When I was studying finite math in high school, I did not think it would have much use in everyday life. However, fantasy baseball has become part of my everyday life. If you are like me, you will soon see how finite math can be applied to everyday life.

In a head-to-head format (points or categories), floor performance is crucial. The approach to target consistent performers rather than “streaky” performers is my preferred approach.

The following theory relates to “stacking” pitchers on the same team and how it is proven to increase your team’s consistency and floor performance.

The simplifying assumptions I will use are as follows:

- Each fantasy manager will roster 5 starting pitchers
- Each week consists of 7 games for all MLB teams (no days of rest)
- A two-start week for a pitcher means that his first start is either on Monday or Tuesday (this is the result of point No. 2 above)
- All MLB teams use a 5-man rotation, which is not necessarily true these days, but these are simplifying assumptions.
- Each pitcher is independent of the other pitchers in terms of timing of starts

Suffice it to say, any one starter has a 40% chance to have a two-start week in this case. If his first start is on Monday or Tuesday—which are 2 of the possible 5 days to have the first start—he will then pitch again on Saturday or Sunday. 2/5 = 40%. Otherwise, he has one start on the Wednesday, Thursday or Friday – a 60% chance of this happening.

So let’s look at probability:

- Odds of exactly 0 pitchers have a 2-start week: C(5,0) x 60% x 60% x 60% x 60% x 60 % = 7.776% (where 5 choose 0 = 5!/(0! x 5!) = 1)
- Odds of exactly 1 pitcher has a 2-start week: C(5,1) x 60% x 60% x 60% x 60% x 40 % = 25.92% (where 5 choose 1 = 5!/(1! x 4!) = 5)
- Odds of exactly 2 pitchers have a 2-start week: C(5,2) x 60% x 60% x 60% x 40% x 40 % = 34.56% (where 5 choose 2 = 5!/(2! x 3!) = 10)
- Odds of exactly 3 pitchers have a 2-start week: C(5,3) x 60% x 60% x 40% x 40% x 40 % = 23.04% (where 5 choose 3 = 5!/(3! x 2!) = 10)
- Odds of exactly 4 pitchers have a 2-start week: C(5,4) x 60% x 40% x 40% x 40% x 40 % = 7.68% (where 5 choose 4 = 5!/(4! x 1!) = 5)
- Odds of exactly 5 pitchers have a 2-start week: C(5,5) x 40% x 40% x 40% x 40% x 40 % = 1.024% (where 5 choose 5 = 5!/(5! x 0!) = 1)

If you don’t understand the math, then you just need to trust me. Allow me to summarize the odds of having 2-start pitchers while rostering five random pitchers from any team:

### 2-start pitchers from random teams

Number of 2 start pitchers | Odds |
---|---|

Number of 2 start pitchers | Odds |

0 | 7.78% |

1 | 25.92% |

2 | 34.56% |

3 | 23.04% |

4 | 7.68% |

5 | 1.02% |

Total | 100.00% |

The odds of having less than 2 pitchers that have 2-starts are 33.696% (adding up the odds of having 0 or 1). The odds of having more than 2 pitchers than have 2-starts are 31.744%.

Question: If you could, would you hedge your bet and guarantee yourself two pitchers with two starts each while sacrificing the chance to have three or more pitchers with two starts?

Answer: It depends. And this is where statistics get derailed. You do not know how many two-start starters your opponent will have as your advantage is only relative. But as I’ve learned, head-to-head fantasy baseball is about consistency and reliability. That’s why Mike Trout will be the #1 pick this year and not his 2018 superiors, Mookie Betts or Jose Ramirez. He was also the #1 pick last year, not Charlie Blackmon. And he should have been in 2016, not Bryce Harper. You want reliability and proven consistency.

So by guaranteeing two starters with two starts, you’ve maximized your outcome in the bottom range of that 68.256% (0, 1, or 2-starts) and hedged your bet. You’ve lost out on the opportunity to have three starters with two starts which happens 23.04% of the time. And to have four or five pitchers luck out, those odds are small anyway.

How do you get this two-start insurance? Let’s go back to the stacking theory. If you draft all five starters on a particular team, you are guaranteed that two of them start on Monday and Tuesday (and Saturday and Sunday in our hypothetical scenario) and the other three on the Wednesday, Thursday, and Friday.

This isn’t a realistic option with some teams because they just don’t have good enough pitchers to make this worthwhile in a standard league. Conversely, you may not be able to draft Kluber, Carrasco, and Bauer all on the same team without sacrificing your hitting. There are several teams this could work for, however.

### 2-3 early round picks required but only plausible in auction scenarios while sacrificing offense:

WASH – Scherzer, Strasburg, Corbin, Ross, Sanchez

CLEV – Kluber, Carrasco, Bauer, Clevinger, Bieber

HOU – Verlander, Cole, James, McHugh, Whitley

### 2 early round picks required:

NYY – Severino, Paxton, Tanaka, Happ, Sabathia

NYM – deGrom, Syndergaard, Wheeler, Matz, Vargas

LAD – Kershaw, Buehler, Ryu, Hill, Maeda

### Other Cheaper Viable solutions:

STL – Flaherty, Mikolas, Reyes, Martinez, Wainwright

CHC – Lester, Quintana, Hamels, Hendricks, Darvish

PHI – Nola, Arrieta, Pivetta, Velasquez, 5th

COL – Marquez, Gray, Freeland, Anderson, 5^{th}

ATL – Foltynewicz, Newcomb, Teheran, Gausman, Soroka/Toussaint

Please note that this theory is simplified and that you may modify it and draft three or four pitchers from the same team. This will not completely ensure that you get two starters with two starts, but certainly decreases the variability. In this case, you would roster other pitchers or combine a streaming strategy to increase the probability of multiple two-start pitchers. Personally, I like the idea of stacking four starters (because the 5^{th} starter is often too weak) and streaming two-start pitchers as my 5^{th} starter. Furthermore, I often roster more than five starters on my head-to-head teams. The deeper your league, the more MLB teams it becomes viable to stack.