Fun with Pythagoras

added 5/9/2005 by Scott Barzilla

Columnist note: This is the second part of a six part series on the Pythagorean record. In this edition, we will look at one run games and the selection of managers as it relates to Pythagorean records.

In the opening portion of our study we saw that the Astros have a far inferior Pythagorean record to the other five teams that have also been highly successful over the last ten years. There are a number of theories we will look at to explain this, but the first and most important is the Astros record in one run games. Without even knowing that record, we could surmise that the Astros are inferior in that category.

We must be careful not to let current situations to cloud our judgment. Coming into the Pittsburgh series, the Astros were 3-8 in one run games, so it would be easy to let that fact lead us to believe that the Astros are deficient. However, over a ten year period it is likely that the situation is not that dire.

Besides, we haven’t even discussed the parameters of our discussion. There are a number of different theories surrounding one run games. We will focus on the three most prevalent. The first theory is definitely the most simplistic. Conventional wisdom says, “the good team win the close ones.” That theory simply doesn’t hold water. The best teams dominate their competition. When people think of the 1927 Yankees, 1929 Athletics, 1954 Indians, 1998 Yankees, or 2001 Mariners they don’t think of teams that won in the late innings. They think of teams that dominated their opponents and rightfully so.

This revelation brought forth the classic overcorrection where people thought one run games are pure luck and therefore result in a .500 record over time. This theory is certainly true over a long enough timeline because almost every team will gravitate towards .500 over decades. Yet, we’re not looking at average teams and we’re not looking at a data set of 50 years. We’re looking at the best teams in baseball over the last ten years.

The theory that holds the most water is that teams will tend to see their records in one run games reflect their overall winning percentage over an extended period of time like a decade. Since most teams gravitate towards .500, the second theory will also hold true in that limited application. Therefore, since the Astros have been a good team over that time they should have a good record in one run games.


        Overall W/L    PCT   1-Run Games    PCT
Braves	    977-623   .611       251-205   .550
Red Sox     888-713   .555       208-202   .507
Indians     874-726   .546       223-199   .528
Astros      869-733   .542       224-225   .499
Yankees	    966-632   .604       222-158   .584
Cardinals   856-744   .535       237-241   .496

These numbers are nice, but they don’t necessarily tell us what we want to know. At first glance, it appears that theory holds. The Yankees and Braves had the best overall winning percentages and they had the best winning percentages in one run games. However, we should note that the Yankees record is far superior to the Braves despite the fact that the Braves have a better winning percentage.

Meanwhile, the Astros and Cardinals also fall in line with the bottom two winning percentages in one run games and the bottom two winning percentages. So, the rankings are not as important as whether each team’s winning percentage jives with their winning percentage in one run games. What we are going to do is take the one run records out of their overall records and see how close they come to matching.


              ADJ W-L    PCT    1-Run W-L    PCT    DIF Rating
Yankees       744-474   .611      222-158   .584   .027     96	
Braves        726-418   .635      251-205   .550   .085     87
Indians       651-527   .553      223-199   .528   .025     95
Red Sox       680-511   .571      208-202   .507   .064     88
Astros        645-508   .559      224-225   .499   .060     89	
Cardinals     619-503   .552      237-241   .496   .056     90

These numbers don’t appear to be the Holy Grail in our search for answers, but these numbers are interesting. The Yankees have the best rating and they have been to the most World Series in the last ten years. Perhaps there is a correlation there. The Indians have the second best rating and have been to the playoffs more often than everyone but the Yankees and Braves. Just to review, here is how the numbers break down with their Pythagorean counterparts


                One Run Rating       Pythagorean Rating
New York Yankees            96               +38
Atlanta Braves              87               +25
Cleveland Indians           95               +14
Boston Red Sox              88                +1
Saint Louis Cardinals       90                 0
Houston Astros              89               -23

The Braves throw this theory for a loop, but the rest of the teams fit fairly well. The important thing for us is that the Astros rank fourth in this ranking system. Essentially, it means that their record is eleven percent below what should be expected based on their record. To put this another way, if their record had been equal to what was expected, they would have won an additional 27 games. Interestingly enough, they fell 23 games below their Pythagorean record over the same time span.

Of course, we shouldn’t jump on the one run game bandwagon quite yet. The problem is that the Astros should have finished far below the competition if this were the panacea we are looking for. However, I think we can all be comfortable saying it is a factor. When you consider one run games as a factor it brings the performance of the manager immediately into question.

Evaluating managers is difficult to say the least. Some managers get a bad rap because they manage bad clubs. Others get a lot of credit they really don’t deserve because they’re loaded with talent. Unfortunately, there isn’t a metric like OBP, SLG, ERA, or fielding percentage to get accurate reads on managers. Some teams look for teaching managers, while teams with veteran clubs look for amateur psychologists that can massage egos.

Unfortunately, Pythagorean records are an underused tool in this regard. A manager cannot help talent that much. Most players are who they are once they come to the big leagues. However, a good manager assembles the lineup, handles the pitching staff, and uses his bench in such a way that will get the most out of that talent. Pythagorean records can really help us determine which ones are good and which ones are bad.

Some clubs instinctively know which of these managers can run their clubs efficiently. Some are struggling. It would be foolish for us to look at the total Pythagorean records for those managers because so much of it is wrapped up in what they are currently doing. For instance, Joe Torre, Bobby Cox, and Tony LaRussa have managed their teams for nine years or more. Obviously, much of their ratings will be tied up in the team’s rating. What we will do instead is take a look at the hiring practices of each team by looking at what these manager’s ratings were before they were hired.


           Previous Rating  Managers
Atlanta Braves          +9  Cox
Boston Red Sox         -11  Francona, Little, Williams, Kennedy	
Cleveland Indians        0  Wedge, Hargrove
Houston Astros         -26  Garner, Williams, Dierker, Collins
NY Yankees              -2  Torre
St. Louis Cardinals    +17  La Russa

Neither Eric Wedge or Mike Hargrove had managerial experience before they were hired. The same was also true of Grady Little, Larry Dierker, and Terry Collins. In particular, the Astros are egregious offenders here as they picked up the worst two managers in Pythagorean rating on the list. In fact, Jimy Williams is easily among the bottom five managers in big league history in Pythagorean rating.

Phil Garner isn’t far behind. Of course, no one can fault the Astros for giving Garner an extension after the late season run last year. In fact, if that partial season is included in his rating he will look much better. Yet, this is something the Astros would bear to keep in mind in the future. In most cases (Williams, Garner, Francona, Collins) managers have continued on their projected path when it comes to Pythagorean ratings. So, going out and spending extra money on someone like Tony LaRussa made sense for the Cardinals.

This makes perfect sense. Certain strategies lend themselves to efficiency and certain personalities work well with most baseball players. Instead of looking for people that emulate that success you can spend the extra million or two and go to the horse’s mouth. The Braves and Cardinals certainly can’t complain about the results they got from those experienced at greatness.

Again, we cannot say that managers have everything to do with whether teams overachieve or underachieve. In fact, we cannot say that either success in one run games or good Pythagorean records for managers predict the majority of success. We can say that it does have some predictive value, so the Astros would be wise to thank about our good buddy Pythagoras when they’re hiring their next manager.

Coming up Next

Now that we have looked at one run games and managerial Pythagorean ratings, its time to get down to the nit and gritty. Next, we will look at some offensive numbers that might point towards inefficiency. Included in this discussion, we will look at strikeouts and double plays. Astros fans will certainly recall times when a key strikeout or double play killed a rally. We will see if this really does play into our efficiency troubles. Stay tuned.

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