And then there were two. Pitchers John Lackey of St. Louis and Andrew Miller of Baltimore are the last ones standing of all of the players traded to playoff contenders on July 31, the last day players could be traded without having gone through waivers. They are the only ones remaining in the playoffs.

There is one other player who was traded that day who is still in the playoffs, but what a circuitous route Kelly Johnson took to get there.

Johnson, a journeyman utility infielder-outfielder, signed with the New York Yankees as a free agent last December. He played for them for the first four months of the season before they traded him to Boston for Stephen Drew July 31.

A month later, after he played 10 games for the Red Sox, they traded Johnson to …

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The website of the independent Atlantic League invites viewers to contribute to an ongoing, seemingly irresolvable baseball problem. “Do you have a suggestion?” the site asks. “Share it with us here.”

The problem the league seeks to solve is the length of games. Call it time of game, call it pace of games. Officials and fans think games are too long and want Major League Baseball to implement steps to shorten them.

This season’s 2,430 games, according to the commissioner’s office, averaged 3 hours and 2 minutes, the first time a season average reached 3 hours and the fourth consecutive year the average rose. That’s not the direction anyone wanted to go.

However, with a simple calculation from Bob Waterman of Elias Sports Bureau I can shave about 10 minutes off the average time of game, and pitchers can shorten games even more by working more efficiently, meaning throwing more strikes and fewer pitches …

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In the five-year period 1976-80, the Kansas City Royals and the New York Yankees played each other four times in the American League Championship Series. The Yankees won their first three encounters, and Kansas City fans became irritated at the one-sided outcome. They also grew annoyed and restless that they were being outperformed by their Yankee Stadium counterparts.

While Royals Stadium fans were quiet and respectable, Yankees fans were clamorous and often obnoxious. By the fourth meeting between the teams, in 1980, the Kansas City faithful were determined at least to match the rowdy New Yorkers.

Their effort was admirable but not quite successful. The behavior didn’t come as naturally as it did to Yankees fans. It was forced.

I recall that Kansas City scene because of the Royals’ …

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