Reshuffling the deck

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How to rate a team's three best starters? We can simply add up their Win Shares and divide by three, giving us the average. But aren't we looking for a balance? Let's say you've got two teams with the following Win Shares distribution:

        SP1  SP2  SP3


Team A   20   20   20


Team B   40   10   10

Add them up, and you get 60 Win Shares for each Big Three, though the trios obviously are completely different. In the interest of balance, and taking a page from one of Bill James' (old) notebooks, we can figure a Big Three Score for every team by the following formula (according to Excel notation):

SQRT((3*(S1WS*S2WS*S3WS))/(S1WS+S2WS+S2WS))

Using this method, Team A scores at 20, but Team B at just 14. I know it looks complicated, and I suppose it's probably more complicated than it needs to be (in case you haven't noticed, baseball columnists aren't exactly graded on their math skills). Anyway, "SQRT" is simply square root, and "S1WS" equals the Win Shares for the team's No. 1 – best, for our purposes – starting pitcher.

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