In the first entry of this series, I looked at some of the math behind the most popular tabletop simulation of real life baseball, Strat-O-Matic Baseball. Today, I’m going to look at a new and simpler tabletop game, Bottom of the 9th.
The premise of the game is pretty simple in baseball terms. The game is tied. The home team is up to bat. The inning should be evident from the name of the game. The talent gap is wide between the two teams, and so favors the visitors that it is considered a miracle the home team even has a chance to win. It is also presumed the visitors will win should the game go to extras.
The game plays out the inning pitch-by-pitch. Each pitch is a turn in the game, and is resolved with 4 or 5 steps. The heart of the game is in the Stare-Down, where the pitcher picks an area of the zone to throw to while the batter tries to guess where the pitch is going. This is simplified into 2 choices: a red disc for height of the pitch (High or Low) and a white disc for which half of the plate (Inside or Away). The batter gets some benefits for guessing right, while the pitcher gets some benefits when the batter guesses wrong.
After this, the pitcher makes The Pitch by rolling 2 dice, one which determines whether the pitch is outside the zone, inside the zone, or paints the corner, and a standard six-sided die for control, where higher numbers are better. This impacts the swing, where the batter rolls one standard six-sided die. The benefits granted to each player from the Stare-Down are applied here before comparing the results of the swing and control numbers.
The die rolls are the simple part to break down mathematically. The pitch dies shows a pitch outside the zone to occur 1/2 of the time, inside the zone 1/3 or the time, and on the corner 1/6 of the time. A ball is called when the Swing result is less than or equal to the Control result. The ball is put in play when the Swing result equals the Control result for a pitch on the corner or when the Swing result is greater than the Control result for a pitch in the zone. All other combinations result in strikes.Based on these dice alone, a ball in play occurs on 16.6% of pitches, a ball is occurs on 29.2% of pitches, and the strike occurs 54.2% of the time.
How does this compare to actual major league rates? It’s a little off. In the 9th inning of games in 2015 (via Baseball Savant), balls occurred on 34.8% of pitches and balls in play occurred on 17.4%of pitches. This is because of the simplified system used in Bottom of the 9th, which values speed of play over simulated accuracy.
Another example of how the game values speed is what happens on a Contact result. The first player to roll a 5 or 6 tips the result in their favor. This requirement can be modified by the player at bat or pitching, and it depends on speed of rolling a die as well as the players involved.
Clearly, this is not a real simulation. That’s not a bad thing. Bottom of the 9th was designed to appeal to board game fans as well as baseball fans. It represents two of the hotter trends in board gaming: it was funded via Kickstarter, and it’s considered a “micro-game”, a simple game that can be played in around 15-30 minutes. It’s a pretty good game, and definitely recreates the feel of the batter-pitcher confrontation. I picked up a copy from my local game store, but I now wish I had funded the Kickstarter.