Batting orders no longer constructed the way they used to be

For generations, batting-order norms were practically a given: The leadoff hitter is a fast guy who can steal bases. No. 2 is a contact hitter who can play hit-and-run and move runners up. No. 3 is your best overall hitter. The cleanup man is your big power guy.

Joe Maddon has been willing to step outside the norms throughout his time as the Cubs’ manager. The experiment with Kyle Schwarber at leadoff might be suspended, but lineup patterns are evolving as metrics point to different optimal batting orders.

In ‘‘The Book: Playing the Percentages in Baseball,’’ Tom Tango, Mitchell Lichtman and Andrew Dolphin tackle lineup construction. Tango, who created many Fangraphs metrics and served as a Cubs consultant earlier in the Theo Epstein regime, now is the senior database architect of stats. He’ll figure prominently as uses are found for much of the information being generated by Statcast.

By ‘‘The Book,’’ on-base percentage is the primary metric to judge leadoff hitters. If you need to choose between OBP and speed, on-base ability has a much stronger correlation to runs.

National League leadoff men had a .346 OBP last season, second only to the .351 by No. 3 hitters and 24 points better than the overall league average. Had Schwarber produced the .355 OBP he had as a rookie in 2015, he would have been in leadoff range.

The Cubs also would have had the benefit of getting extra plate appearances from him before removing him for defense in the late innings. NL hitters in the leadoff spot got an average of 755 plate appearances last season, compared with 738 for No. 2 hitters and progressively fewer for each spot down in the order.

The No. 2 spot, where Schwarber hit Sunday, has been Kris Bryant’s for most of the season. Neither fits the old image of a No. 2 guy giving himself up by hitting to the right side to move a runner from second to third.

‘‘The Book’’ tells us that No. 2 hitters bat in situations with about the same leverage as No. 3 hitters, only with more plate appearances.

An optimal lineup by the numbers would put the better overall hitter No. 2, as Maddon has done with Bryant. Most managers still go with the better hitter at No. 3. The average No. 3 hitter in the NL last season had an .826 OPS, compared with .756 for the average No. 2 hitter, who also trailed the average No. 4, No. 5 and No. 1 hitters (.791, .785 and .769, respectively).

The No. 4 hitter leads off more innings than anyone but the leadoff man, comes up in the highest-leverage situations and should be the best overall hitter with power.

Anthony Rizzo, if he warms up from his .781 OPS through Sunday to his .913, .899 and .928 levels of the last three seasons, has that desired combination of power and on-base ability.

Maddon’s lineups haven’t been by the old-school book, nor strictly by ‘‘The Book.’’ He has paid attention to the metrics. Are more experiments likely to come? You can make book on it.

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