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Demonstração:

CREATE TABLE clans(id INT, name VARCHAR(100), warswon INT, warslost INT);

INSERT INTO clans VALUES (1, 'aaa',  208, 6), (2, 'bbb', 103, 0);

SELECT id, name,warswon, warslost,((warswon + 1.9208) / (warswon + warslost) - 
                 1.96 * SQRT((warswon * warslost) / (warswon + warslost) + 0.9604) / 
                          (warswon + warslost)) / (1 + 3.8416 / (warswon + warslost)) 
       AS ci_lower_bound 
FROM clans 
ORDER BY ci_lower_bound DESC;

SqlFiddleDemo

Resultado:

╔═════╦═══════╦══════════╦═══════════╦════════════════════╗
║ id  ║ name  ║ warswon  ║ warslost  ║   ci_lower_bound   ║
╠═════╬═══════╬══════════╬═══════════╬════════════════════╣
║  2  ║ bbb   ║     103  ║        0  ║ 0.9640439675800224 ║
║  1  ║ aaa   ║     208  ║        6  ║ 0.9401908847803808 ║
╚═════╩═══════╩══════════╩═══════════╩════════════════════╝