In postseason, should we save players for next game?

 September to October marks the postseason. Numerous articles discuss which team holds an advantage in the playoffs during this period. These articles analyze factors such as roster age (experience), head-to-head records, and win probability against teams with over or under .500 records.

 

And yes, no clear evidence that these factors decide the postseason-winning team. In the conclusion of this article, they analyzed about 60 variables, but none of them effectively predicted postseason results. 

 

There is also one conventional wisdom heard during the postseason: 'Do not think about tomorrow.' That means do everything to win today's game, not prepare for tomorrow's game.

 

Does it make sense? I tried to figure out the answer using a simple tree model. In this calculation, the win probability per game changes like in a zero-sum game. If one team's win% goes up 5%p, that team's tomorrow win% go down 5%p.

 

  • Team A win probability for each game = [0.55, 0.55, 0.55, 0.55, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6083
  •  

Let's suppose Team A pushes itself to win game 1. The odds of Team A winning game 1 go up to 60%. Instead, the odds of Team A winning game 2 go down to 50%. They use players in advance. In other games (game3~game7), the win probability is still the same. In this case, Team A's series win probability is approximately 60.84%

 

  • Team A win probability for each game = [0.6, 0.5, 0.55, 0.55, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6084

 

More extremely, Team A does everything to win game 1. They use a starter of game 2 to win game 1. It's not common, but it can happen in real life. As a result, Team A's win probability for game 1 goes up to 80%. In consideration, the win probability of game 2 goes down to 30% because emergency Starter has to start game 2. Well, game 2 for Team A can be a bullpen day, but let's rule out that possibility. In this case, Team A's series win probability is approximately 61.21%.

 

  • Team A win probability for each game = [0.8, 0.3, 0.55, 0.55, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6121

 

The higher the probability of one game-win probability, the greater the probability of a series-win probability.

 

Team A and Team B play a best-of-seven series. In every game, the odds for Team A to win over Team B are 55%. In this case, Team A's win probability for the series is approximately 60.83%. The numbers in [] are Team A's win probability for each game in order.

 

What if, in the case of diversified investment? That means the win probability of game 1 and game 2 goes up to 60%, rather than the game 3 and game 4 win probability goes down to 50%. 

 

  • Team A win probability for each game = [0.6, 0.6, 0.5, 0.5, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6086

 

On the contrary, it's the result of raising the probability of winning game 1 to 65% and lowering the probability of winning game 2 and game 3 by 5%p.

 

  • Team A win probability for each game = [0.65, 0.5, 0.5, 0.5, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6087
  •  

The result is as expected. Increasing the probability of winning only one game is slightly higher. Let's also compare the case of increasing the win probability of three games.  

 

  • Team A win probability for each game = [0.7, 0.5, 0.5, 0.5, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6090

vs

  • Team A win probability for each game = [0.6, 0.6, 0.6, 0.5, 0.5, 0.5, 0.55]
  • Team A series win probability = 0.6087

 

All-in for one game is better. 

 

Comparing the case of increasing four games and all-in for one game.

 

  • Team A win probability for each game = [0.6, 0.6, 0.6, 0.6, 0.5, 0.5, 0.4]
  • Team A series win probability = 0.6091

vs

  • Team A win probability for each game = [0.75, 0.5, 0.5, 0.5, 0.5, 0.55, 0.5]
  • Team A series win probability = 0.6092

 

The calculation showed that increasing the win probability of one game a lot is better than increasing the win probability of some games little, even if the amount of increased probability is the same. But the difference is quite tiny.

 

Finally, a very extreme example. Team A does everything. They use everything to win the game. They made the win probability as 1. Instead, their win probability of the next game is 0.1. 

  • Team A win probability for each game = [1, 0.1, 0.55, 0.55, 0.55, 0.55, 0.55]
  • Team A series win probability = 0.6207 

 This is the biggest probability we ever seen. About 1%p of the probability increased than the case of every game's win probability is 0.55.

 

In conclusion, if we can take out a loan of tomorrow's win probability, we should do that in the postseason. The more you rent, the better. 

 

Of course, the reality doesn't move like this. Win probability is not a zero-sum game. It may or may not be hit harder tomorrow than the win probability you borrowed today. We can not judge baseball by its fragmentary figure. So it would be nice to see this article only for fun.

 

댓글

댓글 쓰기

이 블로그의 인기 게시물

Arm angle and Pitcher type

이미지
Danny Young New York Mets pitcher Danny Young’s Baseball Savant movement profile is as follows. He throws a sinker and a sweeper with significant horizontal movement from a low arm angle. He’s a pitcher with an interesting pitch mix. It’s clear that he confuses hitters more with differences in horizontal movement between pitches rather than vertical movement. Horizontal vs. Vertical Movement Differences This gave me an idea. I looked into which pitchers have the greatest differences in horizontal movement and which in vertical movement when pairing their pitches two by two. As previously seen, Danny Young falls into the former category. The image above shows the movement profile of Cubs pitcher Caleb Thielbar in 2020. Unlike Danny Young mentioned earlier, he features a four-seam fastball and curveball combination from a high arm angle. He falls into the latter category, characterized by a large difference in vertical movement. Based on data from 2020 to 2025 for pitchers who faced at l...
자세한 내용 보기

The Relationship Between Pitch Location Scatter Plots and Arm Slot

이미지
During the last offseason, I was looking at a scatter plot of Cleveland pitcher Tanner Bibee’s pitch locations, and it reminded me of a regression line with a negative slope. I had a similar thought after watching Aaron Nola’s knuckle curve location. However, the slope of Nola’s regression line is more gradual than Bibee’s. While this may be the result of various factors—such as the trajectory and usage of breaking balls, as well as command—I focused on something a little different: arm slot. Nola’s average arm slot is 20 degrees, whereas Bibee’s is 51 degrees. And arm slot does have some correlation with pitch movement. I looked into the relationship between pitch location scatter plots and arm slots. Here’s how: •   I plotted pitch location scatter plots for pitchers who threw more than 100 pitches of each pitch type. •   From these scatter plots, I drew regression lines and calculated the location correlation coefficients for each pitcher. •   Then, I compared the corr...
자세한 내용 보기

Randomness of Pitcher

이미지
 The legendary Major League pitcher Warren Spahn once said, “Hitting is timing. Pitching is upsetting timing.” This statement perfectly captures the essence of both pitching and hitting. A pitch that disrupts a batter’s timing is one that is difficult to react to. So, what kind of pitches are hard to react to? It could be an extremely fast pitch, or a very slow one. But more importantly, it could be a pitch that’s difficult to predict. In this article, I use entropy to simply calculate the randomness of Major League pitchers. Method 1 Here’s how I calculated randomness: I calculated the entropy of each pitcher’s pitch usage rates by pitch type. Then, I normalized each pitcher’s entropy score between 0 and 1 to obtain a “pitch usage entropy score.” The more pitch types a pitcher uses, and the more evenly they’re distributed, the higher this score becomes. I selected every pair of pitch types a pitcher throws (for  n  pitch types, there are nC2 combinations), calculated the...
자세한 내용 보기