Trying to Predict the MLB Standings – Projected WAR vs. Pythagorean Expectation (based on PECOTA Projections)

It’s that time of year again, baseball season is upon us and Hit the Cut is here to provide you with a primer on what to expect in the upcoming season.

Projections that rely solely on the eye-test should, in our opinion, be reserved for water cooler conversations. So, in an effort to provide something more empirical, we’ll be staying away from that. Following, we’ll explore two separate projection methods to map out what we expect the standings will come out as once October arrives.

Method 1: Projecting standings based on Pythagorean expectation

As explored in one of our previous articles, using Pythagorean expectation to predict win percentage involves a formula invented by sabermetrics pioneer, Bill James:

\mathrm{Win} = \frac{\text{runs scored}^2}{\text{runs scored}^2 + \text{runs allowed}^2} = \frac{1}{1+(\text{runs allowed}/\text{runs scored})^2}

To illustrate the effectiveness of this projected win percentage (based on runs scored and allowed), here is a scatter plot showing the relationship between this percentage and actual win percentage from the past ten seasons (2005-2015):


The R-squared value means (for those of you that haven’t taken an intro stats class) that 93% of the variation in win percentage can be explained by Pythagorean expectation (essentially, runs). This leaves 7% for random variation, which we can categorize as luck. This is a very significant relationship and results in Pythagorean expectation win percentage being a prime candidate to predict future team performance. To do this, we took the PECOTA-projected* runs scored and allowed and plugged them into James’ formula. The results:

AL East

Team RS RA W%
 Boston Red Sox 735 675 0.54
 Tampa Bay Rays 702 647 0.54
 Toronto Blue Jays 767 719 0.53
 New York Yankees 725 694 0.52
 Baltimore Orioles 713 775 0.46


AL Central

Team RS RA W%
 Cleveland Indians 718 623 0.57
 Chicago White Sox 696 667 0.52
 Detroit Tigers 692 715 0.48
 Minnesota Twins 683 706 0.48
 Kansas City Royals 640 695 0.46


AL West

Team RS RA W%
 Houston Astros 747 685 0.54
 Seattle Mariners 691 662 0.52
 Texas Rangers 722 733 0.49
 Los Angeles Angels 675 714 0.47
 Oakland Athletics 667 717 0.46


NL East

Team RS RA W%
 New York Mets 677 597 0.56
 Washington Nationals 688 630 0.54
 Miami Marlins 640 690 0.46
 Atlanta Braves 599 708 0.42
 Philadelphia Phillies 614 751 0.40


NL Central

Team RS RA W%
 Chicago Cubs 750 627 0.59
 St. Louis Cardinals 667 664 0.50
 Pittsburgh Pirates 683 692 0.49
 Milwaukee Brewers 688 724 0.47
 Cincinnati Reds 671 748 0.45


NL West

Team RS RA W%
 Los Angeles Dodgers 707 594 0.59
 San Francisco Giants 643 609 0.53
 Arizona D-backs 660 685 0.48
 San Diego Padres 650 693 0.47
 Colorado Rockies 681 751 0.45


Method 2: Projecting standings based on projected WAR (wins above replacement)

Perhaps the most widely used sabermetric statistic, WAR is an attempt to combine everything (offense, defense, fielding, and running) that a player offers in one neat package. When we look at WAR in relation to win percentage, in the same vein as our last comparison, it paints a similar picture (86.6% of the variation in win percentage can be explained by WAR):


Moreover, Fangraphs has projected team WAR values (by combining the projected WAR of the players predicted to be on that team for the upcoming season) so we ranked teams, by division, according to this metric. The results:

AL East

Team WAR
Red Sox 41.7
Yankees 39.8
Blue Jays 39.2
Orioles 35.8
Rays 35.5


AL Central

Team WAR
Indians 42.7
White Sox 36
Tigers 33.9
Twins 33.1
Royals 32.5


AL West

Team WAR
Astros 42.3
Mariners 35
Angels 34.9
Rangers 32.1
Athletics 31.7


NL East

Team WAR
Mets 47.3
Nationals 42.6
Marlins 32.9
Braves 20.6
Phillies 18.3


NL Central

Team WAR
Cubs 51.3
Cardinals 41.2
Pirates 40.3
Reds 29.8
Brewers 25.9


NL West

Team WAR
Dodgers 50.5
Giants 42.4
Diamondbacks 32.9
Padres 28.4
Rockies 26.7


Some thoughts about the projections

Now, looking at information above, there’s really only one major discrepancy between the two rankings – the Tampa Bay Rays. Tampa Bay drops from second in the Pythagorean projection all the way to last in the WAR projection. One reason for this is Tampa Bay is not known for having a plethora of stars. The Rays have only 3 players on their depth chart with a WAR higher than 3.0. Compared to teams like the Blue Jays (6 players with a WAR over 3.0, one with a WAR over 6.0) or the Red Sox (4 players with a WAR over 3.0, 1 with a WAR over 5.0) the Rays just don’t have that type of firepower, nor have they ever. However, they pride the core of their team to defensive excellence (4th in Def, a catch-all fielding statistic) and above-average pitching (12th in SIERA, a catch-all pitching statistic), which is why they rank so well in the PECOTA-projected Pythagorean win percentage.

One team’s projections that might come as a surprise to everyone are the reigning World Series Champs. The Kansas City Royals are ranked last in both projections for the AL Central. The Royals, over the past two seasons, have baffled the sabermetric community with their success. Here is Kansas City’s rank over the past two regular seasons in wRC+ (a catch-all offensive statistic) and SIERA.

  Score MLB Rank 
wRC+ 97 15
SIERA 3.98 26

Nothing special, right? But in this time period, they’ve made it to the World Series twice, winning it all last season. Either KC has found another way to win baseball games that defies sabermetric conventional wisdom, or this team comes back down to Earth and performs how their underlying metrics say they should (which is what our ranking systems and many analysts are predicting).


Adam is a student at McGill University. You can follow him on Twitter @adam_m3318.

Carter is a hockey player, formerly in the WHL for the Vancouver Giants. You can follow him on Twitter @carter_popoff.

You can follow Hit the Cut on Twitter @hitthecutblog.

*PECOTA, an acronym for Pitcher Empirical Comparison and Optimization Test Algorithm, is a sabermetric system for forecasting Major League Baseball player performance.”


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