It feels icky to create a statistical formula based on what “feels right”.
Last month, I introduced a stat called Leadoff Rating, or LOR. The idea was that most systems to identify great leadoff hitters tab players like Ted Williams and Mickey Mantle, who would always hit closer to the middle of the order. I wanted to distinguish players specially suited to batting leadoff. The formula was simple: OBP minus ISO. By subtracting isolated power, we identified players who get on base a lot but aren’t true sluggers. It’s an easy calculation, and it produced fairly reasonable results. Two particular things bothered me:
1. Bad hitters occasionally had good leadoff ratings because of their very low ISO.
2. Rickey Henderson ranked 45th.
We know that leadoff is one of the two or three most important positions in the batting order. As little impact as lineup construction has on winning percentage, leadoff hitters are important. But LOR saw high OBP and low ISO as equally meaningful, so players with no power sometimes rated as desirable leadoff hitters. That seemed like something to correct.
Rickey Henderson is generally recognized as the greatest leadoff man of all time. LOR did not show this, for two main reasons. One was that the formula did not include baserunning. The other was that the all-time list slanted heavily towards Deadball players. Before Babe Ruth, everyone had low isolated power. Ty Cobb was a terrific power hitter, who led the AL in slugging eight times. Cobb’s career ISO (.146) is basically the same as Rickey’s (.140). Henderson only ranked among the top 10 in slugging twice. The game has changed.
Based on the feedback of FanGraphs readers and on my own muddlings, I’ve reworked the leadoff rating formula. The new system is more complicated — it’s annoying to do without a spreadsheet — and it’s kind of haphazard. OBP – ISO was a nice system because of its simplicity. With the updated formula, I’m guessing, choosing numbers that seem right. If someone better than I am at math would care to suggest revisions, please do so. I am fully prepared to give this stat away to smart people.
The formula I’m using now is — wait. There’s another calculation I abandoned, but it’s important for explaining how we arrived at the current iteration, and that middle step looked like this: OBP – ( .75 * ISO ) + ( ( .005 * BsR ) / ( PA / 600 ) )
On-base percentage is the heart of leadoff rating. A good hitter, and especially a good leadoff hitter, must get on base. But I only subtracted 3/4 of ISO, because (1) low ISO is not as important as high OBP, and (2) the original formula was probably a little too hard on doubles hitters. Guys like Rickey and Tim Raines ranked too low because they had more power than players like Jason Kendall and Ozzie Smith.
Commenter foxinsox suggested adding (Constant * BsR) to the calculation, which was a fine idea I should have seen earlier. The hitch was turning BsR into a rate stat. By using BsR/PA or BsR/G, we can incorporate that element smoothly.
When I ran the numbers, the historical lists looked great (Rickey Henderson in the top 10!), but for active players, there were hits and misses. Elvis Andrus came back as the ideal leadoff hitter in 2013, and Craig Gentry (.264/.326/.299) ran away with 2014 to date. Even with the adjustments, LOR rewarded low ISO. While a .250 ISO isn’t really the right fit for the top of the batting order, neither is a sub-.050 ISO. We don’t want a guy who only hits singles, we just don’t want a cleanup hitter. Looking at the historical lists, I found that most of the top players had an ISO right around .100, so I created a Goldilocks formula, preferring a minimal absolute difference from .100 ISO. Rather than simply treating low ISO as desirable, we’re looking for the sweet spot between singles and slugging. The new formula is:
OBP – .75 * | .100 – ISO | + ( .005 * BsR ) / ( PA / 600 )
That’s on-base percentage, minus 3/4 of the absolute difference between ISO and .100, plus .005 times BsR per 600 plate appearances. Now very low isolated power is punished just as much as very high ISO.
Hopefully you want to see some lists. I’ll show you five: the all-time list, the post-Jackie Robinson list, the leaders for the 2013 season, 2014 to date (through July 31), and 2014 rest-of-season projections (ZiPS). We’ll also look at the 2014 leaders (both to date and projected) for every team in the major leagues.
First, the all-time list. Minimum 2,000 hits to qualify for this one:
1. Billy Hamilton, .480
2. Eddie Collins, .432
3. Ty Cobb, .412
t4. Jesse Burkett, .403
t4. Rickey Henderson, .403
6. Stan Hack, .401
7. Wade Boggs, .400
8. Rod Carew, .393
9. George Van Haltren, .392
10. Tim Raines, .391
t11. Joe Sewell, .387
t11. Tris Speaker, .387
t11. Arky Vaughan, .387
t14. Luke Appling, .386
t14. Max Carey, .386
t14. Dummy Hoy, .386
17. Joe Kelley, .382
18. Richie Ashburn, .381
19. Ichiro Suzuki, .380
20. Four tied, .379
This is more intuitive than the original ranking. Henderson is in the top five, and Raines the top 10. Ty Cobb snuck into the top group, but that’s because he had a .433 on-base average, he was a dynamic baserunner, and the formula doesn’t understand Deadball ISOs. Ted Williams rates 94th (out of 300) by this method. Mantle is at 173, Barry Bonds is 212, and Babe Ruth is 240th. This isn’t a list of great hitters, it’s a list of great hitters with leadoff-type stats. Here’s the top 20, sorted by OBP.
Sliding Billy Hamilton leads LOR by a huge margin, and I believe he is the one player in history that, no matter who else was on the team, he would be the optimal leadoff man. Hamilton hit .344/.455/.432 and stole over 900 bases. He had three times as many walks as extra-base hits, and he was the greatest base stealer of his generation. LOR is not park- or league-adjusted, but the simple numbers show Hamilton well ahead of Rickey:
Hamilton: .344/.455/.432, .57 SB/G
Henderson: .279/.401/.419, .46 SB/G
Henderson hit 297 home runs. Hamilton had 40, and I suspect about half of them were inside the park. Hamilton got on base more often, and Rickey was the bigger slugger. If you had both of them, you would bat Hamilton first and Rickey second. And you would score a lot of runs.
The all-time list is still subject to the Deadball effect, so let’s see the top 20 from 1947 on. Minimum 2,000 hits:
1. Rickey Henderson, .403
2. Wade Boggs, .400
3. Rod Carew, .393
4. Tim Raines, .391
5. Richie Ashburn, .381
6. Ichiro Suzuki, .380
7. Tony Gwynn, .376
8. Kenny Lofton, .375
9. Joe Morgan, .371
10. Pee Wee Reese, .370
t11. Brett Butler, .368
t11. Pete Rose, .368
13. Derek Jeter, .366
14. George Kell, .361
t15. Jason Kendall, .360
t15. Willie Randolph, .360
17. Julio Franco, .354
t18. Keith Hernandez, .352
t18. Harvey Kuenn, .352
t18. Tony Phillips, .352
Good OBPs, good baserunners, not a lot of power. The median OBP is .376, the median ISO comes in between Boggs (.115) and Reese (.108), and 16 of the 20 stole at least 150 bases. Morgan leads in ISO (.156), Gwynn leads in SLG (.459), and Rickey leads in HR (297). These players would not be good fits for a cleanup slot, but they’re ideal leadoff hitters.
Here they are in a sortable table. Please remember that the table is default sorted by OBP, not LOR.
When we look only at players of historical caliber — everyone above had at least 2,000 hits in the major leagues — LOR does a very good job of identifying valuable leadoff hitters. With the updated formula, I believe it also does a good job when looking at ordinary players and teams. Below are LOR’s top 20 qualified batters from 2013.
1. Jacoby Ellsbury, .388
2. Joey Votto, .368
3. Mike Trout, .365
4. Dustin Pedroia, .363
t5. Matt Carpenter, .362
t5. Shin-Soo Choo, .362
7. Joe Mauer, .361
8. Andrew McCutchen, .359
9. Daniel Nava, .356
10. Ben Zobrist, .351
t11. Jon Jay, .350
t11. Eric Young, .350
t13. Chris Denorfia, .343
t13. Marco Scutaro, .343
15. Elvis Andrus, .341
16. Michael Brantley, .339
t17. Denard Span, .336
t17. Gregor Blanco, .336
19. Starling Marte, .335
20. Michael Bourn, .334
There are a lot of good players on that list. Eight of the top 20 made the All-Star Game, and nine posted at least 5 WAR. But as a group, these players hit .290/.367/.421, with 2,276 singles, 1,247 walks, and 912 extra-base hits. They stole 395 bases with 119 caught stealing (77%). They averaged 159 H, 62 BB, 11 HR, and 20 SB. That’s a good line for a leadoff hitter.
Let’s take this further. Through July 31 of this season, 271 players had at least 200 plate appearances. Here are the top 20 in LOR:
1. Jose Altuve, .406
2. Angel Pagan, .399
3. Russell Martin, .394
4. Collin Cowgill, .387
5. Dee Gordon, .386
6. Robinson Cano, .383
7. Dexter Fowler, .381
8. Denard Span, .372
9. Matt Carpenter, .371
10. Sam Fuld, .366
t11. Carlos Ruiz, .355
t11. Jayson Werth, .355
13. Howie Kendrick, .354
t14. Coco Crisp, .353
t14. Joe Mauer, .353
t16. Shin-Soo Choo, .352
t16. Brock Holt, .352
t18. Alex Gordon, .351
t18. Gregory Polanco, .351
20. Lorenzo Cain, .349
As a group these players have hit .287/.361/.403, and they’ve already stolen 234 bases. I’ll go ahead and give you the sortable chart, because I want to take a different approach here.
Below is each team’s top player in LOR (min. 200 PA, which means about 9 batters per team). The trade deadline makes this a little tougher to evaluate, so a few players are listed on teams they no longer play for.
Arizona Diamondbacks: Martin Prado, .319 LOR, .270/.317/.370
Unless you want to have Paul Goldschmidt lead off, or trust Miguel Montero (0 SB, 3 CS, -2.6 BsR), Prado actually did have the highest OBP on the 48-61 D’Backs. I guess Montero makes the most sense now.
Atlanta Braves: Jason Heyward, .342 LOR, .260/.350/.379
Heyward edges ahead of Tommy La Stella (.322) due to baserunning, but La Stella has a .370 OBP and 0 HR. Lately B.J. Upton (.218/.284/.335) is leading off, and La Stella’s hitting second. Because, you know, base-clogging.
Baltimore Orioles: Nick Markakis, .325 LOR, .280/.341/.385
Among eight Orioles with at least 200 PA, Markakis ranks 2nd in OBP, 6th in SLG, and 7th in ISO. Adam Jones is the only competent baserunner on the team, and he’s not going to lead off, so that doesn’t really play into this calculation. Markakis is the right leadoff man for the O’s.
Boston Red Sox: Brock Holt, .352 LOR, .302/.350/.422
The Red Sox have six hitters with at least .300 LOR, so the system doesn’t feel strongly about this.
Chicago Cubs: Emilio Bonifacio, .344 LOR, .279/.318/.373
With Bonifacio gone, Chris Coghlan leads the Cubs in LOR, .332. Mike Olt, who is hitting .139/.222/.353, has the lowest LOR in the major leagues. His OBP and ISO are virtually even, and he’s at -0.6 BsR.
Chicago White Sox: Adam Eaton, .358 LOR, .296/.362/.390
Cincinnati Reds: Joey Votto, .313 LOR, .255/.390/.409
Billy Hamilton is at .312 LOR, a virtual tie, so please don’t get too wound up about this. Votto’s OBP is 90 points higher than Hamilton’s, and let’s not pretend it’s obvious that a guy with a .300 OBP should be hitting leadoff.
Cleveland Indians: Jason Kipnis, .341 LOR, .243/.322/.356
Another virtual tie, with Michael Brantley at .339. Kipnis has been leading off now that Michael Bourn is hurt.
Colorado Rockies: DJ LeMahieu, .318 LOR, .280/.332/.354
The Rockies, with their skewed offensive environment, are a real argument for LOR+. It’s not going to happen.
Detroit Tigers: Rajai Davis, .345 LOR, .294/.336/.422
Detroit has three hitters with a wOBA of at least .380. If you bat them somewhere in the 2-5 spots, Davis is probably the best leadoff, especially now that Austin Jackson (.328 LOR) is gone.
Houston Astros: Jose Altuve, .406 LOR, .339/.377/.443
Dexter Fowler also has a strong LOR (.381), but I don’t think anyone would argue against Altuve as Houston’s leadoff batter.
Kansas City Royals: Alex Gordon, .351 LOR, .276/.355/.421
Los Angeles Angels of Anaheim: Collin Cowgill, .387 LOR, .277/.354/.307
Mike Trout has a .280 ISO this season. Hitting him second is perfect. Leading off with Kole Calhoun (.285/.341/.484) makes less sense. Calhoun has basically the same slash line as Albert Pujols. Cowgill or Howie Kendrick should be leading off.
Los Angeles Dodgers: Dee Gordon, .386 LOR, .294/.343/.398
Miami Marlins: Casey McGehee, .345 LOR, .304/.371/.377
Off the top of my head, I might guess that McGehee’s .377 slugging average is the lowest for any cleanup hitter in the majors. McGehee has 2 home runs in 416 at-bats this season.
Milwaukee Brewers: Lyle Overbay, .327 LOR, .232/.313/.337
Here’s one where I’m going to disagree with LOR and agree with Brewers manager Ron Roenicke. Carlos Gomez (.309 LOR) is Milwaukee’s best option at the top of the order. Overbay’s OBP is sixth on the ballclub. The Brewers have a bunch of productive hitters this year and they can afford to pull a slugger out of the middle of the order.
Minnesota Twins: Joe Mauer, .353 LOR, .271/.342/.353
Mauer has a 94 wRC+ this year. We all expect him to improve on that by the end of the season, but right now he’s not the kind of player who has to be in the middle of the order. Maybe there are some baseball politics I don’t appreciate where it would be ruinous to put Mauer at the top of the order, but it seems like a good idea.
New York Mets: Eric Young, .339 LOR, .230/.314/.304
Daniel Murphy is effectively tied with Young, at .338, and is probably a better choice. Four of their nine players with 200 PA have wRC+ of 87 or below, including Young, who is actually dead last (81). Five players on the Mets have an LOR of at least .300, and I don’t think it’s crazy that Curtis Granderson (.302) is leading off.
New York Yankees: Jacoby Ellsbury, .346 LOR, .279/.344/.408
When I ran these numbers with the previous formula, Ichiro Suzuki and Derek Jeter ranked as the Yankees’ 2014 LOR leaders. The new system is better.
Oakland Athletics: Coco Crisp, .353 LOR, .274/.372/.416
New addition Sam Fuld is also an attractive leadoff option. I might bat Craig Gentry ninth, as sort of a second leadoff man when the order comes back around. You won’t miss extra plate appearances from him, but he’s been okay about reaching base and he’s a skilled baserunner.
Philadelphia Phillies: Carlos Ruiz, .355 LOR, .275/.373/.380
Either Ben Revere (.306/.326/.366, .346 LOR) or Ruiz is probably the right choice to lead off. I’d likely go with Ruiz, but Revere deserves consideration because he is a far better baserunner. BsR rates Revere at +6.6 and Ruiz at -1.4. I don’t know if that’s worth 47 points of OBP, but it’s a substantial difference.
Pittsburgh Pirates: Russell Martin, .394 LOR, .278/.408/.386
I know Martin’s a catcher, but it is unequivocally crazy to bat him fifth or sixth in the order. Lately Josh Harrison has been leading off. Harrison’s OBP is 75 points below Martin’s (.333) and his slugging percentage is 87 points higher (.473). Harrison is a better baserunner, but not by nearly enough to justify that lineup order.
San Diego Padres: Chris Denorfia, .295 LOR, .242/.293/.319
Denorfia is a Mariner now. That leaves Yangervis Solarte as San Diego’s LOR leader (.294). Solarte and Seth Smith are the only Padres with wRC+ over 100, and Solarte just joined the team. Before writing this, I don’t think I had really absorbed how bad the Padres’ lineup is. I’m so sorry, San Diego.
Seattle Mariners: Robinson Cano, .383 LOR, .328/.389/.453
Cano has been hitting third all year. I get that Lloyd McClendon kind of has to bat Cano third, and I get that Cano’s .124 ISO is 80 points lower than what he did in New York, and the team expects him to produce the same results he did in Yankee Stadium. His ROS projection is in the high .130s, which is closer to the first half of 2014 than it is to his years in pinstripes.
If I were McClendon, I would move Cano and Kyle Seager to the top of the order, 1-2.
San Francisco Giants: Angel Pagan, .399 LOR, .307/.356/.411
Easy call. Hunter Pence has been leading off in Pagan’s absence, and that works, too. Pence’s LOR is .334.
St. Louis Cardinals: Matt Carpenter, .371 LOR, .286/.380/.394
Carpenter’s 59 BB and .380 OBP lead the team; his .108 ISO is second-to-last. The only standout baserunners have sub-.300 OBPs. Carpenter is the right leadoff man.
Tampa Bay Rays: Matt Joyce, .345 LOR, .279/.362/.425
All nine Rays who qualified for this exercise have leadoff ratings over .280. Actual leadoff hitter Desmond Jennings is the most accomplished base-stealer on the team, but I would probably use Joyce.
Texas Rangers: Shin-Soo Choo, .352 LOR, .240/.351/.361
Elvis Andrus, Choo, and Leonys Martin are all reasonable leadoff choices here. Andrus is the best baserunner and weakest hitter, Choo’s the best at getting on base, Martin’s in between. All have leadoff ratings between .327-.352.
Toronto Blue Jays: Jose Reyes, .332 LOR, .279/.330/.409
Among nine Jays with 200 PA, Jose Bautista ranks second in LOR. And when you look at their lineup, that doesn’t seem totally insane.
Washington Nationals: Denard Span, .372 LOR, .290/.349/.394
Span and Jayson Werth (.355 LOR) are strong options for the Nats to lead off with.
Okay. Thirty teams. What have we learned? I think LOR does a fine job of identifying the optimal leadoff man. But FG commenter filihok suggested that rest-of-season projections make more sense than season-to-date stats. We want to know who should lead off going forward, not in hindsight. ZiPS ROS, min. 140 PA:
1. Jose Altuve, .356
2. Joe Mauer, .355
3. Adam Eaton, .348
4. Jon Jay, .339
t5. Matt Carpenter, .337
t5. Denard Span, .337
7. Billy Hamilton, .335
8. Dexter Fowler, .334
t9. Dustin Pedroia, .331
t9. Joey Votto, .331
t11. Shin-Soo Choo, .330
t11. Rajai Davis, .330
13. Jacoby Ellsbury, .329
t14. Emilio Bonifacio, .327
t14. Nick Markakis, .327
16. Dee Gordon, .326
17. Michael Brantley, .325
t18. James Loney, .323
t18. Casey McGehee, .323
20. Brett Gardner, .322
Best by team (ZiPS projections, min. 140 PA):
Diamondbacks: Ender Inciarte, .305, or Miguel Montero, .300
Braves: Emilio Bonifacio, .327
Orioles: Nick Markakis, .327
Red Sox: Dustin Pedroia, .331
Cubs: Starlin Castro, .291
White Sox: Adam Eaton, .348
Reds: Billy Hamilton, .335, or Joey Votto, .331
Indians: Michael Brantley, .325, or Michael Bourn, .320
Rockies: DJ LeMahieu, .306
Tigers: Rajai Davis, .330
Astros: Jose Altuve, .356
Royals: Billy Butler, .320, or Nori Aoki, .318, or Lorenzo Cain, .315
Angels: Howie Kendrick, .309
Dodgers: Dee Gordon, .326
Marlins: Casey McGehee, .323
Brewers: Jean Segura, .295, or Scooter Gennett or Gerardo Parra, both .293
Twins: Joe Mauer, .355
Mets: Daniel Murphy, .314
Yankees: Jacoby Ellsbury, .329
Athletics: Coco Crisp, .322
Phillies: Ben Revere, .312
Pirates: Russell Martin, .321
Padres: Yangervis Solarte, .306
Mariners: Robinson Cano, .318
Giants: Angel Pagan, .321
Cardinals: Jon Jay, .339, or Matt Carpenter, .337
Rays: James Loney, .323
Rangers: Shin-Soo Choo, .330
Blue Jays: Jose Reyes, .320
Nationals: Denard Span, .337
I’m happy with this system. It’s not precise: I used round numbers and tinkered with the formula until it produced intuitive results. But I think it does produce intuitive results, and I’ve never seen another stat that will accurately identify optimal leadoff hitters. It’s a little thing, but hopefully it’s interesting — and it gives us one more tool to
criticize evaluate managers.
I’d be interested in feedback on whether you think this system works for your favorite team.