Fun with Pythagoras

added 5/4/2005 by Scott Barzilla

Part One

Columnist note: This is the first part of a six part series on the use of the Pythagorean method. The method is used to determine whether a team has under or overachieved in a particular season or time period. Throughout this series, we will evaluate the possible reasons for teams underachieving or overachieving. These include evaluating managers, offense, defense, and pitching. The last leg of the series will tie up the loose ends.

When most of us see the word Pythagoras we cringe. That’s because we mentally travel back in time to high school geometry class where we saw all kinds of triangles and proofs. Don’t worry, we’re not talking “A squared plus B squared equals C squared”. Instead, we’re talking about a cool sounding name for what most of us call “expected record.” Essentially, you take the number of runs a team scores and the number of runs a team surrenders and use that to compile a record that team should have with those numbers.

Those that know me well know I delved into this theory in other places at some length. Tim Purpura was on the air last week and said that the Astros have scored more runs than their opponents. This was something considering that we were 8-12 at the time. Of course, with the recent battering of the Cubs and Bucs this fact has only become that much more blatant. It doesn’t take a Stephen Hawking to know that this means that the Stros have underachieved so far this year.

Of course, we’re getting ahead of ourselves. First, I need to tell the ground rules of expected records before we dive in. The first rule is that expected records and actual records should mirror each other. Rarely will you ever see a team have more than a five game difference either way. The second rule is that these differences should even out over time. Therefore, if you look at a team over a ten year period they should have a Pythagorean rating (or the difference between expected and actual records) around zero.

Keeping these two rules in mind I decided to look at the Astros Pythagorean rating over the past ten seasons. The club has been to the playoffs five times in those ten seasons and have finished outside of first or second place only once (2000). You can’t find too many teams that have been more successful than that. Plus, the Killer Bs have been the nucleus of the team throughout that time.

Interestingly enough, a quick study of Pythagorean records over time shows that the zero rule doesn’t always apply. Great teams usually overachieve. We see this when we look at the greatest dynasties in the game’s history. This seems very basic, but deserves mentioning because the Astros have been a very good team during this period. So, zero might not even be a good expectation for them. If the above pattern fits then the Astros would have overachieved in the past decade. Let’s see how they did do.

     Rating  Finish	
1995     -3       2
1996     +5       2
1997     -9       1
1998     -4       1
1999     +1       1
2000     -9       4 
2001     +5       1
2002     -3       2
2003     -7       2
2004     +1       2

Total   -23      1= four seasons, 2= five seasons, 4= one season

Obviously, this is not what we had in mind. If we assume that team should have finished about five or ten games above average then they fall an average of three games a season under the mark. That would have given them at least one more playoff appearance (2003) and perhaps even two (they came up just short in 1996). Before we move on, let’s take a closer look at these numbers.

Obviously, the club fails the first part of the assumptions: they didn’t wind up anywhere near zero. The other assumption could be altered to say that teams should have as many positive seasons as negative seasons. The Astros don’t fit this description either. They had six negative seasons and four positive seasons. Even that doesn’t begin to describe the situation as two of the positive seasons were +1 ratings. So, legitimately, he has two seasons considerably over average while they have six seasons considerably below average.

This is all well and good, but this doesn’t mean anything without putting it into a context. So, we will compare the Astros to the other five teams to have five or more playoff appearances over the last ten years. This list includes the Braves and Cardinals from the National League and the Yankees, Red Sox, and Indians from the American League.

                   Rating Playoff App. 
Atlanta Braves        +25           10
Boston Red Sox         +1            5
Cleveland Indians     +14            6
Houston Astros        -23            5
New York Yankees      +38           10
St. Louis Cardinals     0            5

There seems to be three tiers of teams here. There are the Braves, Indians, and Yankees that are significantly above average. Then there are the Red Sox and Cardinals that seem to be more neutral and then there are the Astros that seem to be their own category.

Our mission (if we should choose to accept it) is to determine why this is happening. Some out there will attribute this to luck. There is something to be said for that I guess. Cubs and Red Sox fans have spun good yarns about curses and what not. When you consider situations like Don Wilson, J.R. Richard, and Dickie Thon you can buy into an Astros curse if you wish. For me, there’s just too much there to attribute to luck.

Instead of stabbing wildly at pet theories I might have, I’m going to use a scientific approach and evaluate every possible factor I can think of. My gut tells me that there will not be one thing that will be the “Holy Grail” for this issue. However, there could be a combination that could help explain what is happening to this team. We cannot underestimate the importance of this. Imagine adding three wins and taking away three losses every season. This is what we’re talking about here.

Coming up Next

In the second volume of this study, I will look at these team’s records in one run games and Pythagorean records and how they relate to choosing managers. Certainly, there are a lot out there that believe in the ol’ adage that “good teams win the close ones” and that “good managers win the close ones.” We’ll see if that adage holds true.

Scott Barzilla is the author of “Checks and Imbalances” and “The State of Baseball Management”.