The Royals are off to a flying start and I was wondering if we could use PI to figure out where it ranks in their history.
To figure this out you need to use the Pitching Game finder (not the Team Pitching game finder), set pitcher decision to "win" and sort by "teams w/ players in year". If you limit it to Kansas City Royals and in the teams first 13 games, this is what you get.

Here are the Royals teams since 1956 that have won at least 8 their first 13 games.

 KCR 1978    11 Ind. Games
 KCR 2003    11 Ind. Games
 KCR 1975     9 Ind. Games
 KCR 1973     9 Ind. Games
 KCR 2000     8 Ind. Games
 KCR 1977     8 Ind. Games
 KCR 1983     8 Ind. Games
 KCR 1989     8 Ind. Games
 KCR 2008     8 Ind. Games

As you would expect there are a lot of teams from the George Brett era, but some surprising ones as well.
The two teams from the last decade, were the only two seasons in that time span that the Royals won more than 70 games.

Among these teams, the 1977 edition was the best, finishing with 102 wins.

Two teams, 2000 (77-85) and 1983 (79-83) finished with losing records, despite their hot starts.

4 out of the 8 teams finished with 88-92 wins.

While 13 games is not a lot of games to make an assessment on, it does seem to at least indicate that the Royals won't have a miserable season. Maybe they're even in for an enjoyable one.

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