[M]y mathematical aesthetic prefers not to add two fractions with different denominators. Thus, we multiply them.

While I get not wanting to add fractions with different denominators (it bothers me, too), is there any legitimate reason to multiply SLG and OBP? This strikes me as an alternative, not a solution.

If you're of the opinion that OPS undervalues OBP and overvalues SLG, you could multiply them. By using OBP*SLG, a guy who on-bases .400 and slugs .400 would rank higher than a guy who on-bases .340 and slugs .470.

You could also do it if you wanted to make a case that Gil Hodges was a better hitter than Orlando Cepeda.

[M]y mathematical aesthetic prefers not to add two fractions with different denominators. Thus, we multiply them.

God, I've always hated this silliness. OBP and SLG are both expressed as decimals. The denominator is 1 in both cases. There's no mathematical reason the two numbers can't be added. If you have an aesthetic problem with OPS, it's because the units are different, not the denominators. So what are the units for SLOB, anyway? Let's see, (times on base * total bases)/(PA * AB). Yeah, that's informative.

is there any legitimate reason to multiply SLG and OBP?

Actually there is. At the team or league level. Not so much for an individual, since his OBP interacts with his teammates' SLG (and vice versa), not with his own.

While I get not wanting to add fractions with different denominators (it bothers me, too), is there any legitimate reason to multiply SLG and OBP? This strikes me as an alternative, not a solution.

Back in the days before OPS caught on, I believe Bill James was a fan of multiplying instead of adding. The rationale: multiplying would help those strong with both numbers instead of someone heavy w/ one and light w/ another. IIRC, I think multiplying correlates with run scoring better than adding does.

why argue over * versus +; the problem with the article is lack of context. Ranking HoF 1Bmen by raw rate stats is silly regardless.

...... OBP*SLG OPS+
Hodges 0.175 120
Cepeda 0.172 133
Murray 0.171 129
Perez.. 0.158 122
Kelly... 0.153 133 (Joe Kelley, not Kelly)
Chance 0.149 135


How can you elect a FIRST BASEMAN to the HoF who never led his league in ANYTHING?! While playing in a hitter's park?!?

The problem with the multiplicative method is that you are in effect asserting that a home run hit by (say) Frank Thomas is more valuable than one hit by Joe Carter. With extreme players the effect is quite large (maybe a dozen runs with Babe Ruth's better seasons for instance) In 1995 a 1-1 with a HR would have been worth 1.43 runs for Carter and 2.02 for Thomas.

And it glaringly mis-rated high OBP players with no power. An extreme example is Lenny Harris' 2009 strat card vs LHP. 40% on base. No hits at all. That's not worthless.

The basic problem with multiplicative methods is that the value of SLG is (mostly) a function of the league OBP. Or the team's Or the players who bat in front of you. Or some combination of those 3.

Likewise the value of your OBP is not really a function of your SLG. It's mostly a matter of how effectively your teammates (or the league if you prefer) would use the outs that you don't consume plus their power when you're on base.

And it doesn't model team runs scored any better than OPS does, so why bother? I mean I don't carry a calculator with me so if I have to multiply two 3 digit numbers together I'm going to have to use a spreadsheet. And if I have a spreadsheet I can use a better method than SLOB. And if I don't have a computer handy, I can at least add two 3 digit numbers together. And make mental adjustments if a player happens to be OBP heavy.

#4 Trivially. The difference is like .001 in the correlation with runs scored per game and the difference in the standard error is somewhere in the is of similarly trivial difference.

The nice thing about SLOB is that if you multiply by AB you have basic runs created.

Yes, James believed that run creation is best modeled by a multiplicative method. Just doesn't turn out to work that way.

How can you create a quick-and-dirty rate stat to argue a guy for the Hall of Fame and not consider that the HoF voters value longevity via counting stats? Just take OBP * SLG * Plate Appearances. It's still a stupid way to compare players, but at least you're doing a little better at modelling the actual voting standards.

I'm betting that makes Hodges look even worse in comparison, so I guess there's my answer.

Edit: Blast you, Ron Johnson!

"Kelly... 0.153 133 (Joe Kelley, not Kelly)"

Joe Kelley was an OF; George "High Pockets" Kelly was a 1B..

How can you elect a FIRST BASEMAN to the HoF who never led his league in ANYTHING?!

Tony Perez. Well, he did lead the league in GIDP with 25 in 1980.

The only way a reasonable HOF case can be made for Hodges is to consider him as a multi contributor, player + Manager value. Personally, I give managers much less credit for having "value" than others do.

Having said that, I recently devised a quick-and-dirty way of identifying the player/manager candidates. I add their WAR to thier managing wins divided by 40. Here are some of the leading combo HOF candidates (this was not an exhaustive search):



I did this about a week ago, so the active managers are a bit higher. Remember that for WAR alone, 48 in a career puts you on the HOF radar; 61 WAR is pretty much a shoo-in.

#9 Right. And any HOF case based on a comp to "High Pockets" is simply no case at all. I mean Chris Chambliss is a pretty fair comp I think. Except Chambliss lasted longer.

Tony Perez. Well, he did lead the league in GIDP with 25 in 1980.

Hodges lead his league in sac flies twice, FWIW...

Five additions to the list in #11

No kidding.... I happen to have a post up at my blog today about enshrining multi-contributors.

I kept Torre off my list, as well as Billy Martin, Bobby Valentine, and Lou Piniella since I think they could all make Cooperstown purely as managers.

Dan, I didn't realize this could be quantified. Out of curiosity, is there WAR for managers yet?

A long long time ago in baseball stat world, Steven Mann in The Baseball Superstat dealt with this. I remember my feeling of frustration at the time as he very clearly went through OBA times SLG only to finally conclude that "we cannot use the OTS as the basis for the superstats. Due to a quirk in the mathematical properties of the OTS, it can be applied only to teams, not to individual players." OPS+ was how he went, and this was in 1989. I don't think he went into what those mathematical quirks were. I don't know if James ever did either, although I, too, remember his mooting the idea.

How can you elect a FIRST BASEMAN to the HoF who never led his league in ANYTHING?!


Tony Perez. Well, he did lead the league in GIDP with 25 in 1980.

To be fair to Tony, he was actually a 3b most of his peak (his peak was 26-31, he was a 3b from 25-29)

His last productive year as a regular was 1978 when he was 36, and yet he had 3000 more PAs to go as a lead footed .271/.327/.426 hitting 1b

1978-86, 1bs 2000+ PAS:


Those 3000 PAs got his counting stats up to an acceptable level in the eyes of HOF voters, but really he was a below average player for all of that time except a hot streak he had at 43

Perez wasn't any better than Hodges or Hopdges'
comps

but a Perez voter could always say, "guys like Hodges and Colavito and Foster didn't even get 2000 hits, Perez is up near 3000, Perez has 300/400 more ribbies..."

[5] Maybe a blogger looking for material could create "SLOB+". Now, should SLOB+ be a player's SLOB normalized by the league SLOB, or should one multiply OBP+ times SLG+ instead? :)

Wouldn't the argument for Hodges is that he lead a Mets team to its first championship?

Back in the days before OPS caught on, I believe Bill James was a fan of multiplying instead of adding.

Yes; Runs Created is multiplying them.

Regarding managerial wins / 40 - this doesn't add well to WAR because there is no replacement level set. I think a better way to do this would be to set managerial replacement at .420 WP% (worse than that and you'll get fired). I like dividing by 40 which sets the ceiling at about 3 WAR credited to a manager in a year. Then you get this list of managerial wins above replacement for those players mentioned:


Manager G W L rep W mWAR
Torre 4295 2312 1977 1804 12.7
Piniella 3548 1835 1713 1490 8.6
Grimm 2368 1287 1067 995 7.3
O'Neill 1879 1040 821 789 6.3
Scioscia 1748 963 785 734 5.7
Virdon 1918 995 921 806 4.7
Baker 1556 840 715 654 4.7
Howe 2266 1129 1137 952 4.4
Hargrove 1312 721 591 551 4.2
Johnson 1012 595 417 425 4.2
Hutchinson 1666 830 827 700 3.3
Garner 2041 985 1054 857 3.2
Dykes 1850 899 940 777 3.1
F Jones 739 426 293 310 2.9
F Alou 1408 691 717 591 2.5
A Dark 644 366 277 270 2.4
Peckinpaugh 975 490 481 410 2.0
Baylor 910 440 469 382 1.4
Fregosi 486 237 249 204 0.8
Hodges 765 321 444 321 0.0
Bell 1243 519 724 522 -0.1


There are probably other ways to go after this data (looking at pythagorean predicted wins and attributing better than average bullpens, baserunning etc. to the manager). This is a decent quick and dirty way to do it. If you want to add another mWAR per pennant, be my guest.

Rank the Dodger first basemen. Who has the best case for the HOF?

The first line is Dodgers only; second line is whole career.

HOF managers and other interesting guys

Manager G W L rep W mWAR
McGraw 4769 2763 1948 2003 19.0
McCarthy 3487 2125 1333 1465 16.5
Cox 4473 2486 1984 1879 15.2
LaRussa 4897 2620 2274 2057 14.1
Alston 3658 2040 1613 1536 12.6
Anderson 4030 2194 1834 1693 12.5
Mack 7755 3731 3948 3257 11.8
Durocher 3739 2008 1709 1570 10.9
Clarke 2829 1602 1181 1188 10.3
Weaver 2541 1480 1060 1067 10.3
Lopez 2425 1410 1004 1019 9.8
Selee 2180 1284 862 916 9.2
McKechnie 3647 1896 1723 1532 9.1
Anson 2288 1296 947 961 8.4
Huggins 2570 1413 1134 1079 8.3
Wright 2145 1225 885 901 8.1
Stengel 3766 1905 1842 1582 8.1
Lasorda 3041 1599 1439 1277 8.0
Harris 4410 2158 2219 1852 7.6
Williams 3023 1571 1451 1270 7.5
Martin 2267 1253 1013 952 7.5
Southworth 1770 1044 704 743 7.5
Houk 3157 1619 1531 1326 7.3
Herzog 2409 1281 1125 1012 6.7
Griffith 2918 1491 1367 1226 6.6
Cronin 2315 1236 1055 972 6.6
Jennings 2203 1184 995 925 6.5
Hanlon 2530 1313 1164 1063 6.3
Mauch 3942 1902 2037 1656 6.2
Leyland 2979 1476 1501 1251 5.6
W Robinson 2819 1399 1398 1184 5.4
Tanner 2738 1352 1381 1150 5.1
Schoendienst 1999 1041 955 840 5.0

corrected Fregosi 2123 1028 1095 892 3.4

[21] Good stuff, DL. Let's see if I can format that better.

I miscalculated in my head - there is a ceiling of about 1.5WAR per season with this method not 3. Double the numbers if you think managers can add 3 wins above replacement per season.

There are probably other ways to go after this data (looking at pythagorean predicted wins and attributing better than average bullpens, baserunning etc. to the manager). This is a decent quick and dirty way to do it. If you want to add another mWAR per pennant, be my guest.

The problem with either W Pct. or Pythag is neither really take into account the level of talent a manager has on hand and how well above or below expectations he was able to get that talent to perform (which is, I believe, where the abilities of managers are most significant). Frank Robinson and Gil Hodges were probably much better managers than others with better WL and Pyth records, but were given much less talent to work with.

take into account the level of talent a manager has on hand

Player performance in WAR subtracted from their interpolated or predicted performance? Obviously this doesn't work well when looking at players who played their entire career for one manager.

Yes, you quickly get into a quagmire trying to isolate the manager's performance from his teams'. That's why I took an easy approach, giving managers equal credit for however many wins their team won with them, which, along with pennants, is about all HOF voters care about anyway.

Dividing wins by 40 is an attempt to make the result look somewhat like the WAR scale for players, in order to comparatively measure managers for voters' considerations.

Yes, you quickly get into a quagmire trying to isolate the manager's performance from his teams'. That's why I took an easy approach, giving managers equal credit for however many wins their team won with them, which, along with pennants, is about all HOF voters care about anyway.

Sure, but if the idea behind the player stats is to isolate performance, the object of any kind of managerial measurement should be the same. How HoF voters view managerial performance is an entirely separate matter (even if it is what sparked the discussion).

Obviously it's difficult, particularly with long-tenured guys, but just looking at WP or Pyth isn't really a meaningful attempt. Also obviously, Chris's work is a giant step in the right direction.

The basic reason for multiplying OBP by SLG is that OBP * SLG * AB is the most basic form of Bill James' original Runs Created formula. Everything else in Bill's formula was just adjustments to OBP and SLG based on things like GDP, IBB, SB, CS and things like that. There are only two reasons I can think of for wanting to add OBP to SLG:

1) Multiplying takes a (shuddering horror to Old Sportswriters) calculator! They can add three-digit numbers with nothing more than paper, pencil, and maybe ten minutes to get it right.

2) You'd like the rate part (OBP * SLG) to be multiplied by PA as the playing time part, but it isn't; it's AB. Algebra don't lie. The algebraic reason why it's AB instead of PA is related to why points of OBP are worth more than points of SLG. SLG uses AB as the denominator; OBP uses PA.

The first question I would have about Hodges is his career PA. What IS his career longevity compared to other 1B? I did notice that his rate seems lower than George Sisler, who is crucified for his rate after the injury.

- Brock Hanke

One more for manager WAR, Frank Chance:

G W L Rep W mWAR

1178 768 389 495 6.8


Assuming I did all that right, he'd jump to 56.3 career combined WAR

The first question I would have about Hodges is his career PA. What IS his career longevity compared to other 1B?

Nothing special. There are 33 first basemen with 8000 PA and 2000 G in their career (50%+ G at 1B). In the Hall are Gehrig, Anson, Foxx, Murray, McCovey, Beckley, Perez, Sisler and Cepeda. Here are the 24 not in the HOF:

Another take - divide marginal wins by 20. Add a point for a pennant and 2 for a World Series. This is pretty close to conventional wisdom for managers:

Manager G W L rep W mWAR pen WS total
McCarthy 3487 2125 1333 1465 33.0 9 7 56.0
McGraw 4769 2763 1948 2003 38.0 10 3 54.0
Stengel 3766 1905 1842 1582 16.2 7 10 43.2
Mack 7755 3731 3948 3257 23.7 9 5 42.7
Alston 3658 2040 1613 1536 25.2 7 4 40.2
Torre 4295 2312 1977 1804 25.4 6 4 39.4
Cox 4473 2486 1984 1879 30.4 5 1 37.4
LaRussa 4897 2620 2274 2057 28.2 5 2 37.2
Anderson 4030 2194 1834 1693 25.1 5 3 36.1
Huggins 2570 1413 1134 1079 16.7 6 3 28.7
Durocher 3739 2008 1709 1570 21.9 3 1 26.9
Clarke 2829 1602 1181 1188 20.7 4 1 26.7
Weaver 2541 1480 1060 1067 20.6 4 1 26.6
McKechnie 3647 1896 1723 1532 18.2 4 2 26.2
Lasorda 3041 1599 1439 1277 16.1 4 2 24.1
Selee 2180 1284 862 916 18.4 5 0 23.4
Williams 3023 1571 1451 1270 15.1 4 2 23.1
Southworth 1770 1044 704 743 15.0 4 2 23.0
Wright 2145 1225 885 901 16.2 6 0 22.2

Dan G - Thanks! So Hodges' candidacy as a first baseman is similar to, but a slight bit less than, those of Ed Konetchy and Mark Grace, both of whom were outstanding defensively. And none of the three is really in the contest with the guys above them in Dan's list or with Carlos Delgado (whose last name, if I remember my schoolboy Spanish right, means "slim"). Overall, Hodges would end up about tenth on this list, behind everyone listed ahead of him, and Delgado as well. Well, that pretty much settles that. Hodges is not a HoF candidate in any way. He's tenth at best among the unelected.

BTW, isn't it illegal to consider combined candidacies in the HoF? That, as I understand it, is why Buck O'Neill isn't in. He's just short as just a player, and the voters decided that he was just short as just a "contributor." They were not permitted to combine his candidacy, which would be well above entry level. If we're going to talk about combined candidacies, I want to talk about O'Neill a lot before I want to talk about Hodges. - Brock Hanke

Dan, I didn't realize this could be quantified. Out of curiosity, is there WAR for managers yet

It's not WAR, but Chris Jaffe's book on managers does provide a discussion of the contributions of managers in terms of runs.

Once again, Hodges’ Career SLOB ranks him higher than some first basemen already enshrined in the Hall:

Career SLOB
Gehrig 0.283
Foxx 0.261
Greenberg 0.248
Mize 0.221
Terry 0.198
McCovey 0.193
Bottomley 0.183
Sisler 0.176
Hodges 0.175
Cepeda 0.172
Murray 0.171
Perez 0.158
Kelly 0.153
Chance 0.149

Ah, this old chesnut. Make up a stat, and then show how your guy is superior to some HOFers based on this new stat. How about some SLOB's for firstbasemen not in the hall and not getting in anytime soon?

John Olerud - .185
Norm Cash - .183
Jason Giambi - .212
Fred McGriff - .192
Carlos Delgado - .209
Dick Allen - .202
Joe Adcock - .182
Ted Kluszewski - .176
Dolph Camili - .191

and so on. Why Hodges instead of Olerud or Cash or Camili?

Actually the VC is instructed to consider the entirety of the person's contribution to baseball.

"Voting: The Committee shall consider all eligible candidates and voting shall be based upon the individual’s record, ability, integrity, sportsmanship, character and contribution to the game."

All the same, it's generally noted when the Veterans Committee elects someone whether the candidate is going in as a player, manager or executive.