Sports Quiz / World Series Equations

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Can you name the World Series team nicknames based on the pattern of WS appearances since WW II shown in the formula below?

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The formula is a string of consecutive World Series years since 1946. Each letter in the formula represents a team from the league listed. For example, the first formula is National League and Team A played in the WS in years 1, 2 and 16. Team B played in year 3. Team C played in year 4. The same Team can be in different quizzes and please type the team nickname.
Score 0/55 Timer 15:00
(NL)-A+A+B+B+C+D+B+ E+D+F+E+G+E+B+H+A
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(NL)-A+B+A+C+ D+D+E+A+E+A+E
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(NL)-A+B+C+D+B+B+ D+B+B+A+A+B
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(NL)-A+A+B+A+A+C+ D+A+E+F+G+C
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(NL)-A+B+C+D+E+D+D+ E+E+F+B+A+B
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(AL)-A+B+B+B+ A+C+C+D+E+D
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(AL)-A+B+C+B+B+ B+B+B+C+B
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(AL)-A+B+C+D+B+E+ A+F+F+D+B+G+G
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(AL)-A+B+C+A+A+A+ D+D+D+B+E+E+E+A
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(AL)-A+A+A+B+C+ A+D+B+E+C
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