Fun with Pythagoras

added 5/17/2005 by Scott Barzilla

Columnist note: This is the third part of a six part series on the Pythagorean theory. In this edition we will see how the teams fare in terms of offensive efficiency. Then, we will look at some of the individual numbers that play into offensive efficiency.

When people think of offensive efficiency they usually get a puzzled look on their face. It really isn’t that difficult. If you are an efficient offensive team you find a way to get runners home on a consistent basis. Recent Astros history tells us enough to know that this is one of our weak points. Of course, this is where perspective comes in. Even if you have MLB Extra Innings most people cannot go into this discussion with an unbiased view.

All Astros fans have cursed, chain smoked, and paced in their living rooms when the Astros strand a runner on third with less than two outs or leave the bases loaded with no one out. Still, when our pitchers keep the opponents from scoring under the same circumstances it is universally considered a great performance by our pitcher instead of a choke on the part of the other team. This is the way a fan’s mind works. It always has been that way and it always will be that way.

Perhaps this fact is exacerbated for older Astros fans. Anyone older than twenty can remember a time before home runs flew out of the park on a nightly basis. So, fans in that situation have the added bias of remembering the past when the Astros had to scratch and claw for every run they got. That bias usually results in statements like “players today don’t know to hit with two strikes, bunt, or hit with runners on base.” In other words, this is the proliferation of the “back in my day….” thinking.

Yet, this thinking is not entirely accurate. Yes, no one can deny that strikeouts are up overall versus twenty, forty, or eighty years ago, but that is more to do with style than deficiencies of the modern ballplayer. If you look at slugging teams like the 1961 Yankees or the great Athletics teams of the 1970s you will see many of the same issues as the Astros. When you look at this era, you see almost every team playing this type of baseball. Why do they do it? Simply put, it is superior offensive baseball. Don’t believe me? Take a quick look at the runs scored over the last several years.

So, we must make a clear distinction between offensive production and offensive efficiency. I will take this period of offensive production over any period in Astros history. The Astros produce runs at a much better clip than any other era in their history. Yes, part of it is the move from the Astrodome to Minute Maid Park, but even before the move this team was out producing their ancestors by leaps and bounds.

Furthermore, the other five teams in our study play the same kind of game. The successful teams have to play that style. Yes, some teams hit more home runs than others. The 1998 Yankees did not have any player with more than 28 home runs, but they led the league in scoring because they led the league in on base percentage and everyone in the lineup could hit the long ball. Teams that hit more home runs also strike out more often. When you strike out more often you become a little less efficient. So, it should not shock us that all of these teams are somewhat inefficient. The question facing us is whether this inefficiency contributes to a bad Pythagorean rating. In other words, are the Astros less efficient than the other teams with better Pythagorean ratings?

In order to do this, we will take a look a statistic called runs created. Essentially, runs created is a statistic that compiles everything a hitter does (hits, walks, total bases, stolen bases, caught stealing, GIDP, plate appearances) to provide us with an expected number of runs the team should have scored in a season. Runs created does not use strikeouts because they are equal to an out in the eyes of the metric. They also don’t take into account the timely nature of when these events occur. Theoretically, an efficient offense should score as many runs as it creates. The further away your rate is away from 100 the less efficient your offense is.


                     Runs         RC        Dif       Rate
Atlanta Braves       7832       8197       -365       95.6
Boston Red Sox       8619       9044       -425       95.3
Cleveland Indians    8662       8984       -322       96.4
Houston Astros       8116       8505       -389       95.4
NY Yankees           8722       8906       -184       97.9 
St. Louis Cardinals  7849       8254       -405       95.1

So, our suspicions were correct. As we stated earlier, the Yankees have not relied on the long ball nearly as much as the other clubs and it shows. The Cards have used it almost as much as anyone and it shows. In order to test this theory we need to compare the rates with the Pythagorean ratings.


        Pyth. Rating  Off. Rating
Yankees          +38         97.9
Braves           +25         95.6
Indians          +14         96.4
Red Sox           +1         95.3
Cardinals          0         95.1
Astros           -23         95.4

We could certainly do tests of statistical significance on this, but just by eyeballing it we can see there is a slight correlation between these numbers. The top three in Pythagorean rating are also in the top three in offensive efficiency. The bottom three are all in the bottom three. If it were a great correlation the ratings would be in the exact same order, but there is some shuffling there.

As for the Astros, they find themselves in the middle of the pack. They are one full percentage point out of second place (they wound up in fourth), but they are three tenths of a percent out of last. The important thing is not that they are only fourth, but that this is the third major study we have done (managerial Pythagorean rating and one run games were the others) and they have ranked in the bottom half in all of the categories. As for the percentage point, that equals 85 runs over the course of ten years or almost nine runs a season. Think back to some of those one run games over the years and see where eight or nine runs more in a season would have gotten them. It’s staggering to think about how small the difference is between mediocre and very good.

When we think about rallies they fizzle we think of a hitter striking out with a runner on third or ground into a double play with the bases loaded and one out. I still remember shrugging my shoulders on more than one occasion in the Dome when they would blare the sound effects after someone had grounded into a double play with no one out. Yes, a runner scored, but should we really be celebrating that play?

Since we are comparing National League and American League teams we will focus on their rating (percentage above or below the league average) in strikeouts and GIDP than the actual total. After all, things could be worse: we could be an American League fan. The amount of double plays those teams ground into are staggering. Either way, we get to see if our frustration is well-founded.


            SO/9    Rating     GIDP     Rating    Rating2
Braves      6.44      96.2      127      105.8      202.0
Red Sox     6.36     101.8      134      103.9      205.7	    
Indians     6.19      99.0      138      107.0      206.0
Astros      6.73     101.0      129      107.5      208.5
Yankees     6.21      99.4      142      110.1      209.5
Cardinals   6.79     101.4      121      100.8      202.8

Again, we need to compare these numbers with the Pythagorean ratings to see how well they match up. Ironically, the Yankees have the highest percentage of double plays and compounded percentage. Yet, the Astros show why they are where they are with their performance in both categories. Let’s see how the rest fare in comparison with their Pythagorean ratings.


       Pyth. Rating     K Rating   GIDP Rating  Comp. Rating         
Yankees         +38         99.4         110.1         209.5	
Braves          +25         96.2         105.8         202.0
Indians         +14         99.0         107.0         206.0
Red Sox          +1        101.8         103.9         205.7
Cardinals         0        101.4         100.8         202.8
Astros          -23        101.0         107.5         208.5

Here we see some split results. The strikeouts have a slight correlation while the double plays really don’t have much of an impact. I think this is pretty easy to explain. Strikeouts occur with regularity while double plays are a rarer occurrence. Also, strikeouts can occur anytime, but in the immortal words of Bill Worrell, “the Astros always seem to ground into double plays with men on base.” Sometimes announcers can come up with some real doozies.

The compound rating is not necessarily a perfect metric, but it does go to show how well each team does when we combine the categories. The Yankees poor rating in double plays skews the compound rating, but it otherwise intends to demonstrate the cumulative effect of being sub-par in both categories as the Astros are. So yes, the Astros are more inefficient than the average bear, but they weakness in this area is not as blatant as we might think. Again, it is more about the slightest difference making some teams great and others mediocre.

Even though our findings cannot reflect this, this one of the most important areas a manager can control. In many instances, it is when the strikeouts occur that make the biggest difference in the world. For instance, you wouldn’t want a leadoff hitter to strikeout 200 times, but if he had a .350 OBP or higher he would be effective. A run producer with the same number of Ks can hinder the club more because his Ks occur with runners on base more often.

If you were to design the perfect lineup, you would want every hitter to be patient and every hitter to make contact consistently. That simply doesn’t happen. Ironically, patient hitters also seem to strike out more often. This makes sense when you consider that patient hitters work the counts to the point where they will have more two strike counts than a lot of free swingers (there are obvious exceptions). Ideally, you would want your patient hitters on top and your free swingers/low strikeout guys in the middle. Sometimes, the best laid plans cannot be carried out.

A letter writer wrote into the Chronicle and said Lance Berkman should lead off. He is a high strikeout guy and high walk guy, so that part makes perfect sense. However, you aren’t going to take someone that can put up a .600 slugging percentage and put him in the leadoff spot. Still, there are some guys you can move up and down based on these principles. The most classic switch would be Morgan Ensberg and Craig Biggio between the two and five hole. Both hitters perfectly embody the spots they need to be moved to all the way down to Biggio’s higher slugging percentage. The thought has either not occurred to Phil Garner or he is not willing to upset either player.

The great managers get the most out of their lineups by doing these things. They also employ the running game where it helps eliminate double plays and increase the offensive efficiency everyone is looking for. In terms of offensive production, lineups usually don’t have nearly as pronounced an effect as people might believe, but in terms of efficiency every little bit helps.

Coming Up Next

We are officially at the halfway point of our study. Next time, we will continue to the mound to see how bullpen performance effects the Pythagorean rating. Many believe that bullpen performance has a profound effect on one run games. We will test this theory next time.

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