Start the closer so that he pitches to the top of the order, increasing the effectiveness of the "starter".

Rickey Henderson batted leadoff in 98% of his PA. He was elected to the Hall of Fame in 2009. (Voted by BBWAA on 511/539 ballots)

Plate Appearances (PA): Batting first/Total:

13,122/13,346 = 98.3%

Data from: https://www.baseball-reference.com/players/split.fcgi?id=henderi01&year=Career&t=b

Rickey Henderson may have had a higher percentage of PA in one of the nine Batting Order Positions (BOP) than any non pitcher with a lot of PA.

Hall of Fame closers faced bottom of order more: Rivera, Hoffman, Smith. Friday, February 1, 2019

Since 2006 I have maintained that Mariano Rivera would likely have contributed at least as much to his Yankee teams by pitching the first inning in every other game. In other words, about 80 innings in 80 appearances.

1. Rivera would pitch on regular rest. He pitched 80 innings only once as a closer. In his first full season of 1996 Rivera pitched 107 innings as the set up man for closer John Wetteland, who led the AL with 43 Saves in 63 innings.

2. Rivera might be able to pitch into the second inning if he threw few pitches in the first inning.

3. Rivera would always be pitching to the top of the order, not starting with a random selection of 1 through 9 of the batting order.

It turns out that as a closer Rivera pitched to the bottom of the batting order more than to the top. So did other Hall of Fame closers.

PA	PA	PA		BOP	BOP	BOP		PA%	PA%	PA%		%dif	%dif	%dif
Rivera	Hoffman	Smith		Rivera	Hoffman	Smith		Rivera	Hoffman	Smith		Rivera	Hoffman	Smith
624	512	642		8	8	7		12.23%	11.67%	11.92%		10.05%	5.01%	7.24%
617	509	631		7	6	6		12.09%	11.60%	11.71%		8.82%	4.40%	5.40%
612	506	630		6	7	8		11.99%	11.53%	11.69%		7.94%	3.78%	5.23%
580	501	617		5	9	9		11.37%	11.42%	11.45%		2.29%	2.76%	3.06%
571	487	599		9	4	5		11.19%	11.10%	11.12%		0.71%	-0.11%	0.06%
540	484	583		1	5	1		10.58%	11.03%	10.82%		-4.76%	-0.73%	-2.62%
536	467	570		4	1	4		10.50%	10.64%	10.58%		-5.47%	-4.22%	-4.79%
517	466	563		2	2	2		10.13%	10.62%	10.45%		-8.82%	-4.42%	-5.96%
506	456	553		3	3	3		9.92%	10.39%	10.26%		-10.76%	-6.47%	-7.63%
5,103	4,388	5,388	tot	45	45	45	ave	11.11%	11.11%	11.11%

Plate Appearances (PA) are sorted for each of the 9 Batting Order Positions (BOP). Then the BOP is shown. All three closers show BOP that is skewed to facing the bottom of the order more than the top. The PA sample sizes are in the thousands.

All three closers faced the number 3 batter the least. Number 3 is almost always one of the two best hitters in a lineup.

Nine BOP average about 11% per BOP. The percentage and percent differences are shown. Rivera has the biggest extremes between the batters he faced most and least often: 8 and 3.
_____________________________

Rickey Henderson batted 23 more times in BOP 1 than games, presumably because his team batted around and Henderson batted again and/or Henderson batted in BOP 1 as a substitute.

	PA	PA
Henderson	BOP 1	Total	BOP 1%
	13,122	13,346	98.32%
Leading off	2,886	13,346	21.62%

Split	G	PA	PA%
1st inning	2,886	2,909	21.80%
2nd inning	749	737	5.52%
3rd inning	2,033	2,038	15.27%
4th inning	907	901	6.75%
5th inning	1,612	1,612	12.08%
6th inning	1,256	1,250	9.37%
7th inning	1,421	1,421	10.65%
8th inning	1,286	1,282	9.61%
9th inning	940	934	7.00%
Ext inning	189	262	1.96%
Innings 1-3	2,892	5,684	42.59%
Innings 4-6	2,871	3,763	28.20%
Innings 7-9	2,742	3,637	27.25%

Part of the the low number of PA in the 9th inning would be because of games when his team was leading at home and did not bat at all in the 9th. Graph of Henderson PA% of Innings 1 through 9:

Rickey Henderson batted in the first inning in almost 22% of his PA but only 5.5% in the second inning because his leading off the first inning was a sure thing, which greatly reduced his chances of batting at all in the second inning.

As the game moves along Henderson's pattern is reducing in likelihood but is generally innings 1, 3, 5, 7.

Henderson's chances of batting in the 8th inning are about 9.6%. If he leads off the 8th, his chances of batting at all in the 9th are about 5.5%, ... if his team bats in the 9th.

These are rough numbers and my math isn't nearly good enough to do a good job of this but it's clear that some common sense conclusions can be reached.

1. Start the closer. If your one inning wonder starts the game, he will face the top of the order 100% of the time. If the closer is so damn good, this should not be a problem. After all, he's pitching only one inning.

2. If the "starting" pitcher does not pitch in the first inning, he may never face the top of the order as the first batters in an inning.

3. Not pitching the first inning may enable the "starting" pitcher to pitch an additional inning as he will be less stressed in the first and become better acclimated, success breeding success.

4. The "starting" pitcher's times through the batting order would be like any pitcher who does not start. Conversely, if the "starting" pitcher actually does start and pitch the first inning against the top of the order, each additional time facing batters begins with the top of the order, which makes his chances of success less likely. This causes teams to want to remove their starter before he has a chance to fail, a current conventional wisdom both dubious and ill defined.

5. A successful first inning is at least as important as a successful ninth inning. It should make a team more likely to have a lead to protect in the ninth, a lead which pretty much any competent pitcher on the staff should be able to protect.

This stuff is not rocket science but it's kind of amazing how much simple common sense is getting lost and ignored.