Marinomics: A Dismal Baseball Science

Are old teams peering over the edge of a cliff? Are young teams positioning themselves for future success?

For this, I used essentially the same data set from yesterday's post, but did not include data from 2001, 2002 or 2003. Each team has a winning percentage, percentages of playing time allotted to each age group (Young, Prime, PostPrime, Old) and now I added the team's winning percentage in each of the following 3 years. The following table is how each age category is correlated with the winning percentage in the present year and each of the following 3 years, or "what can today's age structure tell us about tomorrow?"

		Present	1Year	2Years	3Years

Young		-0.234	-0.072	+0.030	+0.061

Prime		-0.014	-0.047	-0.061	-0.057

PostPrime	+0.184	+0.103	+0.037	+0.006

Old		+0.121	+0.040	+0.000	-0.011

Two things are not terribly surprising: 1) most of these correlations are very, very close to zero, and 2) the direction of the correlation for playing Young or Old players switches.

To answer the questions I posed above:
Are old teams peering over the edge of a cliff? No, they aren't. Are young teams positioning themselves for future success? It's barely there, but moreso than any other category.

The other thing from the data is year to year correlation, or "what does today's performance say about tomorrow?":

	CurrentWin%

1Year	+0.544		

2Years	+0.422	

3Years	+0.332

The proper interpretation of this would be "the amount of variance in the winning percentage X years in the future explained by today's winning percentage." So, I would add to the answer to the first question by saying that if an old team is kind of lousy, they are probably going to be kind of lousy next year. And probably the year after that, too. But it works the other way, too.

An early Bill James study showed how successful teams tend to display certain age patterns. Dividing players into three piles chronologically by age: young, prime, old (my words, not his...I can't lay my hands on the study at the moment, but if I can I'll come back with a full citation), you can look at a team's distribution of each age bracket. Successful teams tend to have a lot of prime talent, fewer older players, and a smattering of young players. It's not invariable that teams with this distribution succeed or teams without it don't, but there's a strong correlation.
Management by Baseball

Intrigued by this and having a large database and my fingers, I decided to do something a little different. Right now I am more interested in examining the structure of teams than their relative success or failure.

For age categories, I used the same brackets used in this Hardball Times article.
Young: Age 25 and under
Prime: Ages 26 to 29
Past-their-Prime: Ages 30 to 34
Old: Age 35 and over

Data was from 1950 forward and, to get an idea of the percentages given to each age bracket, I used at bats and innings pitched. I'm not completely uninterested in success and failure:

How is playing time for each category

correlated with a team's winning percentage?



		Batting	Pitching

Young		-0.232	-0.168

Prime		-0.061	-0.098

PastPrime	+0.190	+0.124

Old		+0.143	+0.207

The significance on these is okay (owed mostly to a large sample size), but I do find it disconcerting about that the Mariners basically started this season with a team that fits into either past their prime or just plain old. It was obviously intentional to acquire those players, but I restate my earlier query: was it intentional to have the team be that old?

But here's a thought: Has the age structure of a team changed over time?

And the answer is: no, not really. From year to year, it just doesn't jump around much. The average percentage of at bats or innings pitched given to each category since 1950 is:

		Batting	Pitching

Young		0.226	0.255

Prime		0.464	0.445

PastPrime	0.221	0.200

Old		0.089	0.010

It will vary substatially from team to team, though. For comparison's sake, the 2003 Mariners:

		Batting	Pitching

Young 		0.003	0.313

Prime 		0.477	0.370

PastPrime	0.244	0.047

Old		0.276	0.270

And the team with the age distribution most dissimilar from the average: your 1985 California Angels

		Batting	Pitching

Young		0.107	0.539

Prime		0.250	0.076

PastPrime	0.048	0.210

Old		0.596	0.175

Sixty percent of their at bats whent to old guys (like Rod Carew and Reggie Jackson) while 54% of innings pitched went to young guys (like Mike Witt and Kirk McCaskill).

Forthcoming: can an age distribution of a team tell us anything about the future performance of a team?

As Seattle baseball fans wipe the blood from their shirts after their traditional, fierce interleague dogfight with the Padres, I thought it was a good time to look at some interleague attendance figures.

Major League Baseball averaged 31,034 fans per game during Interleague Play, a period covering 19 days and 250 games. Average attendance was 20.1 percent greater than the intraleague average.
MLB Press Release, June 30, 2003

Last season [2003], Major League Baseball averaged 31,112 fans per game during Interleague Play, a period covering 249 dates and 252 games, and that was 12.4 percent greater than the 2003 intraleague average.
June 7, 2004 - Mark Newman / MLB.com

Using the second figures, since it was released later and I assume it's more reliable, it implies that 27,254 fans show up the intraleague games, giving the edge for interleague is 3,858 per game. At roughly $20 a ticket, we're looking at an extra $75-80,000 per game in ticket revenue alone (before the nominally priced concessions and the TV revenue).

But I noticed last week that the M's are in a stretch of games that flip flops inter/intraleague - where interleague is on the weekend. Weekend games draw more fans. Is this showing up/clouding their numbers?

Can multiple regression save us?

Data: I wrote a program to collect and parse ESPN's schedule data from 2002 and 2003. I checked to make sure it was parsed correctly and appended the the attendance data with several pieces of data: 1) average home attendance in that year, 2) away team's attendance in % of capacity * stadium capacity, 3) weekend (dummy), 4) interleauge (dummy) and 5) weekend & interleague together.

There were 4,788 games that were used (some games didn't have attendance data).

Results:

		Coeff	StdErr	t	P

Intercept	-8908	598.8	-14.9	5.57894E-49

WEEKEND		6155	204.0	30.16	0

INTER		951.6	531.1	1.792	0.073226724

INTER-WEEK	2513.9	661.9	3.798	0.000147813

HOME		0.9755	0.0114	85.47	0

AWAY		0.2224	0.0199	11.19	9.83207E-29



R^2 = .66, SE of regression = 6,663

Everything is significant at the 0.0001% level except the normal interleague coefficient, which says that an interleague game during the week draws 952 extra fans over an equivalent intraleague weekday game. A weekend interleague would draw 951 + 2,514 = 3,465 extra fans over an equivalent intraleague weekend game.

Using those coefficients and this year's attendance data let's do a game:

SD @ SEA, this weekend:
Attend = -8908 + 6155 * (1 for weekend) + 951.6 * (1 for inter) + 2513.9 * (1 for week * inter) + 0.9755 * (35,104 SEA avg) + 0.2224 * (47,772 Safeco capacity * 70.7% SD away avg capacity) = 42,470

Actual SD @ SEA attendance = 43,649 (average for Fri/Sat/Sun was 41,280)

And let's do an average basis

The average stadium that a game has been played in is about 45,014 seats, with the home team filling 29,755 of them. Away teams average 65.4% of capacity filled.

So:
-if it's a weekend, an intraleague game has an expected attendance of 32,640. An interleague's extra 3,465 butts in seats is 10.6% higher.

-if it's a weekday, an intraleague game has an expected attendance of 26,485. An interleague game's extra 951 is only 3.6% higher.

Basically, I think the 12.4%/3,858 figure is too high. But I do think that baseball realized there is a real synergy in selling interleague games on the weekend.

The 2002 and 2003 data was mashed together. If I separate it out test for robustness...

		Coeff2002	Coeff2003

Intercept      -8989.3         -8813.8

WEEKEND		6020.6		6290.8

INTER		1806.1#		86.9#

INTER-WKEND	1929.7#		3105.1

HOME		0.9764		0.9747

AWAY		0.2256		0.2187



Every coefficient is significant at the 0.1% level except:

-2002 INTER  @ 0.2% level

-2002 INTER-WKEND @ 3.5% level

-2003 INTER coefficient is insignificant.

Two things to notice: 1) the regular interleague effect disappears while the weekend interleague effect goes up, but 2) the total interleague effect drops from ~3700 to ~3200.

Further stuff and issues to explore: more data for earlier seasons to test these effects over time and a stronger regression (include winning percentages of each team and time effects to pick up the first week and September pennant race effects). Questions: Is the interleague effect being pushed to the weekend, or is this anomalous - as in, has the "novelty" of it has worn off for people who are hearty enough to trek to games Monday through Thursday? Will the weekend interleague effect disappear, too?

While the Dodgers and Yankees are both going hard after Freddy Garcia, one GM on Monday said, "the reading we're getting is that the Mariners are not giving up on this season because of their fans. So (Seattle's trading of) Garcia may be a ways off."
Peter Gammons on ESPN, June 21, 2004

At some point, a bad team needs to look at where they are, what they have done, what other teams have done and decide if they need to give up on the season.

I took at the 2002 and 2003 seasons in the AL West. For each team in each season, a binomial distribution updates the 5th% and 95% critical levels given the number of games remaining and the winning percentage thus far (so each will converge to the final win total as the season progresses).

Here is the the 2002 AL West. The Y axis represents final win total, the X axis is the number of games played. Each team's final win total is represented by a straight line and each team's 95% percentile win total is represented by the more jagged line (95% is included because what we are interested in is the possibility that the M's somehow win a lot of games). Oakland = dark green. Anaheim = red. Seattle = blue. Texas = purple.



Notice that after about 70 games, Oakland's final win total was still underestimated even at the 95% level (you remember that 20 game win streak, right?) by about 5 or 6 games.

In 2003, there was no such surpise.



A very wishful thinking case right now: the Mariners win their 95% total and the other 3 teams only win their 5% total. You know what? The Mariners would still be in last place.

No, this is not a detailed analysis and it isn't particularly strong or meaningful statistics - I don't have the kind of time to dig up the data for that - but I do have time for...

Right now, after 72 games, the M's are 30-42, a winning percentage of .417 - which projects to 67.5 wins if they are actually a .417. What if the Mariners are actually a 90 win team that's been trapped in a much crappier team's body?

Sounds like a job for Monte Carlo simulation! 10,000 simulated seasons of a team that ought to win 90 games, please!

Results: The minimum number of games won at the 72 game pole is 24! That's good! Maybe they really are a 90 win team! But after 162 games the minimum is number of games won by a team that was supposed win 90 games was also 66 games. The maximum? 114. (If Howard Lincoln starts explaining to the press that this season is only the observed 2004 season and that in 9,999 other 2004 seasons that were not observed this team won, on average, 90 games - I will be first in line for 2005 season tickets).

The 90-win team that only won 30 games in their first 72 finished on average, with 80 wins (min of 68 and max of 89). If this seems generous, it's because the M's are probably not a 90 win team (though gamblers think they can win about 75, which is winning their remaining games at a 50% clip).

[For a diversion, how do the M's compare to the 50some out of 10,000 simulated teams that had 30 wins after 72 games? M's are in blue, simulated teams are in gray, average of simulated is in red and the 90% confidence interval is in red ]



But, given the Mariner's wins and losses through the season, how much do they actually look like a 90 win team (compared to all 10,000 simulated seasons)? Or, "how probably" are the M's a 90 win team?

Black line = win total of a 90 win team after X games. Blue line = win total of 2004 M's. Red line = probability of M's being a 90 win team (keeping in mind that at this point they would only be expected to win 80 games).]



Right now, the way the Mariners have played, there's about a 1% chance that they are a 90 win team. Hidden in that 1% is, given they are a 90 win team, the expectation will only actually win 80 games.

Is it time to give up on the season? If the thinking is that they'll somehow win 90+ games, then my vote is "Yes."

Yes, making an out while a runner moves along sometimes makes sense, but it does not always make sense (don't tell those fat cats at ESPN this). And this has been bitched about to death. But numbers? I want some numbers.

Below is a table that gives the values of sacrifice flies and other "productive outs" from several different sources of data on the expected number of runs scored, based on states. The Lindsey data is from a table in Curve Ball, which takes the data from the 1963 George Lindsey paper. Palmer is data from the Pete Palmer book "The Hidden Game", which was used in Gary Skoog's paper that appeared in the 1987 Bill James Baseball Abstract.. Albert is from "Hitting with Runners in Scoring Position", a paper by Jim Albert - author of Curve Ball.

A listing of productive out situations, listed by their value in increase (or decrease) in expected runs.

Init	Outs	Final	Outs	RunsIn	Lindsey	Palmer	Albert	Average

1st+3rd	1	2nd	2	1	+0.182 	+0.260 	+0.200 	+0.214 

Full	0	2nd+3rd	1	1	+0.340 	+0.117 	+0.170 	+0.209 

3rd	1	Zero	2	1	+0.122 	+0.198 	+0.160 	+0.160 

1st+3rd	1	1st	2	1	+0.104 	+0.121 	+0.120 	+0.115 

Full	1	2nd+3rd	2	1	+0.045 	+0.115 	+0.130 	+0.097 

2nd+3rd	0	3rd	1	1	+0.020 	-0.049	+0.180 	+0.050 

1st+2nd	0	2nd+3rd	1	0	+0.089 	-0.009	-0.070	+0.003 

Full	1	1st+3rd	2	1	-0.110	-0.052	+0.090 	-0.024

2nd+3rd	1	3rd	2	1	-0.205	+0.011 	+0.060 	-0.045

1st+3rd	0	2nd	1	1	-0.269	+0.060 	+0.060 	-0.050

3rd	0	Zero	1	1	-0.147	-0.028	-0.030	-0.068

2nd+3rd	1	2nd	2	1	-0.263	-0.023	-0.010	-0.099

Full	1	1st+2nd	2	1	-0.239	-0.089	+0.030 	-0.099

Full	0	1st+3rd	1	1	-0.105	-0.166	-0.040	-0.104

1st	0	2nd	1	0	-0.142	-0.084	-0.170	-0.132

1st	1	2nd	2	0	-0.201	-0.130	-0.200	-0.177

2nd	0	3rd	1	0	-0.214	-0.171	-0.170	-0.185

2nd+3rd	0	2nd	1	1	-0.289	-0.247	-0.080	-0.205

1st+3rd	0	1st	1	1	-0.442	-0.161	-0.110	-0.238

1st+2nd	1	2nd+3rd	2	0	-0.252	-0.227	-0.340	-0.273

1st+2nd	0	1st+3rd	1	0	-0.356	-0.292	-0.280	-0.309

2nd	1	3rd	2	0	-0.316	-0.317	-0.300	-0.311

Full	0	1st+2nd	1	1	-0.281	-0.366	-0.290	-0.312

1st+3rd	0	2nd+3rd	1	0	-0.380	-0.268	-0.300	-0.316

1st+2nd	1	1st+3rd	2	0	-0.407	-0.394	-0.380	-0.394

1st+3rd	1	2nd+3rd	2	0	-0.428	-0.427	-0.590	-0.482

(Lindsey puts a lot higher expected runs scored on the 1st+3rd and 2nd+3rd situations with no one or 1 out - between .2 and .3 runs higher than Palmer or Albert. Note: I excluded the 2 base sacrifice)

ESPN's formula:
What is a productive out?
A productive out occurs when ...
- A baserunner advances with the first out of an inning.
- A pitcher sacrifices with one out.
- A baserunner is driven home with the second out of an inning."

I don't have data on pitchers alone, but let's use the first and third possibilities in 2 ways: 1) straight average and 2) weighted average, by the probability that the initial state situation actually occurs (from Lindsey):

Baserunner advancing with the 1st out of an inning
1. Straight average. -.115 runs.
2. Weighted average. -.138 runs.

Baserunner driven home with the 2nd out of an inning:
1. Straight average. .040 runs
2. Weighted average. .053 runs

Both situations, combined
1. Straight average: -.068 runs
2. Weighted average: -.074 runs

Put simply, this statistic isn't adding anything meaningful to the understanding of the game. At best, it coutning a subset of sacrifice flies. At worst, it's counting plays that are actually harmful to run production on a probabilistic level and clouding one's perception of what's actually important. But you probably knew that. And people that do buy into 'productive outs' (calling something unproductive that you have little or no basis for calling 'productive' is a little backwards - like calling a 'late fee' or 'robbery' a 'free gift') have a weird relationship with statistics and sample sizes - especially those that are broadcasting baseball games in the Seattle market. For them, I'd recommend reading Curve Ball and a few other books.

I resent that "productive outs" is in bold on ESPN's stats page. But there's something that I find unfathomably hilarious...

ESPN data as of Saturday June 26

Winning %, Productive Out Ratio for Batting,

Productive Out Ratio for Pitching and the MLB ranks for each



Team		Win %	POPbat	POPpit	WinRk	PbRk	PpRk

NY Yankees	0.643	0.279	0.298	1	25	12

St. Louis	0.603	0.364	0.328	2	3	22

Texas		0.586	0.326	0.332	3	15	24

Boston		0.569	0.217	0.343	4	30	25

San Francisco	0.568	0.333	0.359	5	10	28

Minnesota	0.569	0.286	0.314	6	24	17

Cincinnati	0.562	0.255	0.308	7	28	13

Chicago Cubs	0.562	0.335	0.294	8	9	10

Oakland		0.556	0.225	0.317	9	29	19

Anaheim		0.548	0.313	0.259	10	17	1

Florida		0.534	0.307	0.310	11	19	14

Chicago Sox	0.529	0.289	0.325	12	23	20

San Diego	0.528	0.336	0.289	13	8	7

Philadelphia	0.521	0.331	0.362	14	12	30

Houston		0.521	0.331	0.293	15	12	9

Los Angeles	0.521	0.270	0.327	16	26	21

Milwaukee	0.514	0.308	0.274	17	18	3

Tampa Bay	0.500	0.328	0.291	18	14	8

NY Mets		0.493	0.295	0.360	19	22	29

Cleveland	0.486	0.323	0.275	20	16	4

Detroit		0.458	0.346	0.286	21	4	6

Atlanta		0.458	0.339	0.294	22	7	10

Baltimore	0.435	0.307	0.329	23	19	23

Toronto		0.438	0.300	0.314	24	21	17

Seattle		0.408	0.263	0.279	25	27	5

Kansas City	0.400	0.346	0.310	26	4	14

Colorado	0.389	0.341	0.352	27	6	26

Pittsburgh	0.386	0.373	0.352	28	2	26

Arizona		0.370	0.333	0.313	29	10	16

Montreal	0.338	0.394	0.272	30	1	2

Pearson correlations
Win% to POP-Batting: -0.436
Win% to POP-Pitching: +0.074

Spearman rank correlations
Win% to POP-Batting: -0.412
Win% to POP-Pitching: -0.173

The correlation is negative. As in, teams that are 'good' at making productive outs are 'bad' at actually winning games. They don't offer data on this for previous seasons, but I'd love to see it. Because my feeling is that these correlations are probably completely random and it's actually very close to zero when you have bigger samples.

Yes, it's beating a pretty dead horse to say the Mariners are old. Because they are. But you may not realize that this team is exceptionally old.

Source: Lahman database for years prior to 2004, ESPN.com for 2004 Mariners

Methodology: weighted average age of the lineup = sum(age of player * at bats)/sum(at bats)

Results:
2004 Mariners average age = 32.86 years

1950 to 2003 average age = 28.77 years (1,262 datapoints, std dev = 1.4 years)

Number of teams since 1950 older than the 2004 Mariners = 5

1982	Angels	32.96

1985	Angels	32.93

1998	Orioles	33.79

1999	Orioles	33.08

2001	D'backs	32.93





1977	SEA	26.63

1978	SEA	27.56

1979	SEA	29.31

1980	SEA	29.17

1981	SEA	29.39

1982	SEA	28.68

1983	SEA	27.30

1984	SEA	27.83

1985	SEA	27.70

1986	SEA	27.27

1987	SEA	27.43

1988	SEA	27.60

1989	SEA	27.22

1990	SEA	28.41

1991	SEA	28.57

1992	SEA	28.66

1993	SEA	28.46

1994	SEA	27.98

1995	SEA	29.23

1996	SEA	29.12

1997	SEA	29.68

1998	SEA	30.19

1999	SEA	29.84

2000	SEA	32.03

2001	SEA	31.84

2002	SEA	31.90

2003	SEA	32.47

Notice anything? Gillick GMed the 1998 Orioles. Hmmm... what about Gillick's Toronto teams?

		Age	Change

1988	TOR	27.77	

1989	TOR	28.23	+0.46

1990	TOR	27.34	-0.89

1991	TOR	27.92	+0.57

1992	TOR	29.83	+1.91

1993	TOR	29.86	+0.03

1994	TOR	30.04	+0.18

Only 13 times since 1950 has a team aged more than 1.9 years (the 1998 Baltimore team aged 1.6). Two of these are Gillick teams.

Also notice that from 1999 to 2000 there is an enormous jump in the Mariners age. The team's lineup aged over 2 years. This should seem pretty exceptional, since keeping the exact same lineup would make the team age only 1 year. In fact, only 2 teams have aged more in 1 off-season since 1950 - the 1957 Giants and the 1977 Rangers. A diversion to see where that age landed in the lineup:

	1999	2000	Change

C	31.56	32.65	+1.09 

1B	30.16	31.05	+0.89 

2B	26.66	33.06	+6.40 

3B	28.87	26.03	-2.84

SS	25.42	24.02	-1.40

LF	27.72	36.72	+9.00 

CF	28.78	27.81	-0.97

RF	30.03	33.55	+3.52 

DH	34.57	36.23	+1.65 

[ These figures are very imperfect - 1999 used games played at position and 2000 used innings ]

The point I'm doing a poor job of arguing is that the 2004 Mariners are very much a Pat Gillick team, not a Bavasi team. I would argue that these numbers suggest that Gillick values age, experience and those elusive qualities we call 'veteran leadership' and 'team chemistry' more than any sane person should and this stems from past experiences he's had with acquiring such things. His Blue Jays age and that season they win the World Series. His Orioles age and that season they win more. His Mariners age and that season they win more. Careful to note that this is (hopefully) more a byproduct of players he acquired and qualities he desired than sitting in his office and thinking, "I need to make this team really old."

I think (hope, actually) the complaints about the organization valuing things like age, 'character' and 'chemistry' far too much are more complaints of Gillick, but I do harbor the fear that he's infected the organization with his thinking. I'm not a fan of Bavasi's and I think we kind of got royally screwed in that GM search, but I'm willing to give him a chance. It's not like I'm given a choice, though.

What?
Seattle Mariners + economics = Marinomics.

Why?
Basically I found my senseless, often quantitative Mariner rantings/ravings spilling over into my other blog/diary/journalish place and emails to friends. And I needed another place to put them. Also, perhaps because they're gawdawful this year and don't have nearly enough good thoughts to fill my brain, I've become increasing frustrated with unsupportable assertions I've seen.

Who?
My real life creds are in economics/econometrics, math and finance.

Also:
1. I believe in data. And the more of it there is, the better.
1.a. I love Monte Carlo simulation.
2. Use of data and statistics needs to be done responsibly (e.g. sample sizes, language, technique/methodology).
3. I tend to think in bigger pictures - usually on an aggregate team basis. Not on an individual player basis.