SIBR:Foul Ball

Disclaimer
The following has been tested up until the end of Season 18. It may not reflect the current simulation.

Foul Balls are a game event that directly contributes to a Ballpark's Filthiness attribute. It was found that the exact amount of Filth contributed was dependent on multiple variables, including player's attributes, player item's, and currently active performance modifications, e.g. Overperforming, Growth.

Foul Ball Filthiness

Foul balls are a factor that contribute to the filthiness of the ballpark the game is played in. The amount of filthiness generated by the foul ball depends solely on the batter. The following formula holds:

$F=(6-4(t_{b}(1+\sum {m})+t_{i}-l_{b}-l_{i}))\times 10^{-5}$

Where:

• $t$ is Tenaciousness
• $b$ is Batter
• $m$ is Modifiers
• $i$ is Items
• $l$ is Indulgence

Tenaciousness and indulgence are base attributes of the batter and their items, while modifiers encompass all things that make the batter perform better or worse, e.g. growth, high pressure, middling, homebody, traveling.

Knowing the formula allows to calculate the values of different modifiers by solving for the modifier and inputting the filthiness generated by the batter's foul ball and check if they stack.

Findings

• Multiple different sources of Overperform do stack, i.e. Ambitious, Homebody, Perk, Earlbirds, Middling, Late to the Party, Power Chaaarge.
• Growth's performance increase follows the following formula: modifier in % = (day-1)*5/99, for 0% on day 1 and 5% on day 100 and later
• Broken items still give their changes to tenaciousness and indulgence (and probably all other attributes), not their modifiers though.
• The Traveling mod on items did not confer the advertised modifier for a while.

Origin of the formula

The formula was found by first identifying sources of filthiness and then correlating them to in game events - identifying foul balls as one source of filthiness. The next step was the observation that the increase in filthiness in ballparks is very consistent for each batter. Next was to look at each individual change in base attributes of a batter to see if that attributes affects the filthiness of their foul balls. This was possible due to parasite pitchers draining single attributes of batters when striking them out during Blooddrain weather. Solving a linear equation for a player with constant indulgence and changing tenaciousness and the other way round identified the factors for tenaciousness and indulgence, followed by the offset. The way modifiers and items apply to the formula were found by tweaking the formula in different ways until the filthiness increase matched up perfectly with the one seen in the ballpark.

Observations

The way the formula is set up means that in some edge case batters with very high tenaciousness and low indulgence can actually reduce filthiness in ballparks through foul balls. Richardson Games in Season 17 is such an example: tenaciousness 2.501, indulgence 1.067 with a traveling modifier of 5% performance increase during away games.