Saturday, March 21, 2015

Did the Orioles have seven of the best 33 defensive teams in the period from 1968-1975?

(That should actually say were 7 of those Oriole teams from 1968-75 in the top 33 covering the years from 1960-98?)

Here is something I posted to the SABR list back in 2013 (I got reminded of this from something mentioned on Twitter-this might not be earth shattering now or even then):

One way to look at the relative roles of pitching and fielding in run prevention would be to run a regression in which team runs allowed per inning is a function of the defense independent pitching stats (DIPS) HRs, Walks, Strikeouts per inning. Using all teams from 1960-1998, the regression equation was

R/IP = .192 - .121*SO/IP + .494*BB/IP + 1.98*HR/IP

the r-squared was .696. The standard error was .036

I then predicted each team's runs per inning and then subtracted the predicted total from the actual total. This residual or difference could be a measure of fielding quality since it shows what share of the runs was not at all affected by the DIPS. Of course, this residual is not completely a result of the fielding either. The more negative the residual, the lower the runs allowed as compared to the prediction of the model. So a big negative number means better defense (at least in theory). A negative .03 means that the team gave up .03 runs less an inning that the DIPS would predict, so that might mean good defense. But what was interesting to me is that when I ranked the teams from lowest (best fielding, starting in negative differentials) to highest (worst fielding, ending in positive differentials), seven of the best 33 defensive teams were Oriole teams in the period 1968-1975. The only Oriole team missing from that group was the 1974 team, but they were negative as was just about every Oriole team between 1960 and 1980. They always were considered a very good if not great fielding team.

The best 10 defensive teams and their differentials were

1972 Cle -0.111
1968 Det -0.104
1981 Hou -0.101
1965 Min -0.099
1970 Cle -0.094
1969 Bal -0.092
1960 LA -0.088
1968 Was -0.086
1985 Tor -0.083
1970 Cal -0.082 

Tuesday, March 10, 2015

How To Lead The League In HRs And Batting Average But Not RBIs Johnny Mize 1939 Edition

Since 1920, 12 players have won the triple crown (it has been won 12 times but Hornsby and Ted Williams each did it twice) and three other players led their league in HRs and AVG but not RBIs. So 80% of the time a player leads in the first two stats they win the triple crown. Click here to see the Baseball Reference list of triple crown winners.

The other two players besides Mize are Ruth, 1924, and Ted Williams, 1941.

Here are the leaders in the NL in 1939

AVG
1.Mize (STL).349
2.McCormick (CIN).332
3.Medwick (STL).332
4.Waner (PIT).328
5.Arnovich (PHI).324

HR
1.Mize (STL)28
2.Ott (NYG)27
3.Camilli (BRO)26
4.Leiber (CHC)24
5.Lombardi (CIN)20

RBI
1.McCormick (CIN)128
2.Medwick (STL)117
3.Mize (STL)108
4.Camilli (BRO)104
5.Leiber (CHC)88

Interesting that Medwick,  a teammate, who hit 14 HRs with a .332 AVG, had more RBIs. The two both split time in the 4th and 5th slots in the lineup. Mize had a .444 OBP while Medwick had .380. So Mize helped Medwick get RBIs more than vice-versa.

Retrosheet does not have complete splits yet for 1939 for Mize (a little less than half of all ABs), but maybe they tell us something. Click here to see Mize's splits for 1939. His AVG-OBP -SLG with no runners on (NONE) were .295-.381-.516. With runners on (ROB) they were .288-.418-.466. His SLG is down quite a bit. Maybe he also got walked often with runners on. With runners in scoring position (RISP) they were .256-.439-.423. If those numbers held up for the whole season, then it might explain the somewhat low RBI total. This is probably just bad luck for Mize.

Click here to McCormick's splits. They are just partial, too. But it looks like they were slightly better with none on.

McCormick had 19 more plate appearances. If Mize had 19 more, he would get about 3 more RBIs using his season's RBI/ PA rate.

McCormick  batted 4th all season and the OBP of the three guys in front of him was a collective .372. Using a weighted average (because Mize split time between slots 4-5), the three guys before him had a .342 OBP. Over 2200 PAs (how many the guys before McCormick had), that works out to an extra 66 base runners.

About a third of NL base runners that year were driven in. If Mize gets that rate, that means another 22 RBIs. It probably should be more, since Mize was a much better hitter than average (although his splits call this into question). But adding in the 3 from the lower PA total, gives Mize 25 more RBIs and enough to win the triple crown.

Mize had 92 walks in 669 PAs. McCormick had 40 walks in 688 PAs. So that may have cost Mize some RBIs. Mize edged him 353-312 in TBs and 86-63 in extra-base hits. McCormick had the edge in hits 209-197.

None of the batters in front of either guys stole many bases. The 3 guys in front of McCormick had 111 2Bs, 34 3Bs and 23 HRs. For Mize (the first 3 guys and part of the 4th slot) it was 137 2Bs, 28 3Bs and 32HRs. It does not look like any major differences in terms of guys getting themselves into scoring position for Mize and McCormick, guys with speed (3Bs) or guys who cleared the bases before they got up (HRs).

The Reds runners might have been faster with their better ratio of 3Bs to 2Bs.

So maybe the what cost Mize the triple crown was the higher OBP that guys in front of McCormick had (and if they were getting on more that might have allowed him to get some of those extra 19 PAs as well).


Friday, February 20, 2015

Should Wes Ferrell Be In The Hall Of Fame?

He is 161st in career WAR among all players (pitchers included). By my count, there are 215 players & pitchers in the Hall who played in MLB. So that rank of 161 looks good. Click here to see the rankings.

He had some decent peak value. In an eight year period, he had six top 5 finishes in WAR for pitchers, including four 2nd place finishes (and 3 in a row, from 1930-32, trailing Lefty Grove each time).

He also led the AL in WAR for all pitchers and players in 1935 with 11.0. That was a year when Grove, Gehrig, Foxx and Gehringer were all still very good or in their primes. Here is the top 10 from that year

1 Ferrell (BOS) 11
2 Grove (BOS) 8.8
3 Gehrig (NYY) 8.7
4 Foxx (PHA) 8.3
5 Gehringer (DET) 7.8
6 Greenberg (DET) 7.7
7 Harder (CLE) 7.1
8 Appling (CHW) 6.7
9 Myer (WSH) 6.1
10 Vosmik (CLE) 5.9

Since 1920, there have been 33 seasons of 11 or higher in WAR. I count 23 players & pitchers in that group. The only ones not in the Hall besides Ferrell are Barry Bonds, Roger Clemens, Dwight Gooden and Dizzy Trout (whose year was 1944, a war year).

Ferrell was 5th in ERA+ that year (1935) while not being in the top 10 in FIP ERA. What helped his WAR was the IP total and the fact that he had a 141 OPS+ (.347 AVG, .427 OBP and .533 SLG). His career WAR is 61.6 and 12.7 of that comes from offense. His career OPS+ is 100. Very, very good for a pitcher.

Ferrell was 3rd in overall WAR the next year (1936). His career after age 29 did not amount to much (maybe because of injuries or behavioral issues-Click here to read the SABR biography by Mark Smith). Only 216 of his 2,623 IP came after age 29.

He led the AL in IP from 1935-37. In 1935 he had 322.1 and 2nd place Mel Harder had 287.1. Ferrell had 7 top 10 finishes in ERA+ and 3 in FIP ERA.

I counted about 100 Hall of Famers who trail him in career WAR. Here are the pitchers (if it is not all of them, it is close). The + means they are Hall of Famers and the number in parentheses is numbers of years played.

Early Wynn+ (23)
Stan Coveleski+ (14)
Dazzy Vance+ (16)
Jim Bunning+ (17)
Rube Waddell+ (13)
Joe McGinnity+ (10)
Whitey Ford+ (16)
Mordecai Brown+ (14)
Eppa Rixey+ (21)
Burleigh Grimes+ (19)
Waite Hoyt+ (21)
Chief Bender+ (16)
Sandy Koufax+ (12)
Bob Lemon+ (15)
Hoyt Wilhelm+ (21)
Dizzy Dean+ (12)
Herb Pennock+ (22)
Addie Joss+ (9)
Rich Gossage+ (22)
Jack Chesbro+ (11)
Catfish Hunter+ (15)
Rollie Fingers+ (17)

Now some notable position players who trail Ferrell in WAR

Harmon Killebrew+ (22)
Yogi Berra+ (19)
Hank Greenberg+ (13)
Willie Stargell+ (21)
Joe Gordon+ (11)
George Sisler+ (15)
Bill Dickey+ (17)
Joe Medwick+ (17)
Enos Slaughter+ (19)
Bill Terry+ (14)
Willie Keeler+ (19)
Gabby Hartnett+ (20)
Mickey Cochrane+ (13)
Kirby Puckett+ (12)
Orlando Cepeda+ (17)
Tony Lazzeri+ (14)
Larry Doby+ (13)
Ralph Kiner+ (10)
Jim Rice+ (16)
Lou Brock+ (19)


Thursday, February 12, 2015

Using Runs Relative To Average To Determine The Best All Around Careers (Part 2)

Click here to see Part 1.

I thought of another way to measure this. Since the  running and fielding ratings were converted to rate stats to be like the hitting stat (OPS+), and that average was 100 once the geometric mean was applied, I could use 80 as replacement level. Then 80 was subtracted from each player's rating and multiplied by the number of seasons they played (a full season was 700 PAs). Then that would give me an all-around rating above replacement level. That way, guys whose careers ended early did not have the advantage of missing their decline years. So here is the top 25

Rank Player OPS+ Run Field Rating Seasons WAR
1 Barry Bonds 182 102.2 110.9 127.2 18.0 850.5
2 Hank Aaron 155 101.9 105.2 118.4 19.9 764.1
3 Willie Mays 156 104.4 111.6 122.0 17.9 749.8
4 Babe Ruth 206 98.4 105.5 128.8 15.2 740.1
5 Ty Cobb 168 102.6 99.3 119.6 18.7 739.9
6 Stan Musial 159 99.2 102.6 117.3 18.2 678.2
7 Tris Speaker 157 99.4 105.7 118.1 17.1 652.7
8 Carl Yastrzemski 130 99.2 110.2 112.4 20.0 647.3
9 Honus Wagner 151 101.7 105.3 117.3 16.8 626.5
10 Rickey Henderson 127 108.3 103.3 112.4 19.1 617.6
11 Frank Robinson 154 101.8 100.9 116.5 16.8 611.7
12 Mel Ott 155 98.9 103.0 116.4 16.2 590.0
13 Ted Williams 190 99.5 96.6 122.2 14.0 589.5
14 Eddie Collins 142 102.1 101.7 113.8 17.2 581.1
15 Al Kaline 134 101.9 110.2 114.6 16.6 572.6
16 Rogers Hornsby 175 98.5 104.1 121.5 13.5 561.5
17 Lou Gehrig 179 98.4 99.5 120.5 13.8 558.9
18 Mickey Mantle 172 103.5 95.9 119.4 14.2 558.2
19 Alex Rodriguez 143 103.5 101.2 114.4 16.2 557.0
20 Albert Pujols 162 100.5 111.8 122.0 13.2 555.0
21 Pete Rose 118 100.0 96.5 104.3 22.7 552.7
22 Eddie Murray 129 98.7 103.3 109.5 18.3 540.4
23 Nap Lajoie 150 98.4 105.9 116.0 14.9 538.3
24 George Brett 135 101.8 102.7 112.1 16.6 533.2
25 Mike Schmidt 147 99.2 109.8 116.9 14.4 531.1

Click here to see the complete rankings.

Wednesday, February 11, 2015

Using Runs Relative To Average To Determine The Best All Around Careers

See Using Runs Above Average To Determine The Best All Around Careers for a similar analysis.

The idea is to reward balance. I used the Baseball Reference Play Index in the post mentioned above.

In that study, I called up all the seasons with at least 0.1 in each of the following stats: fielding runs (Rfield), base running runs (Rbaser) and batting runs (Rbat). Those are all above average (no seasons came up from 1876-1885, maybe because they don't have SB data for those years).

Then all three stats were multiplied by each other. Then I took the cube root to get the geometric mean.  But that means that any seasons with a negative number or a zero in any of the three stats did not count.

If I use career totals, then there can still be negatives and zeroes so using the cube root probably does not make sense. So here I tried to convert each stat into a rate stat (the explanation is at the end in technical notes). It involved OPS+ and turning the running and fielding stats into something like OPS+. Also, OPS+ itself was adjusted to be an "above replacement" stat. The others were not as it is probably easy to find average runners and fielders in the minors.

That meant that OPS+ went up for most players (if not all). They got credit for more runs and that increased their estimated OPS+. If a player had negative fielding runs, his fielding OPS+ would be less than 100. If positive, above 100 (100 is average in OPS+). Then I found the geometric mean of all three stats. I used all players with 5000+ PAs and their career stats.

Here are the top 25. I don't know if this is better than the other method. Just different. If you look at the complete lists, some players move up quite a bit.


Rank Player OPS+WAR Run Field Rating
1 Babe Ruth 227.71 98.40 105.51 133.15
2 Barry Bonds 197.59 102.22 110.86 130.76
3 Albert Pujols 184.56 100.50 111.81 127.46
4 Willie Mays 176.96 104.45 111.61 127.24
5 Ted Williams 214.00 99.49 96.58 127.10
6 Rogers Hornsby 198.70 98.54 104.06 126.71
7 Lou Gehrig 206.75 98.36 99.49 126.42
8 Billy Hamilton 177.94 105.10 102.60 124.20
9 Joe DiMaggio 180.51 100.93 104.63 123.93
10 Ty Cobb 186.43 102.64 99.32 123.81
11 Tris Speaker 179.95 99.40 105.70 123.59
12 Mickey Mantle 190.49 103.48 95.88 123.58
13 Jimmie Foxx 188.39 98.93 101.30 123.53
14 Dan Brouthers 197.65 97.42 97.80 123.43
15 Larry Walker 166.61 103.47 109.05 123.36
16 Hank Aaron 175.33 101.89 105.15 123.33
17 Shoeless Joe Jackson 187.26 98.55 100.93 122.98
18 Jeff Bagwell 175.24 102.06 104.05 122.94
19 Roger Connor 177.86 97.75 107.03 122.94
20 Hank Greenberg 182.26 100.15 101.64 122.82
21 Jackie Robinson 160.59 103.71 110.95 122.65
22 Stan Musial 181.03 99.17 102.58 122.51
23 Mel Ott 179.95 98.93 102.99 122.33
24 Chase Utley 148.97 104.06 118.24 122.32
25 Mike Schmidt 166.69 99.20 109.84 121.95

Click here to see the complete rankings.

Technical notes: I ran a regression with OPS+ as the dependent variable and batting runs above average per PA as the independent variable. Here is the equation

OPS+ = 832.14*BattingRuns/PA + 99.32

So for all three stats, the runs per PA was plugged into this equation.

Friday, February 6, 2015

Using Runs Above Average To Determine The Best All Around Careers

Using the Baseball Reference Play Index, I called up all the seasons with at least 0.1 in each of the following stats: fielding runs (Rfield), base running runs (Rbaser) and batting runs (Rbat). Those are all above average (no seasons came up from 1876-1885, maybe because they don't have SB data for those years).

Then all three stats were multiplied by each other. Then I took the cube root to get the geometric mean. Each player then had their individual seasons added up. Here are the top 25

1 Willie Mays  197.0106
2 Rickey Henderson  174.8769
3 Barry Bonds  150.7554
4 Al Kaline  111.9025
5 Hank Aaron  103.7591
6 Roberto Clemente  90.52869
7 Kenny Lofton  87.87493
8 Jeff Bagwell  87.33088
9 Chase Utley  85.69787
10 Larry Walker  84.28949
11 Alex Rodriguez  82.69314
12 Albert Pujols  80.61014
13 Honus Wagner  79.79136
14 Eddie Collins  78.96287
15 Ichiro Suzuki  76.79083
16 Frank Robinson  76.45436
17 Carl Yastrzemski  73.22376
18 Jackie Robinson  72.24035
19 Ty Cobb  69.82541
20 Scott Rolen  68.84928
21 Max Carey  68.3932
22 Frankie Frisch  67.90673
23 Joe Morgan  65.48298
24 Ken Griffey2  65.37055
25 George Brett  65.01004

Click here to see the complete rankings

Wednesday, February 4, 2015

Using Runs Above Average To Determine The Best All Around Seasons (Part 2)

See Click here to read Part 1. I used the Baseball Reference Play Index and stats that measured batting, fielding and running. Balance mattered and I measured that with a geometric mean.

The new part here was to take all the the seasons with an all around rating of 10 or higher and see which players had the most. There have been 272 such seasons. A 10 would result if a guy had 10 runs above average in all 3 stats or any combination that resulted in 1,000 when they were multiplied by each other (the cube root of 1,000 is 10).

Here are the leaders in seasons with a rating of 10 or higher.

Willie Mays  12
Rickey Henderson  9
Al Kaline  7
Barry Bonds  7
Alex Rodriguez  5
Hank Aaron  5
Albert Pujols  4
Carl Yastrzemski  4
Chase Utley  4
Eddie Collins  4
Frankie Frisch  4
Jackie Robinson  4
Joe Morgan  4
Roberto Clemente  4
Ty Cobb  4

It seems like all these guys were or will be (or could have been except for suspected PED use), first ballot Hall of Famers except for Utley (it is also hard to tell with Frisch but it did not take long for him to get in). Maybe he should be, too. His WAR credentials are pretty good. He is 111th in career WAR among position player and had 5 straight years in the top 3 in the NL. He ranks 13th among 2Bmen right now. With 5.4 more WAR, he would crack the top 10. And his all-around ability shows he might have excelled in any era.

Now getting to Willie Mays, who is often said to be the greatest all-around player ever, he has a significant lead over Henderson and Henderson did go over 10 in 1981, a strike year of about only 108 games. Henderson had about 7.5 in the 1994 strike season and that might pro-rate to at least 10. But even so, Mays is still 2 ahead.

Here are all the guys who had 3 seasons of a 10+ rating. There are not many of those either, so what Mays did is pretty incredible.

Brian Jordan  3
Cal Ripken  3
Carlos Beltran  3
Duke Snider  3
George Sisler  3
Honus Wagner  3
Hughie Jennings  3
Ichiro Suzuki  3
John McGraw  3
Ken Griffey  3
Kenny Lofton  3
Ross Barnes  3
Tim Raines  3
Willie Wilson  3

Technical note: This time I called up all the of the following seasons using the Baseball Reference Play Index:

Seasons with 10+ batting runs, 0.1+ fielding runs, 0.1+ base running runs
Seasons with 0.1+ batting runs, 10+ fielding runs, 0.1+ base running runs 
Seasons with 0.1+ batting runs, 0.1+ fielding runs, 10+ base running runs 


Friday, January 30, 2015

Using Runs Above Average To Determine The Best All Around Seasons

Using the Baseball Reference Play Index, I called up the best seasons in fielding (Rfield), base running (Rbaser) and batting (Rbat). But when I called up the leaders in one category, they also had to meet some minimum level in each of the other two stats (more details at the end of the post).

To rate "all-aroundness," I used a geometric mean. For example, if a player was 10 runs better than average in all three stats, I multiplied 10*10*10 = 1000. Then I took the cube root of that, which gives us 10. The geometric mean rewards balance, so a guy with 20 in all three stats is better than someone who had 100 in batting and just 1 in each of the other two.

Here is the top 25. It seems heavily weighted to 1980-2001 (15 cases) and it seems that base running usually had to be pretty good. There were only two seasons from 1911-1960. There were 8 cases from 1996-2001, by 8 different players.


Rank Player Rfield Rbat Rbaser Year Rating
1 Rickey Henderson 13.2 47.5 17.7 1985 22.30
2 Mike Trout 21 52.5 9.8 2012 22.10
3 Eddie Collins 24 33 9.9 1910 19.86
4 Rickey Henderson 24.1 32 10.1 1989 19.82
5 Joe Morgan 13.7 54.9 10.1 1975 19.65
6 Willie Wilson 23.9 18.6 16.5 1980 19.42
7 Rickey Henderson 18 41 9.3 1980 19.00
8 Willie Mays 15.1 54.5 8.3 1958 18.97
9 Willie Mays 16.8 53.5 7.3 1964 18.72
10 Rickey Henderson 16.1 61.5 6.1 1990 18.21
11 Craig Biggio 18.7 43.5 7.2 1997 18.02
12 Alex Rodriguez 15.9 58.1 6.1 2000 17.79
13 Barry Bonds 9.9 69.8 7.8 1996 17.53
14 Darin Erstad 28.8 35.3 4.7 2000 16.84
15 Ellis Burks 12.4 47.9 8 1996 16.81
16 Larry Walker 9.6 69.6 6.6 1997 16.39
17 Ken Griffey 32.3 39.8 3.4 1996 16.35
18 Carl Yastrzemski 23.3 69.4 2.7 1967 16.34
19 Willie Mays 19.9 55.2 3.9 1962 16.24
20 Frankie Frisch 37 23.1 5 1927 16.22
21 Ichiro Suzuki 15.2 29.9 9.4 2001 16.22
22 Lenny Dykstra 25.4 29.2 5.7 1990 16.17
23 Hank Aaron 23.4 43.9 4.1 1961 16.14
24 Carl Yastrzemski 24.7 47.3 3.6 1968 16.14
25 Al Kaline 29.2 39.3 3.6 1961 16.04


Click here to see the complete rankings. After the top 50 or so, you might start to see duplicate entries. That is because as I called up these lists, some cases appeared on both of them and then I merged them all together and sorted them to get the ranking.

Criteria:

Seasons with 44.1+ batting runs, 0.1+ fielding runs, 0.1+ base running runs (197 cases)
Seasons with 0.1+ batting runs, 17.9+ fielding runs, 0.1+ base running runs (198 cases)
Seasons with 0.1+ batting runs, 0.1+ fielding runs, 5.8+ base running runs (190 cases)
Seasons with 30+ batting runs, 3+ fielding runs, 3+ base running runs (161 cases)


Sunday, January 25, 2015

Introducing A New Stat: Weighted Gray Ink (WEGRI)

Like we need another one. Maybe this will secure my sabermetric legacy. Well, Larry Granillo did something like this back in 2009. Click here to see it. But I did something similar back in 2006 and mentioned it on the SABR list. Someone (Rosen380) also just mentioned it in a discussion at Tango's blog. Click here to go to it.

The idea is a point system based on finishing in the top 10 in a stat. A guy gets 10 points for 1st place, 9 for 2nd and so on. Ties split the difference. If you are tied for 1st you get 9.5.

The stat I used is TRAA from Lee Sinins (Total Runs Above Average). Click here to read what Sinins has to say about this. That combines RCAA or runs created above average with FRAA or fielding runs above average. RCAA is park adjusted. I called up all the top 10 lists for the AL & NL (it goes back to 1893). Then summed each guys's points and ranked them. Here is the top 25:

Rank Player Points
1 Barry Bonds  149.5
2 Ty Cobb  148.5
3 Tris Speaker  143
4 Babe Ruth  142
5 Willie Mays  136.5
6 Ted Williams  136
7 Stan Musial  132.5
8 Hank Aaron  128.5
9 Honus Wagner  120
10 Rogers Hornsby  118.5
11 Mel Ott  113
12 Mickey Mantle  111.5
13 Lou Gehrig  104
14 Mike Schmidt  102
15 Nap Lajoie  97
16 Albert Pujols  94
17 Rickey Henderson  88
18 Frank Robinson  86.5
19 Jimmie Foxx  84
20 Joe DiMaggio  77.5
21 Ed Delahanty  77
22 Johnny Mize  76
23 Eddie Mathews  71.5
24 Paul Waner  69.5
25 Elmer Flick  68.5

Click here to see the complete rankings. It might be useful to take into account a player's position. For example, Piazza is the highest ranked catcher at 109.

Here are some interesting tidbits:

Ted Williams could have been first but he missed so much time in military service. Of course, Ruth would do better if I included his years as a pitcher.

Elmer Flick at 25th. Wow. So guess who is 26th? Keith Hernandez. Joe Jackson is 40th despite being banned at age 30. Todd Helton is 41st. And that takes park effects into account.

Tim Raines is 47th and is having a hard time getting into the Hall of Fame. Edgar Martinez is 49th, despite being mostly a DH.

54-56: Jimmy Sheckard, Sherry Magee, Gavvy Cravath.

Charlie Keller-60, Joey Votto-62. George Foster 68. Roy White 76.

Jackie Robinson is 79th and only played 10 seasons.

There are a total of 819 players listed so you can check to see how your favorite did.

Saturday, January 24, 2015

The Base in Baseball (sabermterics from 1935)

This is a very early kind of sabermterics. It was from Esquire in 1935. It is kind of like run expectancy. Baseball Think Factory has had it up on their site for many years. I am posting this in case anyone has missed it and is interested. Click here to read all of it.

Excerpt:
"We worked out a system with the base as a unit.  We gave the batter credit for the number of bases he achieved for his team, compared to the number of bases it had been possible for him to achieve.  If he came to bat with no one on base his “possible” was four bases. If he singled, then, he got credit for 1 base—.250; if he hit a home run he earned 4—1.000.  If there were men on base he got credit for the bases he advanced them—a homer with the bases full would give him 10 bases (count it for yourself) out of a possible ten.  We were actually measuring a player’s performance in realistic terms, as accurately, we thought, as figures could do it."