Introduction

This project looks at the 2024 MLB standings through Pythagorean expected wins. Instead of only judging teams by their actual wins and losses, this gives another way to look at how strong each team was based on runs scored and runs allowed.

The first part of the project calculates each team’s Pythagorean expected win proportion using the exponent 1.86. The reason this assignment uses 1.86 instead of the original exponent of 2 is because baseball does not always follow the basic squared version perfectly. The 1.86 exponent is commonly used because it better fits MLB run scoring patterns and gives a more realistic estimate of how often a team should win based on runs scored and runs allowed.

The second part of the project builds off that by calculating Lucky Wins, which shows how many games each team won above or below its Pythagorean expected win total.

\[ \text{Pythagorean Expected Win Proportion} = \frac{RS^{1.86}}{RS^{1.86} + RA^{1.86}} \]

In this formula, RS means runs scored and RA means runs allowed.

After finding the Pythagorean win proportion, I converted it into Pythagorean expected wins by multiplying it by 162, because MLB teams play 162 regular season games. For example, if a team had a Pythagorean win proportion of 0.600, the expected win total would be \(0.600 \times 162 = 97.2\) wins.

\[ \text{Pythagorean Expected Wins} = \text{Pythagorean Win Proportion} \times 162 \]

\[ \text{Lucky Wins} = \text{Actual Wins} - \text{Pythagorean Expected Wins} \]

A positive Lucky Wins number means the team won more games than expected. A negative number means the team won fewer games than expected. The main goal is to compare what actually happened in the standings to what the teams’ run profiles suggested should have happened.

Part 1: Pythagorean Expected Win Proportion

Assignment Questions

For Part 1, the assignment asks:

Which team had the highest Pythagorean expected win proportion in MLB? Which team had the lowest? Are these the same as the teams that had the highest and lowest actual win proportion in MLB?

Division Results

The table below ranks each division by Pythagorean expected wins.

2024 MLB Pythagorean Expected Win Proportion by Division
Teams are ranked within each division by Pythagorean expected wins
Pyth Rk Team Act. W Pyth W Pyth L Lucky Wins Actual Win% Pyth Win Prop.
AL Central
1 Cleveland Guardians 92 90.0 72.0 2.0 0.571 0.556
2 Kansas City Royals 86 89.8 72.2 −3.8 0.531 0.555
3 Detroit Tigers 86 84.7 77.3 1.3 0.531 0.523
4 Minnesota Twins 82 82.7 79.3 −0.7 0.506 0.510
5 Chicago White Sox 41 47.2 114.8 −6.2 0.253 0.291
AL East
1 New York Yankees 94 95.8 66.2 −1.8 0.580 0.591
2 Baltimore Orioles 91 90.8 71.2 0.2 0.562 0.560
3 Boston Red Sox 81 81.0 81.0 0.0 0.500 0.500
4 Tampa Bay Rays 80 73.3 88.7 6.7 0.494 0.452
5 Toronto Blue Jays 74 72.4 89.6 1.6 0.457 0.447
AL West
1 Houston Astros 88 91.5 70.5 −3.5 0.547 0.565
2 Seattle Mariners 85 90.5 71.5 −5.5 0.525 0.559
3 Texas Rangers 78 74.2 87.8 3.8 0.481 0.458
4 Athletics 69 68.9 93.1 0.1 0.426 0.426
5 Los Angeles Angels 63 64.1 97.9 −1.1 0.389 0.395
NL Central
1 Milwaukee Brewers 93 94.6 67.4 −1.6 0.574 0.584
2 Chicago Cubs 83 88.0 74.0 −5.0 0.512 0.543
3 Cincinnati Reds 77 81.0 81.0 −4.0 0.475 0.500
4 St. Louis Cardinals 83 75.7 86.3 7.3 0.512 0.467
5 Pittsburgh Pirates 76 72.4 89.6 3.6 0.469 0.447
NL East
1 Philadelphia Phillies 95 92.8 69.2 2.2 0.586 0.573
2 Atlanta Braves 89 92.2 69.8 −3.2 0.549 0.569
3 New York Mets 89 87.7 74.3 1.3 0.549 0.541
4 Washington Nationals 71 70.8 91.2 0.2 0.438 0.437
5 Miami Marlins 62 59.8 102.2 2.2 0.383 0.369
NL West
1 Los Angeles Dodgers 98 96.9 65.1 1.1 0.605 0.598
2 San Diego Padres 93 91.2 70.8 1.8 0.574 0.563
3 Arizona Diamondbacks 89 89.7 72.3 −0.7 0.549 0.554
4 San Francisco Giants 80 81.0 81.0 −1.0 0.494 0.500
5 Colorado Rockies 61 58.6 103.4 2.4 0.377 0.362
Pyth Rk = division rank using Pythagorean expected wins. Lucky Wins = actual wins minus Pythagorean expected wins.

Visual Comparison

This visual compares actual win proportion to Pythagorean expected win proportion. The dashed line shows where actual performance equals expected performance.

Full MLB Table

The table below ranks all MLB teams by Pythagorean expected wins.

2024 MLB Teams Ranked by Pythagorean Expected Wins
All teams combined
Pyth Rk Team Act. W Pyth W Pyth L Lucky Wins Actual Win% Pyth Win Prop.
1 Los Angeles Dodgers 98 96.9 65.1 1.1 0.605 0.598
2 New York Yankees 94 95.8 66.2 −1.8 0.580 0.591
3 Milwaukee Brewers 93 94.6 67.4 −1.6 0.574 0.584
4 Philadelphia Phillies 95 92.8 69.2 2.2 0.586 0.573
5 Atlanta Braves 89 92.2 69.8 −3.2 0.549 0.569
6 Houston Astros 88 91.5 70.5 −3.5 0.547 0.565
7 San Diego Padres 93 91.2 70.8 1.8 0.574 0.563
8 Baltimore Orioles 91 90.8 71.2 0.2 0.562 0.560
9 Seattle Mariners 85 90.5 71.5 −5.5 0.525 0.559
10 Cleveland Guardians 92 90.0 72.0 2.0 0.571 0.556
11 Kansas City Royals 86 89.8 72.2 −3.8 0.531 0.555
12 Arizona Diamondbacks 89 89.7 72.3 −0.7 0.549 0.554
13 Chicago Cubs 83 88.0 74.0 −5.0 0.512 0.543
14 New York Mets 89 87.7 74.3 1.3 0.549 0.541
15 Detroit Tigers 86 84.7 77.3 1.3 0.531 0.523
16 Minnesota Twins 82 82.7 79.3 −0.7 0.506 0.510
17 Boston Red Sox 81 81.0 81.0 0.0 0.500 0.500
18 San Francisco Giants 80 81.0 81.0 −1.0 0.494 0.500
19 Cincinnati Reds 77 81.0 81.0 −4.0 0.475 0.500
20 St. Louis Cardinals 83 75.7 86.3 7.3 0.512 0.467
21 Texas Rangers 78 74.2 87.8 3.8 0.481 0.458
22 Tampa Bay Rays 80 73.3 88.7 6.7 0.494 0.452
23 Pittsburgh Pirates 76 72.4 89.6 3.6 0.469 0.447
24 Toronto Blue Jays 74 72.4 89.6 1.6 0.457 0.447
25 Washington Nationals 71 70.8 91.2 0.2 0.438 0.437
26 Athletics 69 68.9 93.1 0.1 0.426 0.426
27 Los Angeles Angels 63 64.1 97.9 −1.1 0.389 0.395
28 Miami Marlins 62 59.8 102.2 2.2 0.383 0.369
29 Colorado Rockies 61 58.6 103.4 2.4 0.377 0.362
30 Chicago White Sox 41 47.2 114.8 −6.2 0.253 0.291
Pyth Rk = MLB rank using Pythagorean expected wins. Lucky Wins = actual wins minus Pythagorean expected wins.

Highest and Lowest Teams

Highest and Lowest Teams
Comparing Pythagorean expected win proportion to actual win proportion
Category Pythagorean Team Pyth Win Prop. Actual Team Actual Win% Same?
Highest Los Angeles Dodgers 0.598 Los Angeles Dodgers 0.605 Yes
Lowest Chicago White Sox 0.291 Chicago White Sox 0.253 Yes

Part 1 Analysis

The Los Angeles Dodgers had the highest Pythagorean expected win proportion in MLB at 0.594. That means their run profile projected them for about 96.2 wins over a 162-game season. They actually won 98 games, so they finished about 1.8 Lucky Wins above their Pythagorean expectation.

The Chicago White Sox had the lowest Pythagorean expected win proportion at 0.294. That translates to about 47.6 expected wins, but they only won 41 games, so they finished about 6.6 Lucky Wins below their Pythagorean expectation.

These results matched the actual standings extremes. The Dodgers also had the highest actual win proportion in MLB, while the White Sox had the lowest actual win proportion. So for the highest and lowest teams, the Pythagorean model told the same basic story as the real standings. In fact, the only team that would have finished differently in their division would have been the St. Louis Cardinals who finished 2nd in the NL Central, but according to Pythagorean Exp. Wins, they would have finished 4th.

Part 2: Lucky Wins and Pythagorean Playoff Comparison

Assignment Questions

For Part 2, the assignment asks:

Which MLB team was the luckiest? Which team was the most unlucky? Would the playoff teams have been different if playoff spots were assigned according to Pythagorean expected wins instead of actual wins?

All Teams Ranked by Lucky Wins

The table below ranks every MLB team by Lucky Wins. Teams at the top won more games than expected based on their run profile, while teams at the bottom won fewer games than expected.

2024 MLB Teams Ranked by Lucky Wins
Lucky Wins = actual wins minus Pythagorean expected wins
Rk Team Act. W Pyth W Pyth L Lucky Wins Actual Win% Pyth Win Prop.
1 St. Louis Cardinals 83 75.7 86.3 7.3 0.512 0.467
2 Tampa Bay Rays 80 73.3 88.7 6.7 0.494 0.452
3 Texas Rangers 78 74.2 87.8 3.8 0.481 0.458
4 Pittsburgh Pirates 76 72.4 89.6 3.6 0.469 0.447
5 Colorado Rockies 61 58.6 103.4 2.4 0.377 0.362
6 Philadelphia Phillies 95 92.8 69.2 2.2 0.586 0.573
7 Miami Marlins 62 59.8 102.2 2.2 0.383 0.369
8 Cleveland Guardians 92 90.0 72.0 2.0 0.571 0.556
9 San Diego Padres 93 91.2 70.8 1.8 0.574 0.563
10 Toronto Blue Jays 74 72.4 89.6 1.6 0.457 0.447
11 Detroit Tigers 86 84.7 77.3 1.3 0.531 0.523
12 New York Mets 89 87.7 74.3 1.3 0.549 0.541
13 Los Angeles Dodgers 98 96.9 65.1 1.1 0.605 0.598
14 Washington Nationals 71 70.8 91.2 0.2 0.438 0.437
15 Baltimore Orioles 91 90.8 71.2 0.2 0.562 0.560
16 Athletics 69 68.9 93.1 0.1 0.426 0.426
17 Boston Red Sox 81 81.0 81.0 0.0 0.500 0.500
18 Minnesota Twins 82 82.7 79.3 −0.7 0.506 0.510
19 Arizona Diamondbacks 89 89.7 72.3 −0.7 0.549 0.554
20 San Francisco Giants 80 81.0 81.0 −1.0 0.494 0.500
21 Los Angeles Angels 63 64.1 97.9 −1.1 0.389 0.395
22 Milwaukee Brewers 93 94.6 67.4 −1.6 0.574 0.584
23 New York Yankees 94 95.8 66.2 −1.8 0.580 0.591
24 Atlanta Braves 89 92.2 69.8 −3.2 0.549 0.569
25 Houston Astros 88 91.5 70.5 −3.5 0.547 0.565
26 Kansas City Royals 86 89.8 72.2 −3.8 0.531 0.555
27 Cincinnati Reds 77 81.0 81.0 −4.0 0.475 0.500
28 Chicago Cubs 83 88.0 74.0 −5.0 0.512 0.543
29 Seattle Mariners 85 90.5 71.5 −5.5 0.525 0.559
30 Chicago White Sox 41 47.2 114.8 −6.2 0.253 0.291
Positive Lucky Wins means the team won more games than expected. Negative Lucky Wins means the team won fewer games than expected.

Lucky Wins Visual

This chart shows which teams won more or fewer games than their Pythagorean expected win total.

Luckiest and Most Unlucky Teams

Luckiest and Most Unlucky Teams
Based on actual wins minus Pythagorean expected wins
Category Team Act. W Pyth W Pyth L Lucky Wins Actual Win% Pyth Win Prop.
Luckiest Team St. Louis Cardinals 83 75.7 86.3 7.3 0.512 0.467
Most Unlucky Team Chicago White Sox 41 47.2 114.8 −6.2 0.253 0.291
Lucky Wins = actual wins minus Pythagorean expected wins.

Playoff Comparison Method

For the playoff comparison, I used the actual MLB playoff format. Each league gets six playoff teams: three division winners and three Wild Card teams. The actual playoff teams are selected by actual wins. The Pythagorean playoff teams are selected the same way, but using Pythagorean expected wins instead.

Actual Playoff Teams vs. Pythagorean Playoff Teams

Actual Playoff Teams vs. Pythagorean Playoff Teams
Using the actual MLB playoff format: division winners plus Wild Card teams
Seed Type Division Team Act. W Pyth W Pyth L Pyth Win Prop. Lucky Wins
Actual Wins
AL #1 Division Winner AL East New York Yankees 94 95.8 66.2 0.591 −1.8
AL #2 Division Winner AL Central Cleveland Guardians 92 90.0 72.0 0.556 2.0
AL #3 Division Winner AL West Houston Astros 88 91.5 70.5 0.565 −3.5
AL #4 Wild Card AL East Baltimore Orioles 91 90.8 71.2 0.560 0.2
AL #5 Wild Card AL Central Kansas City Royals 86 89.8 72.2 0.555 −3.8
AL #6 Wild Card AL Central Detroit Tigers 86 84.7 77.3 0.523 1.3
NL #1 Division Winner NL West Los Angeles Dodgers 98 96.9 65.1 0.598 1.1
NL #2 Division Winner NL East Philadelphia Phillies 95 92.8 69.2 0.573 2.2
NL #3 Division Winner NL Central Milwaukee Brewers 93 94.6 67.4 0.584 −1.6
NL #4 Wild Card NL West San Diego Padres 93 91.2 70.8 0.563 1.8
NL #5 Wild Card NL East Atlanta Braves 89 92.2 69.8 0.569 −3.2
NL #6 Wild Card NL West Arizona Diamondbacks 89 89.7 72.3 0.554 −0.7
Pythagorean Expected Wins
AL #1 Division Winner AL East New York Yankees 94 95.8 66.2 0.591 −1.8
AL #2 Division Winner AL West Houston Astros 88 91.5 70.5 0.565 −3.5
AL #3 Division Winner AL Central Cleveland Guardians 92 90.0 72.0 0.556 2.0
AL #4 Wild Card AL East Baltimore Orioles 91 90.8 71.2 0.560 0.2
AL #5 Wild Card AL West Seattle Mariners 85 90.5 71.5 0.559 −5.5
AL #6 Wild Card AL Central Kansas City Royals 86 89.8 72.2 0.555 −3.8
NL #1 Division Winner NL West Los Angeles Dodgers 98 96.9 65.1 0.598 1.1
NL #2 Division Winner NL Central Milwaukee Brewers 93 94.6 67.4 0.584 −1.6
NL #3 Division Winner NL East Philadelphia Phillies 95 92.8 69.2 0.573 2.2
NL #4 Wild Card NL East Atlanta Braves 89 92.2 69.8 0.569 −3.2
NL #5 Wild Card NL West San Diego Padres 93 91.2 70.8 0.563 1.8
NL #6 Wild Card NL West Arizona Diamondbacks 89 89.7 72.3 0.554 −0.7
Lucky Wins = actual wins minus Pythagorean expected wins.

Playoff Teams That Would Change

The table below shows which teams would change if playoff teams were selected by Pythagorean expected wins instead of actual wins.

Playoff Teams That Would Change
Comparing actual playoff teams to Pythagorean expected win playoff teams
Category Team Division Actual Seed Pyth Seed Act. W Pyth W Pyth L Pyth Win Prop. Lucky Wins
Made Actual Playoffs, Missed by Pythagorean Expected Wins Detroit Tigers AL Central AL #6 NA 86 84.7 77.3 0.523 1.3
Missed Actual Playoffs, Made by Pythagorean Expected Wins Seattle Mariners AL West NA AL #5 85 90.5 71.5 0.559 −5.5
Lucky Wins = actual wins minus Pythagorean expected wins.

Playoff Seed Changes

This table only includes teams that made the playoffs under both systems but would have had a different seed using Pythagorean expected wins.

Playoff Seeds That Would Change
Teams that made the playoffs under both systems but would have moved seeds
Team Division Actual Seed Pyth Seed Act. W Pyth W Pyth L Pyth Win Prop. Lucky Wins
Cleveland Guardians AL Central AL #2 AL #3 92 90.0 72.0 0.556 2.0
Houston Astros AL West AL #3 AL #2 88 91.5 70.5 0.565 −3.5
Kansas City Royals AL Central AL #5 AL #6 86 89.8 72.2 0.555 −3.8
Philadelphia Phillies NL East NL #2 NL #3 95 92.8 69.2 0.573 2.2
Milwaukee Brewers NL Central NL #3 NL #2 93 94.6 67.4 0.584 −1.6
San Diego Padres NL West NL #4 NL #5 93 91.2 70.8 0.563 1.8
Atlanta Braves NL East NL #5 NL #4 89 92.2 69.8 0.569 −3.2
Lucky Wins = actual wins minus Pythagorean expected wins.

Part 2 Analysis

The St. Louis Cardinals came out as the luckiest team in MLB by this measure. They won 83 games, but their Pythagorean expected win total was about 75.9 wins, so they finished roughly 7.1 Lucky Wins above expected.

The Chicago White Sox were on the other side. They won 41 games, but their run profile projected them for about 47.6 wins, meaning they finished about 6.6 Lucky Wins below expected. That is honestly kind of wild because they were already the worst team in the league by actual record, but they also came out as the most unlucky team by this calculation.

The playoff field would have looked a little different if spots were based on Pythagorean expected wins instead of actual wins. The Detroit Tigers made the actual playoffs, but under the Pythagorean version, the Seattle Mariners would have taken that spot. Some playoff seeds would have changed too, which could have mattered a lot because seeding changes can affect matchups and home-field advantage.

Summary

This project answered two main questions. First, it looked at which teams had the highest and lowest Pythagorean expected win proportion. Second, it looked at which teams were the luckiest or most unlucky based on the difference between actual wins and Pythagorean expected wins.

For Part 1, the Los Angeles Dodgers had the highest Pythagorean expected win proportion in MLB at 0.594, while the Chicago White Sox had the lowest at 0.294. Those were also the same teams that had the highest and lowest actual win proportions, so the Pythagorean model matched the real standings at the top and the bottom.

For Part 2, the St. Louis Cardinals were the luckiest team because they won about 7.1 more games than their run profile expected. The Chicago White Sox were the most unlucky team because they won about 6.6 fewer games than expected.

The playoff comparison also showed that the playoff field would not have been exactly the same. The Detroit Tigers made the actual playoffs, but if playoff spots were based on Pythagorean expected wins, the Seattle Mariners would have replaced them. That does not mean the actual standings were wrong, but it does show how useful Pythagorean expected wins can be for looking past the record and getting a better feel for how strong a team’s overall run profile really was as well how lucky or unlucky a team was that season.