What if Baseball Were More Like Mario Kart?
If you haven’t played Mario Kart before, first of all: I’m sorry. It’s honestly the best. It’s a racing video game series with a variety of beloved Nintendo characters, but there’s one part I care about most for the purposes of this article: the game actively works to slow down the leader and speed up the laggards. If you’re out front, you can expect middling power-ups and specifically targeted countermeasures to slow you down a bit. If you’re bringing up the rear, the game gives with both hands to help you get caught up. It’s possible to run away with a race, but the game is working hard to make it less likely.
To explore these options, I built a simplistic baseball model. Simplistic might give it too much credit, in fact. Every plate appearance is governed by a random number generator: each possible outcome occurs at the rate it happened in the 2020 regular season. For every play, in essence, the model rolls a many-sided die and chooses an outcome based on that. Then the base and out states change, and the next batter “hits,” on and on until a game has been completed.
The model plays an arbitrarily large number of games — a million in this case. We can then construct winning percentages based on how often each team wins from a given state. For example, here are the calculated winning probabilities (it’s a Monte Carlo method, so they’re not deterministic) based on various leads and deficits after the first four innings:
| Home Team State | Win% |
|---|---|
| Up by 6 | 96.9% |
| Up by 5 | 94.6% |
| Up by 4 | 90.7% |
| Up by 3 | 84.8% |
| Up by 2 | 76.1% |
| Up by 1 | 64.4% |
| Tied | 50.0% |
| Down by 1 | 35.6% |
| Down by 2 | 23.9% |
| Down by 3 | 15.2% |
| Down by 4 | 9.3% |
| Down by 5 | 5.4% |
| Down by 6 | 3.1% |
These percentages don’t exactly match real baseball because they’re simulated based on average batting and pitching lines. They’re within a percentage point or so of actual outcomes though, which means that the simulation works fairly well.
That’s how baseball works right now. Next, let’s break it! A game where the home team is 9.3% likely to win after only four innings sounds boring. More than half of the game happens with one team close to hopeless. Let’s give the trailing team a Golden Mushroom or Bullet Bill and tighten things up!
Four Outs
This one is simple: at the top of each inning, we check the score. If the visiting team is ahead, the home team gets four outs this inning. If the home team is ahead, the visiting team gets four outs this inning. If the game is tied, it’s normal baseball. Why check at the top of the inning? It keeps the home team from getting a large advantage by dint of batting second. Every time we check for bonuses, each team has batted an equal number of times, which is important when we’re breaking the rules of the game.
Playing with four outs is a huge deal! If teams played nine innings with four outs per inning they would have scored seven runs per game this year, markedly more than the 4.6 they managed in reality. An average team with four outs would mop the floor with the best team in baseball with only three outs to work with, obviously enough. How does that affect leads?
| Home Team State | Standard Win% | 4-Out Win% |
|---|---|---|
| Up by 6 | 96.9% | 91.5% |
| Up by 5 | 94.6% | 87.1% |
| Up by 4 | 90.7% | 81.2% |
| Up by 3 | 84.8% | 73.7% |
| Up by 2 | 76.1% | 64.9% |
| Up by 1 | 64.4% | 55.8% |
| Tied | 50.0% | 50.0% |
| Down by 1 | 35.6% | 44.2% |
| Down by 2 | 23.9% | 35.0% |
| Down by 3 | 15.2% | 26.3% |
| Down by 4 | 9.3% | 18.8% |
| Down by 5 | 5.4% | 12.9% |
| Down by 6 | 3.1% | 8.5% |
We’re doing it! That 10% chance of winning a game before has doubled to 20%. Under our new rule set, a team down six runs is still nearly 10% likely to win the game. Will people ever turn off baseball when a three-run deficit gets overturned a full quarter of the time?
Well, they might, not least because four outs means longer baseball games. Rob Manfred hates extra baseball. He’d like baseball to be as short as possible, within reason. This rule clearly won’t fly. I mean, it wouldn’t fly anyway because it’s a massive rules change, but it especially wouldn’t fly given how insistent the league is on shortening games. Even if we were going to change the rules of baseball so drastically, adding meaningful running time to the game might not be a great idea. Let’s try some other options.
Two Outs
Instead of giving the trailing team a bit of turbo boost, what if we threw a banana peel in front of the winning team? In this version, the team with the lead going into an inning gets only two outs that inning. Up by four? Better hope those four runs are enough! Scoring with two outs is shockingly hard, fewer-than-2.5-runs-a-game hard if you had to do it for all nine innings. Does that do enough?
| Home Team State | Standard Win% | 2-Out Win% |
|---|---|---|
| Up by 6 | 96.9% | 95.7% |
| Up by 5 | 94.6% | 92.6% |
| Up by 4 | 90.7% | 87.8% |
| Up by 3 | 84.8% | 80.7% |
| Up by 2 | 76.1% | 70.9% |
| Up by 1 | 64.4% | 58.8% |
| Tied | 50.0% | 50.0% |
| Down by 1 | 35.6% | 41.2% |
| Down by 2 | 23.9% | 29.2% |
| Down by 3 | 15.2% | 19.4% |
| Down by 4 | 9.3% | 12.2% |
| Down by 5 | 5.4% | 7.4% |
| Down by 6 | 3.1% | 4.3% |
Nope! This isn’t a good plan at all; slowing down the team that’s ahead doesn’t work because it doesn’t increase the trailing team’s chances of scoring enough runs to meet the original tally. That’s at the beginning of the fifth inning, which obscures the main effect of this rule, which is preventing leads from snowballing in the first place. Even if we look at deficits after one inning, however, it simply doesn’t do enough:
| Home Team State | Standard Win% | 2-Out Win% |
|---|---|---|
| Up by 6 | 93.7% | 90.5% |
| Up by 5 | 90.3% | 85.9% |
| Up by 4 | 85.3% | 79.8% |
| Up by 3 | 78.9% | 72.1% |
| Up by 2 | 70.6% | 63.6% |
| Up by 1 | 60.9% | 55.0% |
| Tied | 50.0% | 50.0% |
| Down by 1 | 39.1% | 45.0% |
| Down by 2 | 29.4% | 36.3% |
| Down by 3 | 21.1% | 27.8% |
| Down by 4 | 14.6% | 20.3% |
| Down by 5 | 9.7% | 14.1% |
| Down by 6 | 6.3% | 9.5% |
Big early leads are still difficult to recover from. Being down three after the first inning with the two-out rule gives your squad a 27.8% chance of recovering in the last eight frames. Compare that to the earlier four-out rule: down three after four innings, you’ll still win 26.3% of the time. The four-out game packs as much excitement into the last four innings as the two-out game does into the final eight.
Ghost Runner on Second
What the heck, we already have a rule that puts runners on second base to start innings. Let’s just give the trailing team an automatic runner on second base whenever a team is trailing. Here’s win probability starting from the fifth inning in this world:
| Home Team State | Standard Win% | 2B Win% |
|---|---|---|
| Up by 6 | 96.9% | 81.7% |
| Up by 5 | 94.6% | 74.7% |
| Up by 4 | 90.7% | 67.2% |
| Up by 3 | 84.8% | 60.1% |
| Up by 2 | 76.1% | 54.4% |
| Up by 1 | 64.4% | 50.7% |
| Tied | 50.0% | 50.0% |
| Down by 1 | 35.6% | 49.4% |
| Down by 2 | 23.9% | 45.6% |
| Down by 3 | 15.2% | 40.0% |
| Down by 4 | 9.3% | 32.8% |
| Down by 5 | 5.4% | 25.3% |
| Down by 6 | 3.1% | 18.3% |
Now we’re talking! Being down five runs after four innings still gives you a one-in-four chance of winning. Giving the trailing team the better part of a run in every inning does wonders to tighten leads. Want more baseball games to end close and with the bases juiced? This is your ticket.
Super Star
We can do more. What if we gave the trailing team a runner on second and also four outs? That’s a lot of runs of expected value we’re gifting the trailing team now. No lead is safe:
| Home Team State | Standard Win% | 4O, 2B Win% |
|---|---|---|
| Up by 6 | 96.9% | 66.9% |
| Up by 5 | 94.6% | 60.7% |
| Up by 4 | 90.7% | 55.8% |
| Up by 3 | 84.8% | 52.5% |
| Up by 2 | 76.1% | 50.6% |
| Up by 1 | 64.4% | 50.4% |
| Tied | 50.0% | 50.0% |
| Down by 1 | 35.6% | 49.6% |
| Down by 2 | 23.9% | 49.4% |
| Down by 3 | 15.2% | 47.5% |
| Down by 4 | 9.3% | 44.2% |
| Down by 5 | 5.4% | 39.3% |
| Down by 6 | 3.1% | 33.1% |
Even for me, this goes too far. There’s almost no difference between being tied and down three, which makes the prospect of catching up a little less exciting. Leads need to have some significance to make catching up feel exciting.
All of these options carry pros and cons. Change too little, and you’re messing with the fundamental rules of baseball without actually making the sport more fun. There’s not much point in altering the fundamental underpinning of the sport to add a few unlikely comebacks. Change too much, and you’re looking at an NBA situation; why tune into the first four innings if 3-0 and 0-3 are roughly the same when it comes to your team’s chances of winning?
As one final bow on these different methods I came up with off the top of my head, I decided to check how many lead changes they’d produce. I looked for three types of event: going from behind to tied, breaking a tie, and going from behind to ahead. Win 1-0, and your game has one instance of breaking a tie and nothing else. Go down by a run and come back in a dramatic ninth inning, and you get one instance of breaking a tie and one instance of going from down to up. It’s pretty straightforward.
How do my Mario Kart baseball rules affect lead changes? I’m glad you asked. I re-ran these simulations over a full nine inning game and counted up:
| Ruleset | Broken Ties | Re-Ties | Flipped Leads |
|---|---|---|---|
| Normal | 1.54 | 0.54 | 0.41 |
| 4 Outs | 1.75 | 0.75 | 0.67 |
| 2 Outs | 1.62 | 0.62 | 0.48 |
| Ghost Runner | 2.34 | 1.34 | 0.90 |
| 4O Ghost Runner | 2.54 | 1.54 | 1.31 |
That doesn’t sound like many lead changes, but the truth is that many games of baseball come down to one team getting ahead and holding their lead. My hypothetical world doesn’t include any team disparities or any concentrated parts of a lineup where runs are more likely, so it won’t perfectly mirror real life, but the general concept holds: baseball simply doesn’t have that many opportunities for lead changes, because the game is tied for most of the time and most half innings end without any score.
Would baseball be better if it were more like Mario Kart? Sadly, I don’t think so. It’s not all bad — adding drama to the game can be gimmicky, but it can also be great. Increasing the odds of a comeback makes regular games — a 5-2 lead in the sixth, say, or a 4-2 lead in the fourth — feel less like a foregone conclusion.
The biggest downside is that all of the carefully calibrated parts of baseball might not work with extra outs. Batters would come to the plate more often every game. Teams would need to cobble together more outs every game, which would act as a drain on all pitchers. The better your team, the more you’d be penalized by facing opponents with extra baserunners or extra outs. Comparing one team’s line to another, particularly when it comes to scoring runs, would be nonsensical if teams were working with variable numbers of outs.
In the end, baseball probably doesn’t need a mechanism to help the trailing team. The best catch-up mechanism is that tomorrow is a new game. With 162 of them, there’s no issue of falling too far behind in one contest — you can simply come back tomorrow and start over. The quasi-random nature of each individual game and sheer length of the season gives fans of every team plenty of chance to see the home nine end the day victorious. That doesn’t mean it isn’t fun to imagine a blue shell chasing the Dodgers around the bases, though.