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Friday, January 24, 2003

1871 National Association

This will be the first recap of a 19th Century season. Besides baseball-reference.com my main sources will be The Stats All-Time Handbook, The Stats All-Time Sourcebook and The Great Encyclopedia of the 19th Century Major League Baseball.

To save space, I’ll post the standings here, commentary inside the thread.

I’ll be presenting two sets of standings, the first, the games as they were played. The second set will show what the standings would have been over a balanced schedule, with the aim for somewhere between 154 and 162 games where possible.

I have a complex set of formulas that adjusts for the unbalanced schedule. I don’t want to get into too many details here, but I adjust each team’s skill rate based on schedule strength.

Then I prove out the actual W-L record to within .05 for each team (in most cases) using the actual schedule, and the formula for W-L between two teams A and B: (WpctA*LpctB)/((WpctA*LpctB)+(WpctB*LpctA)). I plug that formula in for every combination (multiplied by actual games played), and prove out the records. With wacky schedules sometimes the numbers have to be manually tweaked, but that just improves the accuracy. I’ll send you the spreadsheet if you have any interest in the gory details.

Once that is done, the sheet computes a second set of standings based on a balanced schedule. Since there were 9 teams in the 1871 NA, I had each team play each other 20 times (160 game season). I take one final step of rounding up enough teams to make the standings ‘add up’. Sometimes due to rounding, the whole league comes out 1001-999 or something when you add up the rounded numbers. So I find the team over .5 by the least and round them down instead of up (or vice versa if the league is 999-1001). It’s just for appearances, that’s all. The PCT is based on the actual numbers of adjusted wins and losses, as many decimals as excel calculates.

Since we care about individuals more than teams for this exercise, once we get the Win Shares spreadsheet adjusted for 19th Century purposes, I’ll be computing adjusted NA Win Shares based on the second set of standings (adjusted to 162 game seasons of course), so we account for unbalanced schedules. It’s especially important, with the short, haphazard schedules, to remove this bias.

One other note on the 1871 NA. Rockford’s manager/catcher Scott Hastings played with New Orleans over the previous winter to earn some extra \$\$. On April 16, New Orleans played Chicago in an exhibition game (this was before the first NA season opener).

There was a rule to discourage revolving, a player under contract with one team could not play for another team for 60 days after his last game. Even though New Orleans wasn’t in the NA, all other teams protested, and all Rockville wins prior to June 16 were forfeited to the teams they beat. This gave Philadelphia two extra wins and the ‘pennant’. The standings below give Rockford back those 4 wins, so they differ from those shown on Baseball Reference, and make the league more reasonable from top to bottom. The best teams were as good (relatively) as the 2001 Mariners, the worst were a little worse than 1998 Marlins, but that’s about the range. There was no one as bad (relative to the league) as the 1899 Spiders here.

Here are the results (the actual standings only include games actually played, no forfeits):

```Actual Standings*:              Adjusted Standings:
W    L    PCT   GB                  W   L  PCT  GB
Chicago       19    9   .679  — Chicago       113  47 .704 —
Boston        20   10   .667  — Boston        108  52 .676   5
New York      16   17   .485  5.5  New York       79  81 .492  34
Washington    14   16   .467  6.0  Washington     77  83 .482  36
Troy          12.2 15.8 .436  6.8  Troy           70  90 .438  43
Fort Wayne     6.8 12.2 .357  7.8  Fort Wayne     55 105 .344  58
Cleveland     10   19   .345  9.5  Cleveland      54 106 .341  59
Rockford       8   17   .320  9.5  Rockford       51 109 .319  62
```

*see posts 6, 8 and 10 for explanation of Troy and Fort Wayne’s records

You can see that Philly and Chicago both played pretty tough schedules (their adjPCT is .026 higher than actual) while Boston didn’t. In reality, Chicago probably would have won the pennant if it wasn’t for The Fire (see discussion). Boston would have won if it weren’t for an injury that cost George Wright half the season.

There’s more, including a Silver Slugger team in the discussion portion.

The Philadelphia Athletics, managed by pitcher Dick McBride won the ‘pennant’ with a 21-7 record, defeating the Chicago White Stockings (19-9) and Boston Red Stockings (20-10) by 2 games.

This was not without controversy though. Based on the Hastings issue mentioned above, I’d be willing to say that there should have been a 3-way tie for the pennant.

Chicago jumped to the early lead, winning their first 7 games. Their first loss was to the New York Mutuals, who moved into first and then tanked, to the point where there were rumors of them throwing games.

The Chicago Fire destroyed the team’s stadium October 8. They finished the season on the road and lost their final 3 games and the pennant (although they truly fell into a tie, the Rockford forfeits counted in the official standings). The clincher came on October 30, the last day of the season, when they lost 4-1 to Philly in Brooklyn.

Ft. Wayne folded in late August, which is why they only played 19 games. In the official standings (but not counted on baseball-reference), their last 9 opponents were given wins, fortunately for the pennant race Philly, Chicago and Boston each received 1 win.

The offensive star of the season was Philadephia 3B Levi Meyerle, who hit .492/.500/.700, leading the league in all three categories. He also led the league in OPS+ at 241. His team also played the toughest schedule in the league, so there isn’t any issue there. According to Baseball Reference, the park factor was 99.

A Silver Slugger team (no clue about defense yet):

1B - Joe Start (NY) .360/.372/.422 (age 28)

2B - Ross Barnes (BOS) .401/.447/.580 (age 21), split season between 2B and SS. One might move Barnes to SS and put Jimmy Wood (CHI) who hit .375/.425/.563 in the 2B slot.

SS - George Wright (BOS) .412/.453/.625 (age 24), played just 16 games (84 in 162 game season) but he was incredible. John Bass (CLE) hit .303/.326/.640 and led the league with 10 triples, but only played the equivalent of 123 games. Could go either way here.

3B - Levi Meyerle (PHI) .492/.500/.700 (age 25); Ezra Sutton (CLE) hit .352/.357/.555 but Meyerle’s incredible year leaves him off the team.

LF - Steve King (TRY) .396/.400/.549 (age 29).

CF - Dave Eggler (NY) .320/.338/.408 (age 20).

RF - Lip Pike (TRY) .377/.400/.654 (age 26).

C - Cal McVey (BOS) .431/.435/.556 (age 20).

Troy’s pitching (most likely defense) was awful, worst in the league, so King and Pike might not be deserving if this were an “All-Star Team” instead of a “Silver Slugger Team”. Fred Treacy (CHI) played LF for the best team in the league and hit .339/.349/.573, and he led the league with a .918 FPct in the outfiled, so he could be a better choice than King for an all-star team, but Chicago was a hitters park before it burned down, so I went with King as a hitter.

George Zettelin of Chicago led the league in ERA+ at 168, obviously I have no idea if that means anything. He was 3rd in the league with .82 K/9 IP and he led the league with just .93 BB/9 IP. Al Pratt from Cleveland led the league with 1.36 K/9 IP (and 34 K) and and was 4th with a 110 ERA+.

Let me know what else you’d like to see. It took quite a few hours to write this up, so 1 per day was probably overreaching a little, but I’ll try my best here, and things will move faster once we get to 1876, when I can just post the Stats All-Stars, etc.

Joe Dimino Posted: January 24, 2003 at 05:35 AM | 30 comment(s) Login to Bookmark
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1. MattB Posted: January 24, 2003 at 04:02 PM (#511520)
"Fred Treacy (CHI) played LF for the best team in the league and hit .339/.349/.573, and he led the league with a .918 FPct in the outfiled, so he could be a better choice than King for an all-star team, but Chicago was a hitters park before it burned down, so I went with King as a hitter."

An important word about "park effects" as reported in b-r.com for NA teams. and why they may not be accurate, especially for Troy:

In the NA, there was no standardized ball, and a number of manufacturers made varying degrees of "live" and "dead" balls over the years. Now here's the catch -- the visiting team would generally supply the ball!

So, if your team favored the dead ball approach to hitting, you'd use the weak, soggy ball in all of your road games, and a mix of balls in your home games (as selected by your opponents). That could make your home park seem to favor hitters even if it didn't. Conversely, Troy in particular was famous for using a "live ball" on the road, effectively bringing the mountain (a 19th Century Rockie Mountain Coors Field) to Muhammed.

An increase in road scoring due to a "live ball" on the road essentially can work to counteract any actual park factor. (If you score more on the road, your home park factor goes down.) It is only conjecture, but why would a team want to increase scoring on the road, unless to try to recreate an offense-friendly home park?

Of course, the sample sizes are small, but most Troy regulars had sizeable drops in OPS+ when they went to other teams (there are only two data points for pitchers). This indicates that the hitters and pitchers were getting credit for a neutral park, when in fact they were likely both playing at a hitters park at home, AND taking a hitters park (live ball) with them on the road.

I find this explanation convincing, and discount Troy offense accordingly. Lip Pike hurdles even the higher bar, but I would give the LF Silver Slugger to Treacy.
2. robc Posted: January 24, 2003 at 11:23 PM (#511523)
I was unfamiliar with Levi Meyerle. I looked him up on b-r.com. Very interesting. Ichiro! is currently #4 on his comp list. He has effectively 2 full seasons of play over his 8 seasons, with an 164 OPS+.
3. jimd Posted: January 25, 2003 at 12:15 AM (#511524)
You forgot one position Joe. Otherwise, great job.

P - Rynie Wolters (NY) .370/.412/.543 (age 28)

His OPS+ (182) puts him in the middle of this list (ahead of CF, LF, 1B, and C). (Note that OPS+ will have the same problems as ERA+ noted by MattB.)
--------------
Eggler vs Hall

CF - Dave Eggler (NY) .320/.338/.408 (age 20). FPct .910 RF 2.76
CF - George Hall (Was) .294/.333/.404 (age 22). FPct .913 RF 2.97

Pretty close. Eggler is 2 years younger so you might project him to have a better career. However, Eggler, like Barnes, seems to have been affected by the fair/foul rule change in 1877. OTOH, Hall was severely affected by the Louisville scandal in 1877 (he was banned for life).
--------------
The fair/foul rule: during these early years, whether a ball was fair or foul was determined solely by where the ball landed. No doctored infields, no waiting for the ball to roll foul, no blowing the ball foul. If it landed fair, it was fair, even if it immediately bounced or rolled foul.
--------------
The "Hastings affair" was not resolved until a league meeting after the season ended (in Philadelphia). Because of this nobody knew what the "real" standings were, who was in first, or who really won until then. It's a wonder the Association survived it. (Then again, nothing like a little controversy to stir up interest.)

4. jimd Posted: January 25, 2003 at 04:28 AM (#511525)
Joe, there are 4 different kinds of forfeits in the 1871 season:
a) the four games that Rockford won but were later declared forfeits due to the ineligible player
b) the eight games that Ft. Wayne did not play because they folded
c) one game by New York to Boston on Oct 16, apparently considered as "not played"
d) one game by Ft. Wayne to Troy described here which is counted as a win for Troy in your actual standings, though they were losing before the forfeit was declared.

Considering how much impact a win has on the adjusted standings, this may not be appropriate.

Considering how much consideration the members of the Ft.Wayne and Troy teams will get for the HOM, this may not be worth bothering with. (I suppose it does impact Bobby Mathews...)

5. Tangotiger Posted: January 26, 2003 at 08:50 PM (#511526)
Mark makes an excellent point regarding regression towards the mean.

If the intent is to put things on a "160 scale" so that things have some meaning, that is fine, and you don't need to regress. However, if you are going to be using this as REPRESENTATIVE of what actually happened over 30 games, then you must regress. Not should, but must.
6. Rob Wood Posted: January 29, 2003 at 09:08 PM (#511529)
Based upon a simulation I just performed (using the per inning runs scored distribution generated from TangoTiger's program), I find that a team leading 6-3 after 6 innings in 1871 could be expected to go on to win that game 78% of the time.

Regarding the regressing to the mean issue, we have to be careful here and think about what we are trying to accomplish. For 19th century team records, I don't think it matters for the Hall of Merit discussions. The main purpose is to translate team records into the more familiar 162-game schedule. I like that idea. In addition, we know that leagues were much more unbalanced back in the early days, so the degree of regression to the mean that would be appropriate in the 1970's is not germane to the 1870's.

For players, the Shane Spencer example is not compelling. Our main purpose is to "uplift" players' contributions in shorter seasons to be placed on equal footing with modern day 162-game season players. (A pennant is the equalizer.) That is, we are not taking a 30-game partial season of a player just up from the minors and before the league figures out how best to pitch to the rookie and extrapolating up to 162-games. That would be dangerous.

Instead, we are taking the complete full-season accomplishments of all the league's players and "uplifting" them to a 162-game statistical basis. There is an important distinction between the two.

Anyway, just doodling awhile ago I wrote a post to one of these threads that suggested that the appropriate "regression to the mean" adjustment would be quite small in these cases. The basic reason is that the basis for the uplift is plate appearances, not games played, so that even in seasons of only 40 games, the regular players are apt to accumulate far more than 100 (even 200) plate appearances. By my reasoning, there is not much need to "regress" downward achievements over that many plate appearances. I cannot find the post right now, but I think my back of the envelope estimate was for something like a 3% discount. Probably not even worth doing in most cases. Any quality of play adjustments (league-wide) would be far greater than these player regress-to-the-mean adjustments.
7. jimd Posted: January 30, 2003 at 01:59 AM (#511530)
How does "regression to the mean" apply to the extrapolation of these W-L records? Or, more precisely, how do we calculate that mean so we can regress to it?

I can see how, today, a team with an 0-11 start would be projected to play more like their record of the preceding year or two.

But that wouldn't apply in this era. In 1872 the Washington Nationals (different team from the Olympics of 1871-2) started 0-11 and then gave it up. They had paid their money to join (\$10 entry fee) and then discovered they were over their heads. I can see no reason for presuming that this team could play .500 ball or even play at "replacement level" for the rest of the season. Maybe at their pythagorean level (.150). Any argument for them being better than that would have to be based on analyzing the individual players and determining that they collectively stunk compared to the rest of their careers.
8. MattB Posted: January 30, 2003 at 09:13 PM (#511532)
"Let's say that the 2003 Phillies start out 19-9, while the 2003 Mets start out 16-17. That's a 5.5 game difference over ~30 games. When both teams complete the 162 game schedule, what's the likelihood that Philly ends up 34 games ahead? Obviously, that's not easy to calculate since we don't know the true ability of the Phils, but based on historical evidence, we'd think it's not very likely at all."

But that is not what Joe is trying to show with his extrapolations.

What he is showing is that, for Philadelphia to go 19-9 in 1871 was equivalent in VALUE to a team going 113-47 today. Not that they would have actually done so.

Assume that, for 2004, the NFL expands to a 160 game schedule. Three of four quarterbacks are needed to play every day, rosters expand, etc. Teams that used to go 12-4 no longer have a chance to got 120-40 because of the grind of the season.

Someone in the future may try to project the Eagles' 12-4 season and say that, over 160 games, they would have gone 120-40. That would be ridiculous. But, if the futuristic projector was merely trying to demonstrate how important a win was in 2002, then it makes sense to say, "A win back then is the same as ten wins now." A rusher who rushed for 1,000 yards in 2002 HELPED HIS TEAM AS MUCH AS a rusher who rushed for 10,000 yards in 2004 (even though no rusher would ever rush for 10,000 yards in one season.)

When measuring value, there is no need to regress, because the value of the contributions are directly proportional. A pitcher in 1871 was much more valuable than a pitcher in 1971, even if he wasn't nearly as good.
9. Marc Posted: January 31, 2003 at 02:46 AM (#511534)
With all due respect to all participants in this discussion, and especially to Joe who is doing all the work and I am doing none....

But with all due respect I think the point is to have a HoM vote sometime before we all die. Maybe year by year summaries are not necessary to this venture...?
10. John (You Can Call Me Grandma) Murphy Posted: January 31, 2003 at 10:08 PM (#511538)
We are VERY (2-3 weeks?) close to having NA Win Shares, with several modifications that will help to resolve many of the issues people have with Win Shares in general. I really think this would add a lot to the discussion.

Will Win Shares be computed for every player or only for selected ones?
11. jimd Posted: March 13, 2003 at 01:45 AM (#511539)
From a cached page at www.google.com:

"Among the number of Lansingburgh Union players who joined the National Association's Haymakers was a third baseman named Esteban Enrique "Steve" Bellan, a.k.a. "The Cuban Sylph." More than a half-century before Jackie Robinson broke baseball's color barrier, the Haymakers employed a Latino player in a league which otherwise was entirely lily-white. Steve Bellan, who was born in Havana, Cuba, was the first Latin player in professional baseball. He learned the game as a student at Fordham University and played well enough to join the Unions of Morrisania, one of the prominent organized teams around that time. Bellan played organized baseball in the United States for six seasons, four of them with the Lansingburgh Unions and the Troy Haymakers. During his tenure in the States, he played (primarily) third base and compiled a batting average of around .250. Returning to his homeland around 1873, he helped introduce the game to Cuba and, as a player-manager, led his Havana team to three league championships."
12. Paul Wendt Posted: June 27, 2004 at 05:48 PM (#701118)
Isn't this an awful way to organize information?
I will post this here and at 1927 Ballot Discussion.

In 1927 Ballot Discussion #1-48 (#643002) and passim, David Foss posted some batting data derived from Marshall Wright NABBP 1857-1870, for seven(?) star players and for the 1869 and 1870 seasons.

In #1-53, David referred to Athletics Reach & McBride. Later, he featured Al Reach but not Dick McBride (or I missed it).

Total Baseball 8 includes an article by John Thorn on the greatest player of all-time, historically considered. Based on email consultation several months ago, I expect that that article lists the five greatest players for each decade from the 1850s, and that Dick McBride is one of the five listed for the 1860s.
Right?

Dick McBride is one, maybe "the obvious" candidate for the treatment David Foss has given to other 1860s stars.
13. Paul Wendt Posted: June 27, 2004 at 05:56 PM (#701153)
McBride's personal decade overlapped 1871, perhaps 1866-1875 or close to that. In effect, 1865-1870 is often treated as a decade.

McBride was a top batter for a while, but was below average in the NAPBBP 1871-1875. I suspect that he could not hit a curve. (Maybe couldn't throw one.)
14. John (You Can Call Me Grandma) Murphy Posted: August 06, 2004 at 05:46 PM (#781344)
This thread is fully restored now.
15. Paul Wendt Posted: August 06, 2004 at 09:53 PM (#781968)
I wrote:
Total Baseball 8 includes an article by John Thorn on the greatest player of all-time, historically considered. Based on email consultation several months ago, I expect that that article lists the five greatest players for each decade from the 1850s, and that Dick McBride is one of the five listed for the 1860s.
Right?

That is, I haven't seen TB8, so I know of this article only from some advance discussion with author JT.
16. Paul Wendt Posted: May 04, 2006 at 11:50 PM (#2004374)
.
135 years ago today the National Association of Professional Base Ball Players or "professional association" opened its first championship season at Fort Wayne, Indiana. This was the first Major League game by the most common unofficial definition of major league baseball (and the one used by the official encyclopedia before 1969).

Read about the game, with retrosheet-standard play by play and box score.
1stGame by retrosheet

The Kekionga club of Fort Wayne defeated the Forest City club of Cleveland 2-0, which would be the lowest score of the entire season. Cleveland catcher Deacon White, now enshrined in the Hall of Merit, led off with a double but Bobby Matthews escaped that inning and completed a 4-hit shutout. Another honoree, Ezra Sutton fielded third and batted seventh for Cleveland.
17. Paul Wendt Posted: May 05, 2006 at 12:02 AM (#2004409)
Sigh. At least I have occasion for another 1871 article:
make that Bobby Mathews
18. Mark Shirk (jsch) Posted: May 05, 2006 at 12:10 AM (#2004431)
Wow, the NA and I have the same birthday! I knew there was a reason I loved this game.
19. Paul Wendt Posted: May 05, 2006 at 12:16 AM (#2004445)
In 1871, no one was permitted to play for two NA clubs.
So it is straightforward to calculate the share of one full season played by each player.

We have two-team players beginning in 1872, with big differences among teams in the number of games played, the biggest between teams that go out of business mis-season and those that complete the season. Does anyone have a suggestion for measuring full seasons played in these conditions?

For example, Forest City of Cleveland played its last game August 19, and 0514 to 0819 is the span played by both White and Sutton. Captain Scott Hastings, on the other hand, played 0514-0819 with Cleveland and then 0829-1031 with Baltimore. Twelve people played for two teams.
20. Paul Wendt Posted: May 05, 2006 at 12:50 AM (#2004549)
Wow, I can't post two successive articles even here on a long dead thread!
--

Howie Menckel closes his annual analysis of HOM members by fielding position with this note, quoted from 1976 Ballot Discussion #40.
P.S. I'd be open to 'improvements' on numbers for McVey/Sutton/Ruth/Caruthers types, and all Negro Leaguers.

Howie means the seriously multi-position player-careers. The reason I don't have a "program" to pro-rate season statistics (a more basic problem) is that I have no solution for the multi-team player-seasons --crucial at least where length of season is seriously variable by team. That problem in turn is most serious for the NA and 1884, 1890-1891. Team games played is otherwise relatively uniform within each league-season, and team games played to a decision (for you Win Shareholics) more uniform yet.
21. Brent Posted: May 05, 2006 at 03:22 AM (#2004892)
Deacon White, catcher for Forest City of Cleveland, made 9 putouts--all on foul pop-ups! I remember Bill James commenting that fouls pop-ups have continuously decreased throughout the history of baseball, but I don't recall if he gave a reason.
22. Joe Dimino Posted: May 05, 2006 at 10:28 AM (#2005047)
Paul, what I'd do is combine them.

Figure out how many games were available to be played by the player.

Hastings played every game for Cleveland.

He played 13 for Baltimore. If Baltimore played 13 games from 8/29-10/31, I'd give him credit for 1.00 seasons.

If they played 18 games and he only appeared in 13, I'd give him credit for 35/40 or .875 of a season.
23. Joe Dimino Posted: May 05, 2006 at 10:32 AM (#2005049)
Brent, James hasn't said this but at least in the 19th Century, didn't most catchers play way behind the batter, as opposed to crouched in right behind him?

If the catcher is only half-squatting a few feet back, some of the 'line-drive' fouls back behind the plate are going to be caught, wheras, now those plays are impossible to make.

I'd imagine that has to have at least something to do with it.

Also, at least through 1920, guys weren't hitting the ball nearly as hard as they do now. Bigger, heavier bats, mushier, deader baseballs - that would mean many more 'soft pop-ups' behind the plate that wouldn't even make it to the stands or get very high in the air, etc..

Also, how often has the distance from home plate to the backstop changed. Did they even have backstops way back when? More foul territory behind the plate - more foul pop-ups to catch.
24. Joe Dimino Posted: May 05, 2006 at 10:35 AM (#2005050)
Also, I would think runners were more aggressive back then which means more runners thrown out at the plate. Have outfield assists been declining also?
25. Howie Menckel Posted: May 05, 2006 at 11:45 AM (#2005065)
Well, my issue with guys like McVey and Sutton is that my pcts reflect actual games played. But since the season lengths varied so much and they kept changing positions, it probably makes more sense to call 'a season a season,' and weigh each equally.
So 4 seasons as a 3B and 3 seasons as a C count as 57 pct 3B and 43 pct C.
Except they split positions in those years too, so it's back to square one.
26. Paul Wendt Posted: May 05, 2006 at 03:10 PM (#2005214)
> Deacon White, catcher for Forest City of Cleveland, made 9 putouts--all on foul pop-ups!

That is nine foul fly outs and bound outs (caught on the first bounce), which retroscoring does not distinguish.

> some of the 'line-drive' fouls back behind the plate are going to be caught,
> whereas now those plays are impossible to make.

Under the foul tip rule (today or a century ago), the batter is not liable to be put out by the catcher on a foul "line drive" except with two strikes, when it is simply strike three not a fly out. In 1871, every ball off the bat is a fly, and then a bound after its first bounce, with the batter put out by any catch.
27. DavidFoss Posted: May 05, 2006 at 03:19 PM (#2005224)
bound outs (caught on the first bounce)

Wow... I did a double take on this one and had to look it up. They got rid of this rule for fair balls in 1865, but kept it for foul balls until 1883.
28. Paul Wendt Posted: May 05, 2006 at 03:20 PM (#2005228)
> Paul, what I'd do is combine them.
> Figure out how many games were available to be played by the player.
. . .

How many games were available to White and Sutton?
Did they play 60% of a full season in 1872?
Or did they play 100%, a greater share than Hastings?
29. Joe Dimino Posted: May 06, 2006 at 01:59 AM (#2006456)
Paul, if Sutton and White only played for Cleveland (too lazy/busy to look it up) and played all of their games, I'd call it a full season.
30. Joe Dimino Posted: May 06, 2006 at 02:02 AM (#2006474)
Howie - KJOK and someone else helped out awhile back when I was setting up Win Shares spreadsheets, with splitting out the portion of each season played by players at each position. I don't have them handy now, but if I remember, I'll try to get them to you.

Basically if player X played 45 games of a 50 game season, and 25 at 2B and 20 SS, I'd give him .50 seasons at 2B and .40 seasons at SS. For games where he switched positions, say it's 45 games 30 at 2B and 20 at SS, I'd take the 5 'double' games and split them 2.5/2.5. So it'd be 27.5 at 2B and 17.5 at SS, or 55% 2B, 35% SS.

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