DECEMBER 11, 2003
Team Outs Efficiency Percentage
By Steve Lombardi, NetShrine.com

Sometimes, you just step in it.

On the morning of December 9, 2003, I began to ponder how to expeditiously measure a team’s cumulative ability to manage Outs.  Specifically, I was thinking about the combined efficiency to avoid making Outs on offense and to collect Outs on defense.

Why?  It is well established through sabermetrics that Outs are the key to success in baseball.  In the field you must gather Outs with efficiency and at the plate you want to avoid making Outs. This is how to win. 

To that end, I embarked on considering Outs per Plate Appearance (O/PA) for batters (as a measure of efficiency in avoiding Outs) and Batters Faced per Innings Pitched times three (BF/IP*3) for pitchers (as a measure of efficiency in garnering Outs).

Clearly, a low O/PA for a team’s offense was good as was a low BF/IP*3 for a team’s defense.  To get an overall rating for a team, I decided to multiply the two results – and the lower the total, the better for the team.  Because Outs are equal – meaning that for every Out made by a batter in a game, some pitcher in the game earns an Out – the multiplication result would be subtracted from “1” in order to calculate the overall efficiency margin above or below “perfect average.” 

I ran these numbers for every major league team in 2003 and the overall result leader list looked much like the overall team standings for 2003.  

On the fly, I chose to call this “Team Outs Efficiency Percentage” (or TOEP, which is pronounced somewhat like the word “taupe”).

Then, I decided to sleep on it.

The next day, I set off on thinking about the administrative ease of such a calculation.  I had a program that could calculate Outs and Batters Faced.  But, what about the person who did not have such a program to run these numbers - what would they have to do?  The next step was to take the formula of (O/PA)*(BF/IP*3) and expand it with the component variables needed to calculate Outs and Batters Faced.

This effort was not making matters more straightforward.  I was looking for a formula that could be considered “quick and dirty” and which could be “done on the back of an envelope.”  Yet, instead, the calculation, while now more user-friendly in terms of inputs, was becoming longer and more complex.

At a crossroads, I stared at the pieces of scrap paper with the sundry formulas scrawled on them - see, I do not only scrawl on scorecards! – and contemplated ditching the whole idea.

Suddenly, like a scene out of the film “A Beautiful Mind” something happened.  No, I did not get a visit from an imaginary roommate or secret service agent.  The formula, in long form, rapidly started appearing very short to me.  I saw common items on the top and bottom – and both sides – that would cancel out, if one were willing to start allowing variables which were “close” to be “close enough” to offset.  I took out my red pen and started to slash.

When I was done, before me I saw:  TOEP = 1 - (((HA+BBA) - HE)/BBE)
 - - where
HA = Hits allowed by pitchers (on defense)
BBA = Walks allowed by pitchers (on defense)
HE = Hits earned by batters (on offense)
BBE - Walks earned by batters (on offense)

This was what I was searching for – simplicity.  Four variables, each easily attainable – in fact, if you wanted to apply it to a game score application (to compare two teams efficiencies) you could do it with a box score – or even just your naked eye (watching the game) and counting hits and walks.  What is not to like about that?

Alas, but first, the short-form of TOEP needed to be tested.  Therefore, I ran it for all major league teams using 2003 season statistics.  The results were much the same as when I first starting playing around with an attempt to determine Team Outs Efficiency Percentage.  Here are the "quick calculation" 2003 TOEPs, best to worst (positive numbers are good, negatives are bad, and zero means dead-average):

0.4932 Mariners
0.4774 Redsox
0.4605 Yankees
0.3174 Braves
0.2949 Twins
0.2719 Phillies
0.2327 Giants
0.2140 A's
0.1939 Astros
0.1862 Cardinals
0.1751 Diamondbacks
0.1580 Whitesox
0.1484 BlueJays
0.0563 Marlins
0.0399 Angels
0.0041 Cubs
-0.0077 Expos
-0.0151 Pirates
-0.1097 Padres
-0.1106 Dodgers
-0.1454 Rockies
-0.2124 Indians
-0.2794 Royals
-0.3565 Brewers
-0.3666 Orioles
-0.4095 Devil Rays
-0.4795 Rangers
-0.5460 Mets
-0.5630 Reds
-0.9436 Tigers

This was a good “sniff test.”  The eventual playoff contenders and teams were at the top and the “everyone knows they are bad” teams were at the bottom.  The rankings in the middle of the pack seemed reasonable based on actual 2003 team performance.

The Mariners were somewhat vexing – being the top team in TOEP (while not winning their division or a wildcard in 2003).  However, digging into them further, it all made sense.  

In 2003, the Mariners were not consistent.  Their 1st half 2003 TOEP was .590.  Their second half 2003 TOEP was .370.  It was self-evident:  they slumped themselves out of contention.  And, we had another use for TOEP – comparison of a team’s overall out efficiency before and after the All-Star break.

Having “sniffed” and “whiffed” before, the prudent thought was to run another “sniff test” with a slightly different approach.  Being a lifelong Yankees fan, I wanted to see the short-form TOEP for every Yankee team and then rank them in order.  I knew which Yankee teams were good and which ones were bad – in my own mind and opinion – and I wanted to see what TOEP thought, in comparison.  Here are the Yankees, all time, year by year, ranked by TOEP:

1927    0.738317757
1998    0.696784074
1939    0.637660485
1904    0.560897436
1942    0.558375635
1931    0.55126498
2002    0.525
1937    0.481741573
1997    0.468934911
1976    0.463829787
2003    0.460526316
1994    0.456603774
1935    0.453642384
1932    0.448366013
1953    0.441221374
1934    0.432857143
1977    0.427767355
1981    0.42455243
1999    0.422005571
1923    0.410958904
1943    0.409309791
1928    0.391459075
1978    0.386138614
1921    0.382608696
1962    0.375
1930    0.368012422
1958    0.366852886
1980    0.359253499
1926    0.356697819
1922    0.351405622
1957    0.347593583
1936    0.341428571
1929    0.332733813
1954    0.329230769
1947    0.327868852
1945    0.323101777
1961    0.320441989
1986    0.31627907
1983    0.307692308
1938    0.303070761
1985    0.301612903
1906    0.296072508
1993    0.282988871
1941    0.280844156
1964    0.280769231
1948    0.277688604
1996    0.275316456
1952    0.274336283
1920    0.272556391
1995    0.2704
1971    0.263339071
1910    0.245689655
1963    0.244239631
1950    0.243440233
1951    0.24212272
1970    0.224489796
1933    0.224285714
1919    0.220207254
2001    0.217726397
2000    0.217115689
1946    0.188197767
1975    0.183127572
1940    0.182380216
1956    0.180487805
1973    0.1799591
1984    0.170411985
1955    0.161449753
1903    0.156626506
1960    0.148975791
1916    0.131782946
1911    0.117647059
1949    0.112482853
1972    0.109979633
1979    0.100196464
1988    0.098639456
1944    0.095602294
1914    0.093587522
1982    0.076271186
1974    0.069902913
1969    0.056637168
1987    0.052980132
1917    0.030241935
1909    -0.00982801
1924    -0.014613779
1966    -0.045360825
1959    -0.04595186
1968    -0.051236749
1915    -0.1
1905    -0.119444444
1992    -0.125
1965    -0.149284254
1913    -0.153558052
1967    -0.184210526
1989    -0.197211155
1912    -0.218142549
1991    -0.264270613
1925    -0.276824034
1918    -0.310626703
1907    -0.638157895
1990    -0.700234192
1908    -0.930555556

This was another good “sniff test.”  The great Yankee teams were at the top and the poorly performing teams were at the bottom (and the other teams fell in the middle, ranked as you would expect them).  

At this junction, feeling groovy, a test more stringent than sniffing was required.  The first thought was to compare the big league teams from 2003 in terms of short-form TOEP ranking versus a ranking by Pythagorean Winning Percentage*.  These were the results:

Rank    TOEP                   Pythagorean    Rank    Diff P%-TOEP

1       0.493174061    M's     0.611111111    1       0
2       0.477419355    Redsox  0.586419753    6       4
3       0.460526316    Yankees 0.598765432    3       0
4       0.317431193    Braves  0.598765432    2       -2
5       0.294921875    Twins   0.524691358    15      10
6       0.271889401    Phils   0.561728395    8       2
7       0.232715008    Giants  0.583850932    7       0
8       0.214028777    A's     0.586419753    4       -4
9       0.193895871    Astros  0.586419753    5       -4
10      0.186206897    Cards   0.549382716    9       -1
11      0.175141243    Dbacks  0.524691358    14      3
12      0.157996146    W-sox   0.549382716    10      -2
13      0.148351648    BJays   0.537037037    12      -1
14      0.05631068     Marlins 0.543209877    11      -3
15      0.039915966    Angels  0.49382716     17      2
16      0.004065041    Cubs    0.530864198    13      -3
17      -0.007662835   Expos   0.49382716     18      1
18      -0.015122873   Pirates 0.469135802    21      3
19      -0.109734513   Padres  0.401234568    28      9
20      -0.110565111   Dodgers 0.518518519    16      -4
21      -0.1453958     Rockies
0.475308642    20      -1
22      -0.212446352   Indians 0.444444444    23      1
23      -0.279411765   Royals  0.481481481    19      -4
24      -0.356489945   Brewers 0.401234568    27      3
25      -0.366589327   Orioles 0.450617284    22      -3
26      -0.40952381    D'Rays  0.413580247    26      0
27      -0.479508197   Rangers 0.419753086    25      -2
28      -0.54601227    Mets    0.422360248    24      -4
29      -0.562977099   Reds    0.382716049    29      0
30      -0.943566591   Tigers  0.290123457    30      0

For the most part, the rankings by short-form TOEP and by Pythagorean Winning Percentage are very close – within one or four slots of each other.  Not close enough for some perhaps; but, “ballpark” enough for me - again, remember, TOEP is meant to be a quick and dirty tool. 

The Twins and Padres were the exception in this comparison test.  For them, there is a larger gap in the rankings by TOEP and Pythagorean.  What happened?  Minnesota was 23rd in MLB in 2003 in OPS w/RISP**.  San Diego was 28th.  While both were about average in avoiding Outs on offense in 2003, neither did a very good job in capitalizing on their opportunities.  Without the runs, it would impact their Pythagorean ranking.  Perhaps this was the difference?  With TOEP, it only looks at efficiency in avoiding and getting Outs - - not actually scoring - - meaning only getting into good position to score or prevent scoring.  

In any event, being nearly in synch (short-form TOEP and full-blown Pythagorean) 93% of the time is not too shabby - using the quick and dirty yardstick.

That said, here the natural sidebar thought might be  - "So, which is better to use: Pythagorean Winning Percentage or Team Outs Efficiency Percentage?"  Actually, it should not be a head to head contest.  If you have a spreadsheet to do all the “heavy lifting” for you, then perhaps Pythagorean Winning Percentage is the way to go to determine team performance.  If you desire to determine a performance rating quickly, doing the math in your head for the most part, and jotting results on paper, then short-form TOEP could be seen as an easier approach than Pythagorean.  Again, as long as you are comfortable with a “ballpark” type approximate.

Before taking the initiative to document the TOEP evolutionary process and test findings here, for purposes of a peer review, the concept was shared (for one day) with the members of the NetShrine Discussion Forum.

The principal issue that most had with the notion of TOEP was the formula:

TOEP = 1 - (((HA+BBA) - HE)/BBE)
 - - where
HA = Hits allowed by pitchers (on defense)
BBA = Walks allowed by pitchers (on defense)
HE = Hits earned by batters (on offense)
BBE - Walks earned by batters (on offense)

Subtracting batter’s hits from teammates pitching results?  Having a mix of offense and pitching in the numerator but only offense in the denominator?  This makes no sense.  

One person called it “anti-intuitive” and another concluded that “the metric seems totally arbitrary.”

It is very troublesome to argue with this feedback - as, frankly, I feel the same way about the formula.  Nonetheless, if I do not focus on the short-form TOEP formula, only use it, and look at the results, I have an equally difficult time not respecting the outcome.  Perhaps the motto of short-form TOEP should be "Don't measure me by my methods; but, rather by my results"?  Further, TOEP is useful as it is era independent – since the offense and pitching used in the formula happened in the same season.

In summary, the goal of Team Outs Efficiency Percentage (TOEP) should be stressed:  To serve as a “quick and dirty” tool which could be “done on the back of an envelope” to determine overall efficiency of a baseball team.

Therefore, for that goal,

TOEP = 1 - (((HA+BBA) - HE)/BBE)
 - - where
HA = Hits allowed by pitchers (on defense)
BBA = Walks allowed by pitchers (on defense)
HE = Hits earned by batters (on offense)
BBE - Walks earned by batters (on offense)

is a success.

I have run the above TOEP calculation for a number of teams (like the aforementioned Yankees study).  Every time, the great teams were at the top and the poorly performing teams were at the bottom (and the other teams fell in the middle, ranked as you would expect them).  

Take the “TOEP Challenge.”  With apologies to Tiny Tim (as much as he should probably be apologizing to us!):  Come, tip TOEP, through the 'tistics with me.  Try it for yourself.  Run the numbers.  Compare teams in a season.  Compare seasons of a franchise.  Compare 1st half season results and 2nd half season results of teams who collapsed or rose in the standings in a given year.  See the results.  

Test the short-form TOEP outcome like you would a wine in a tasting contest.  Look at them.  Smell them.  Feel the texture.  The results may not register like an aged imported rarity wine.  All the same, do you truly need that class of vintage every time to enjoy your wine experience?  On occasion, does not something closer to pedestrian suffice when you do not have the means or time to go "all out"?

Four variables, each easily attainable.  Sometimes, you just really step in it.

POSTSCRIPT - DECEMBER 17, 2003:  To further "test" TOEP subsequent to the publishing of this feature, TOEP was calculated for every active MLB team - for every one of their seasons.  In total, this was 2,199 seasons.  

Various forms of analysis was applied to the data produced in relation to actual team results (both in Won-Loss records and run creation and prevention compared to league averages).  This larger and more comprehensive testing effort established that TOEP was inconsistent (on the larger scale of results) in terms of achieving its goal of determining overall efficiency of a baseball team.  

Therefore, in the words of Emily Litella..................."never mind."  Sometimes, when you step in something, all that really happens is that you now need to scrape it off the bottom of your shoe.  It appears this was one of those times.  On the plus side, I now have a spreadsheet with a whole heap of mammoth data on it.  Time to go play with the data.........brace for impact.......  :-)


* Pythagorean Winning Percentage, developed by Bill James, is the predicted winning percentage based on runs and runs allowed. The formula is as follows:  Runs^2/(Runs^2+Runs Allowed^2)

Here is the calculation for the 1999 Yankees. The Yankees scored 900 runs and allowed 731 runs:  900^2/(900^2+731^2)=.603

Thus, the Yankees would be predicted to have a .603 winning percentage. In actuality, the Yankees had a .605 winning percentage. A more precise calculation uses a factor of 1.83, but a factor of two works almost as well. From Pythagorean winning percentage it is possible to figure Pythagorean wins (PW) and Pythagorean losses (PL).

** OPS w/RISP** is “On Base Average plus Slugging Percentage with Runners in Scoring position.”

Steve Lombardi is the Creator & Curator of NetShrine.com.  Scrawling On The Scorecard appears regularly during the baseball season and sporadically during the off-season.  Steve can be contacted at sots@netshrine.com

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