best baseball team
With the Yankees flirting with a record-breaking pace this year, the idea is being bandied about that this team might be the best team in baseball history. People are comparing them with the 1927 and 1961 Yankees, or the 1906 Cubs (the usual suspects) in categories like winning percentage, run differential, et cetera. (How come we're not hearing more voices in defense of the 1880 Chicago White Stockings and their amazing .798 winning percentage? Or the St. Louis Maroons, the scourge of the Union Association with their .832 winning percentage in 1884? Ah. You say the 19th century doesn't count? Well, so's your old man.)
Some people (not many, thank goodness) enter this discussion with the unstated assumption that competitive balance has remained constant throughout baseball history, and that therefore it is just as difficult to post a .700 winning percentage in 1927 as it is in 1998. Most people (and certainly most statheads) regard this as hogwash. It is generally known that "competitive balance", no matter how you choose to measure it, has been constantly on the increase since the start of professional play, or at least was on the constant increase until about 1991. It has slacked off a little bit since; it is thought that by 1991, competetive balance had (with apologies to Oscar Hammerstein) gone about as fur as it could go. Nevertheless, it's still thought to be pretty high nowadays.
In practical terms, what this means is that it's tougher for a good team to win ballgames, because the opposition has gotten better. Baseball teams, as a whole, have only gotten better and better in the last 125 years.
Does this mean that all of the best teams in baseball history are teams of recent vintage? Not necessarily. While the good teams are, in a general sense, getting better, I believe that there is some sort of upper limit on how good a team can be, and that any era is just as likely as any other to produce such an extraordinary team. Keep in mind: while an extraordinary team of the 1880's might post a winning percentage of about .800, a similarly extraordinary team of the 1990's would have a record of, say, .670. The great teams are just as good, but these days the bad teams are catching up to them.
Of course, since the aggregate winning percentage of any league is always .500 (or at least was until interleague play started), it's tricker to measure the quality of a league. The usual method involves some sort of application of standard deviations; my article here uses these as well.
Okay. Down to brass tacks.
Determination of the Method
A) Defining Quality
The problem I set to myself was to determine the best team in baseball history, while taking competetive balance into account. The only data I woud allow would be the wins and losses of each team in a given league-season. This defines "quality" purely in terms of wins and losses, which makes a certain amount of sense. Runs scored, runs allowed, team batting average, and all of those other stats are secondary to, and supportive of, Wins and Losses.
The question then becomes: given only wins and losses as your raw data, how do you measure the quality of a team? I wanted to use a method which would produce a number which was an accurate rendering of the relative quality of a team. How can I find this?
For the answer to that question, I turned (of course) to Bill James. Specifically, I turned to his article "Pythagoras and the Logarithms", which occupies pp. 104-110 of the 1981 Baseball Abstract. (Yes, it's his last self-published one.) I'll quote extensively from it here:
This story starts with an off-hand remark I made in the Baseball Abstract three years ago, which was that we can calculate that a .400 team should beat a .600 team about 30% of the time--and, in fact, .400 teams do beat .600 teams about 30% of the time. Well, wrote Dallas Adams, how do you calculate this? Damn, I did forget that part, didn't I? That calculation comes from a method I developed about five years ago but which has, somehow, never found its way into print before. I call it the log5 system since it is, essentially, a logarithmic system which is based upon a weighted comparison of each team to a .500 team. How often should a .600 team beat a .500 team? Obviously, a .600 team should win 60% of the time, since its overall .600 WL% is compiled against a league which is, overall, .500. The log5 of the .600 team, then, is that number which, if added to .500 and divided by the sum, produces .600.
X / (X+.5) = .600 X = .750
And so the log5 of a .600 team is .750. In essence, I am assigning a "talent weight" of .750 to a .600 team by asking the question, "How much talent does it take to beat a .500 team--a team with 500 units of talent--60% of the time?" Answer: 750 units of talent.
In the same way, the log5 of a .400 team is discerned to be .333. If you put the two together, then, how often will the .600 team beat the .400 team?
.750 / (.750 + .333) = .692
And the .600 team should win about 69.2% of the time.
The balance of that article is devoted to some more of the theoretical underpinnings of this system, some emprical confirmation from Dallas Adams and Pete Palmer, and some analogues to the Pythagorean method of determining WL% from R/OR ratio.
One thing which James never got around to doing in his article was simplifying the math to determine the log5 of any one team. His defining equation is excellent for determining winning percentage from log5; of course, usually we'd want to do it the other way around. Surprisingly, determining log5 from Wins and Losses reduces to a very simple equation:
log5 = W/2L Neat, huh?
The log5 system is just what I was looking for here, since it quanitifies relative value. Returning to James' example: in a relative sense, a .600 team is more than twice as good as a .400 team. This is demonstrated by the fact that, in head-to-head competition, the .600 team wins more than twice as often as the .400 team. So I settled on log5 as the numerical measurement of a team's quality.
B) Defining Competitiveness
In general, my hypothetical candidate for the Best Team Ever would fulfill three qualifications:
They would win a whole bunch of ballgames. (That's obvious.)
No other team in the league would win nearly as many ballgames. (This would indicate that it's not that easy to win a bunch of ballgames, since only one team was able to do so.)
No other team in the league would lose that many ballgames, either. (This would show that there weren't any patsies in the league that our Best Team Ever could beat up on; every win was, on some level, against a quality opponent.) By qualification 1), a team would have a large number of wins, a high winning percentage, and thus a high log5. Qualifications 2) and 3), to show a competitive league, would group all of the rest of the teams as close to .500 as possible. Here's where standard deviation comes into play. A competitive league would have a low standard deviation of whatever measure of quality you use (wins, WL%, log5, whatever), while a noncompetitive league, filled with teams both great and terrible (the 1962 National League comes to mind) would have a high standard deviation of these measures.
So, the method could be: divide the log5 of a team by the standard deviation of the log5s for all of the league's teams. Let me clarify that with some parentheses:
divide (the log5 of a team) by (the standard deviation of (the log5s for all of the league's teams)) Ideally, I should give the resulting number a name and an abbreviation. Very well. The resulting number is now called the team's Competitive Quality Comparison Quotient. This abbreviates to CQCQ, which can be pronounced "cuckoo".
One problem, though: a really good team will throw off the standard deviation for the league, and really good teams are what we're looking for here. So, we eliminate the team we're looking at from consideration when computing the standard deviation. The addition of one more word in our defining equation should do the trick:
CQCQ = (the log5 of a team) divided by (the standard deviation of (the log5s for all of the league's *other* teams)) Okay. There's the method. The higher a team's CQCQ is, the better it showed the ability to win in a competitive league.
So let's get back to the original question. When factoring in the competitiveness of a league, what were the best teams in the history of major league baseball?
When looking at this question, I only considered first-place teams. Once divisional play came in, I only considered the teams with the best Won-Loss percentage in the league. Also, I only considered leagues where every franchise played the entire season. (The last "ineligible" major league was the 1891 American Association.)
I did not take unbalanced scheduling into account. In an ideal world, there would be slight (and I do mean slight) modifications for the 1969-92 National League results and the 1969-76 American league results. Because of interleague play, slight adjustments for 1997 might also be called for. (However, I went for simplicity in this study, so those adjustments will probably have to wait until my next period of unemployment, when I have the time to figure those sorts of things out.)
For all of the qualifying leagues, I figured the CQCQ for the first-place team. Then I ranked them in order, and the top team came out the winner. All in all, 229 league-seasons were considered, so there were 229 teams ranked in this order. Average CQCQ(first place teams, by epoch) pre-1901: 5.70 1901-1919: 6.00 1920-1945: 6.14 1946-1960: 6.19 1961-1976: 6.89 1977-1997: 7.04
To get a sense of comparison: the average CQCQ of a first-place team over all of major-league history was 6.33. In the chart on the right, you will see the average CQCQ of first place teams in baseball history. This is consistent with the assumption that, with competitive balance increasing over time, the best teams have generally been getting better. Not by an extraordinary amount, though.
So, a typical first-place team has a CQCQ in the 5-7 range. An especially strong first-place team would be in the 8-9 range. Having a CQCQ over 10 is a tremendous achievement: only twelve teams have done this in major league history. I'll enumerate them at the end of this article.
Conversely, a first-place team with a CQCQ of under 5 isn't really that strong. Not that they're bad teams, mind you; just that they were lucky to have a not especially competitive league to play in. In a "normal" league, they probably would not have won. The most recent first-place team to have a CQCQ below 5 was the 1977 Royals, with a CQCQ of 4.58. Despite their 102-60 record, this isn't really surprising: three other teams in that league (the Yankees, Orioles and Red Sox) had 97 or more wins, suggesting that winning about 100 games wasn't all that difficult to do. And with three sub-.400 teams in that league (the expansion Mariners and Blue Jays and the free agency-decimated A's) one can see who these teams were beating up on. 1886 National League(final win-loss standings) Team W L Pct GB CHI 90 34 .726 -- DET 87 36 .707 2.5 NY 75 44 .630 12.5 PHI 71 43 .623 14 BOS 56 61 .479 30.5 STL 43 79 .352 46 KC 30 91 .248 58.5 WAS 28 92 .233 60
By this method, the least impressive first-place team in history was the 1886 Chicago White Stockings (or Colts). Their 90-34 record (.726 winning percentage) looks impressive, but the Detroit Wolverines were hot on their heels at 87-36. The 1886 National League is breathtaking for its lack of competitive balance, as you can see from the final standings.
In some leagues these days, every single team is between .400 and .600; in the 1886 National league, only one team (out of eight) was in that range. Gosh. With two sub-.300 teams to play regularly, and another sub-.400 team, .726 isn't that impressive a percentage for a first-place team.
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