilities in the process. In setting themselves up to succeed on the sequencing front, they, unlike the Dodgers, were able to produce above expectations.

We frequently speak about the team that wins the World Series as a “Team of Destiny” because it feels like things just go right for them all October long. They’re the team that the universe smiled on, while other talented teams weren’t so lucky. It can feel frustrating that something like luck weighs so heavily on the postseason, that despite all other efforts, you still have to hope that your team is The Chosen One. And for teams heavily constructed of Marios, they do have to hope that players keep finding Super Star power-ups from one series to the next. And that strategy does work. It worked for the 2020 Dodgers. But when the power-ups aren’t as plentiful it can also lead to talented teams making early exits, as was the case with the 2022 and ’23 Braves.

Many consider this an unavoidable structural reality of the postseason. Get in and everyone rolls the dice. But what if something less thrilling and less cool, like being an “outfit-repeater,” could weight the dice in your favor? What if inviting a few Doug Funnies to the party is the key to getting to throw a real rager of an afterparty in the clubhouse?

Or just hit all the home runs.