Prospect League Game Theory Part 2: The Effects of Uneven Scheduling
Author: Jared Weber
The process of creating schedules is a task that all professional sports leagues across America have given a different approach. However, one constant rule has always remained the same in most of these leagues. They always schedule all of their teams to play the same amount of games.
The typical reasoning behind this is that an uneven schedule is unfair to the team having to play more games because they have less time to rest and readjust in preparation for games.
While this is most certainly a factor of uneven scheduling, there also happens to be a vast number of intricacies that come into play just based on the pure math of competition. This article will go into detail on what the playoff structure for the Prospect League is, and how the uneven schedule structure can leave some teams at an inherent disadvantage just by math alone.
The Playoff Format
As laid out the previous game theory article, the Prospect League playoff format has teams solely competing against their divisions to secure a playoff spot. After the first half of the season, all 4 teams currently leading their division secure a home playoff spot. Then in the second half, the team’s records are reset. At the end of the second half, the 4 division leaders that didn’t already win the first half secure the last 4 playoff spots. Teams cannot make it to the playoffs unless they win their division in one of the two halves.
To start this demonstration, we will look at a very basic example where 3 teams in a division all have a 1-game “season”. Because this is a completely neutral setting, we will say that the 8 possible scenarios in this season that are equally likely, and they follow as such:
| S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | ||
| Team A | W | L | W | W | L | L | W | L | |
| Team B | W | W | L | W | L | W | L | L | |
| Team C | W | W | W | L | W | L | L | L |
Next, we will look at their placements in every scenario, and count how many times they are 1st, 2nd, 3rd in the division.
| S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | Placements | |
| Team A | W 1-0 1st | L 0-1 3rd | W 1-0 1st | W 1-0 1st | L 0-1 2nd | L 0-1 2nd | W 1-0 1st | L 0-1 1st | 1st 5 2nd 2 3rd 1 |
| Team B | W 1-0 1st | W 1-0 1st | L 0-1 3rd | W 1-0 1st | L 0-1 2nd | W 1-0 1st | L 0-1 2nd | L 0-1 1st | 1st 5 2nd 2 3rd 1 |
| Team C | W 1-0 1st | W 1-0 1st | W 1-0 1st | L 0-1 3rd | W 1-0 1st | L 0-1 2nd | L 0-1 2nd | L 0-1 1st | 1st 5 2nd 2 3rd 1 |
This is a good start, but it doesn’t include the existence of any tiebreakers, which are needed to reflect the scenarios of the Prospect League or really any sports league.
So to continue with the neutral logic, we will say that for any situation where two teams are tied for a spot, they will have a 50% chance of getting the higher ranking and a 50% chance that they get the lower ranking. This can be done by giving each team a “half of a placement” for both of the placements they could possibly get in the tiebreaker. The same process is done with teams in a three-way tiebreakers by giving them 1/3 of a placement.
| S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | Placements | |
| Team A | W 1-0 1st(1/3) 2nd(1/3) 3rd(1/3) | L 0-1 3rd | W 1-0 1st(1/2) 2nd(1/2) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | W 1-0 1st | L 0-1 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 2.67 2nd 2.67 3rd 2.67 |
| Team B | W 1-0 1st(1/3) 2nd(1/3) 3rd(1/3) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 3rd | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | W 1-0 1st | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 2.67 2nd 2.67 3rd 2.67 |
| Team C | W 1-0 1st(1/3) 2nd(1/3) 3rd(1/3) | W 1-0 1st(1/2) 2nd(1/2) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 3rd | W 1-0 1st | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 2.67 2nd 2.67 3rd 2.67 |
As expected, the teams all turn out to have the same odds of getting every placement in the neutral setting.
However, when we add a game to Team C’s schedule, the odds now become skewed.
| S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | ||
| Team A | W 1-0 1st(1/3) 2nd(1/3) 3rd(1/3) | L 0-1 3rd | W 1-0 1st(1/2) 2nd(1/2) | W 1-0 1st(1/2) 2nd(1/2) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 3rd | L 0-1 3rd | |
| Team B | W 1-0 1st(1/3) 2nd(1/3) 3rd(1/3) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 3rd | W 1-0 1st(1/2) 2nd(1/2) | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | W 1-0 1st | W 1-0 1st | |
| Team C | WW 2-0 1st(1/3) 2nd(1/3) 3rd(1/3) | WW 2-0 1st(1/2) 2nd(1/2) | WW 2-0 1st(1/2) 2nd(1/2) | LW 1-1 3rd | WL 1-1 3rd | WW 2-0 1st | LW 1-1 2nd | WL 1-1 2nd | |
| S9 | S10 | S11 | S12 | S13 | S14 | S15 | S16 | Placements | |
| Team A | W 1-0 1st | W 1-0 1st | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | W 1-0 1st | L 0-1 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 5.67 2nd 4.67 3rd 5.67 |
| Team B | L 0-1 3rd | L 0-1 3rd | W 1-0 1st(1/2) 2nd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 2nd(1/2) 3rd(1/2) | W 1-0 1st | L 0-1 2nd(1/2) 3rd(1/2) | L 0-1 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 5.67 2nd 4.67 3rd 5.67 |
| Team C | LW 1-1 2nd | WL 1-1 2nd | LL 0-2 3rd | LW 1-1 1st | WL 1-1 1st | LL 0-2 2nd(1/2) 3rd(1/2) | LL 0-2 2nd(1/2) 3rd(1/2) | LL 0-2 1st(1/3) 2nd(1/3) 3rd(1/3) | 1st 4.67 2nd 6.67 3rd 4.67 |
We can see by the chart that Team A and B are more likely to get a 1st place finish than Team C AND they are more likely to get a last place finish than Team C. These likelihoods are evened out by the fact that Team C has an even bigger likelihood to have a 2nd place finish than the other two.
If this was a competition of seeing who has the highest average record, these discrepancies wouldn’t make a difference. Because we’ve decided that every game is decided by essentially a coin flip, the teams will always have the same average record of .500, no matter the number of games they play.
However, because this is a competition of teams trying to get 1st place only, it does matter. This creates a scenario where getting 2nd place is no better than getting 3rd place. When it comes to the Prospect league Playoffs, if you ain’t first, you’re last.
Having more games on your schedule inherently means that you are more likely to stay in the middle of the standings, which may help you stay away from being in the bottom of the division, but it will hurt your chances of getting to the top.
Exceptions
While having less games in your schedule is generally beneficial to your chances of winning your division, there are actually a lot of exceptions to the rule that manage to cancel out the polarization of teams having less games.
In a scenario with: Team A: 2 Games, Team B: 2 Games, Team C: 3 Games
Each team has an equal chance of winning
In a scenario with: Team A: 3 Games, Team B: 3 Games, Team C: 4 Games
Team C now has better odds of winning the division
In a scenario with: Team A: 3 Games, Team B: 4 Games, Team C: 6 Games
Team B actually has the best odds of taking the division crown
You can test out different scenarios yourself by making a copy of this Excel link and changing the number of games in the bottom-left corner.
Prospect League Game Theory Copy.xlsx
Prospect League Application
Now that we have this method established, we can use it on the schedule for the second-half of the Prospect League to see how significant the different game discrepancy is when all competition is made neutral.
In the beginning of the second half of the season, the 3 remaining teams in the Wabash River Division: Normal, Springfield, and Terre Haute, were all put in a competition where only the best second-half record of the 3 would advance to the playoffs.
In this second half, Normal had 31 games to play, Springfield had 29 games, and Terre Haute had 33.
Solely due to this difference in games, Springfield had a 2% advantage over Normal and a 3% advantage over Terre Haute even before any sort of strength of schedule could be factored in.
Conversely in the Ohio River Valley, Lafayette, the team with more games on their schedule gained the early advantage, albeit a smaller difference at 0.67%.
Acknowledgements
I want give a special thanks to Grant Jones for helping me work through some of the Excel formulas that made this possible.
I’d also like the thank the entire Cornbelters Analytics team for a fantastic summer at the Corn Crib!