Pythagorean Winning Percentage, initially established by Bill James, has been a useful tool for measuring how many games a given team “should” have won in a given amount of time, usually over the course of the better part of a full season of baseball. Given the general depth of knowledge in the VEB community, many of you probably already know how this metric is calculated. For those unfamiliar, though, the original formula was established as follows:
Runs^2 / [(Runs^2) + (Runs Allowed^2)]
I won’t get into the guts in this article as to how this formula has been refined since its first iteration, but I recently learned how to apply the current formula in R Programming which means you all get an article about it. Using the Lahman baseball database to look at data as far back as 1882, I thought it would be a fun exercise to see which teams in the history of the Cardinals franchise over-/underperformed their Pythagorean Win estimates by the widest margins. One disclaimer I have is that I’m not sure whether this formula is meant to be used across so many baseball eras, but I’m going on the assumption that it’ll work well enough for a fun exploration of the Cardinals’ history.
After running the calculations for the Pythagorean Winning Percentages for each team, I took the difference between their Actual Winning Percentage and their Pythagorean Winning Percentage and marked the three teams that overperformed the most (biggest positive differences between Actual and Pythag. Win Percentages) and the three teams that underperformed the most (biggest negative differences between the two factors). Below are brief overviews of the top position players and pitchers, as well as short summaries for each team. A reminder that a team underperforming doesn’t necessarily make them a worse team than one that overperformed. The following rankings are simply how each performed compared to their own individual expectations for that season.
The Bottom Three
W-L: 84-78-1 | Pythagorean Wins: 93-69
Runs: 774 | Runs Allowed: 664 | Run Differential: +10
Actual Win %: .519 | Pythagorean Win %: .576 | Actual % - Pyt %: -0.058
The 1962 Cardinals featured a 41-year old Stan Musial in his second-to-last season with the Birds on the Bat. Despite his age, Musial didn’t disappoint, slashing .330/.416/.508 which was good for a 137 OPS+. 1962 was also the year that Bob Gibson became a mainstay in the Cardinals rotation, throwing 233.1 innings and leading the Cardinals’ staff with 208 strikeouts. Despite these performances, the Cardinals fell seven wins short of where Pythagorean projections would have put them, leaving them 17.5 GB of the Giants in the National League who would go on to lose to the Yankees in the World Series.
W-L: 74-88 | Pythagorean Wins: 84-78
Runs: 738 | Runs Allowed: 710 | Run Differential: +28
Actual Win %: .457 | Pythagorean Win %: .519 | Actual % - Pyt %: -0.063
Looking at the slash lines for the 1980 Cardinals lineup, one might be surprised to learn that they finished the season 17 GB of the Philidelphia Phillies in the then six-team National League East, missing its Pythag. projection by ten games. The pitching staff, however, seemed to have trouble, as their staff posted a 3.93 ERA that ranked last in the National League that year.
W-L: 65-89 | Pythagorean Wins: 76-78
Runs: 740 | Runs Allowed: 750 | Run Differential: -10
Actual Win %: .422 | Pythagorean Win %: .493 | Actual % - Pyt %: -0.071
The 1924 Cardinals, managed by Branch Rickey, were highlighted by a herculean season from Rogers Hornsby, who posted a ridiculous 1.203 OPS and 222 OPS+. The 1924 team was an elite offensive unit, but pitching again was the issue that seemed to hold the team back, as the staff ranked sixth or worse in the eight-team National League in most pitching statistics tracked at the time. That’s probably why the team missed its Pythag. projection by eleven games, though the difference would have had few consequences in the NL title race. The 1924 Redbirds finished sixth in the NL, 28.5 GB of John McGraw’s New York Giants that went on to lose the World Series to the Washington Senators in seven games.
The Top Three
W-L: 87-67-1 | Pythagorean Wins: 76-78
Runs: 795 | Runs Allowed: 794 | Run Differential: +1
Actual Win %: .565 | Pythagorean Win %: .501 | Actual % - Pyt %: 0.064
Coming just off of the prime years of the Gashouse Gang, the 1936 Cards featured another solid offensive season from Joe “Ducky” Medwick, who posted a 158 OPS+, and a breakout season from rookie Johnny Mize, who outpaced Medwick with a 162 OPS+. Though not listed in the top positions on Baseball Reference, first baseman Ripper Collins also tallied a 144 OPS+ in 327 PAs. No summary of a 1930’s Cardinals team would be complete without a mention of Dizzy Dean, who, in his sixth season with the team, led the Major Leagues in complete games (28), saves (11), and innings pitched (315). The team outperformed their projection by eleven wins but fell five games short of the New York Giants, who eventually lost to the Yankees in the World Series.
1882 Brown Stockings
W-L: 37-43 | Pythagorean Wins: 31-49
Runs: 399 | Runs Allowed: 496 | Run Differential: -97
Actual Win %: .463 | Pythagorean Win %: .393 | Actual % - Pyt %: 0.070
I’ll admit that this one isn’t quite fair to the more modern teams in the Cardinals franchise, given that the shorter season causes more fluctuation in win percentages than the 162-game seasons we see now. But, 19th-century baseball doesn’t typically get too much love these days and there is one interesting tidbit related to this team. Charles Comiskey, the eventual founder of the Chicago White Sox, played first base for the team and is incidentally the only player with a recorded RBI value for the season, and I have no idea why. Anyways, the 1882 Brown Stockings managed to outperform their projected wins by six games despite a gross -97 run differential, which is significant in a season that’s only 80 games long. They ended the season in fifth place in the American Association, 18 GB of the Cincinnati Red Stockings.
W-L: 82-70 | Pythagorean Wins: 71-81
Runs: 531 | Runs Allowed: 567 | Run Differential: -36
Actual Win %: .539 | Pythagorean Win %: .467 | Actual % - Pyt %: 0.072
The 1917 Cardinals are the second team on this list to feature Rogers Hornsby, who put up another solid season that was complemented by good years from outfielders Walton Cruise and Jack Smith. The offense as a unit was middling, though, and the pitching staff again was one of the worst in the National League according to their Baseball Reference rankings. Despite their struggles, the Cardinals outperformed their projection by nine games but still fell short of the New York Giants who eventually lost to Comiskey’s White Sox in the World Series that year.
There’s no such thing as a perfect statistic, and Pythagorean Winning Percentage certainly has its flaws. It doesn’t account for teams that perform extraordinarily well or poorly in one-run games, which usually leads to the defiance of these expectations. However, it is still a useful tool in the toolshed for general analysis and can provide a fun lens through which to view different eras in baseball history.