Well, the 2004 Cardinals had the bigger offensive stars while we had more people like Bellhorn, Mueller and a longer list of .800 OPS people, and that worked out pretty well.

And Manny and Ortiz...kind of an important part if it.

Because we had better much pitching.

I didn't say we didn't have stars; I said they had more and bigger stars and we had more depth, both true. I wasn't making any big claim, excepting offering a pretty obvious counter-example to Pumpsie's theories on roster construction.

The Cardinals had 3 guys with OPS's over 1.000, none of whom did much and two of whom did nothing whatever in the Series -- against our better pitching.

Meanwhile, Bellhorn with his .800 OPS was the probably the real mvp.

The Cardinals had as big a core group of big offensive talents as anyone, and did nothing against our good pitching. On the other hand, there are plenty of counter-examples the other way, where lineups with fewer stars get stuffed.

The conclusion I draw from that, is that there are all sorts of ways to build a team, any of them can work, and you just have to keep working to maximize your advantages. But you can't conclude, as Pumpsie seems to be saying, that only lineups with mega stars can win.

WTE, I read your initial post to be different than your follow-up. Maybe something was lost in translation, or maybe it was just me.

This was Pumpsie's point:



Then you said:



To me, that kind of leaves ou the HUGE factor that the Sox had two 1.000 OPS stars PLUS all the .800 guys. It is true that the Sox had much better depth behind their stars, but the offense worked because they had depth + stars...not one or the other.

If you want to put forward that depth can win without stars, that might be a viable thesis---not sure which recent team really fits it well, but that's a longer discussion. But the 2004 Red Sox really aren't the right team to support that, are they?

Come to think of it, how would that study be structured....the difference between the top three OPS+ on the team and the next three? Top two and remaining six or seven bats? Not really sure.

Except for the Cardinals 1.000 OPS hitters, who couldn't hit Schilling, Pedro, and Lowe?

If you want a counter example on lineup construction, how many 1.000 OPS hitters did the '96-'00 Yankees have?

Aren't constructing a roster for a single game/series and constructing a roster for an entire season two totally different things though? How can the results of the 2004 World Series be used as part of an argument about roster construction in terms of lots of good hitters vs a few great ones and some not so good.

This is an interesting one, thanks to whoever split it off.

Using OPS+, something around 150 in a non-Coors park is roughly the type of guy we are talking about; Juicin' Jason had a .971 OPS and a 154 OPS+ last year, Thome a 1.014 and a 156 OPS+ in a favorable park, etc.

So, here's the Yankees OPS+ for those teams:

1996: Williams 132, O'Neill 122. Regulars under 100: 3 (Girardi, Boggs, Sierra). Their RS/RA was 871/787 and they won 92 games.
1997: Williams, 148, Tino 144, O'Neill 138. Regulars under 100: 2 (Girardi, Hayes). RS/RA was 891/688 and they won 100 games
1998: Williams 159, O'Neill 129, Straw 131 (295 abs), Tino 123. Regulars under 100: 1 (Chad Curtis). RS/RA 965/656, 114-48.
1999: Jeter 161, Williams 157, Knoblauch 125. Regulars under 100: 2 (Posada at 97, Brosius). RS/RA 900/731. Won 98 games.
2000: Williams 136, Posada 134, Jeter 123. Regulars under 100: 4+ (Tino, Knoblauch, Brosius, O'Neill, plus 500 cumulative OF/DH abs amongst three guys). RS/RA 871/814. Won 87 games.

So, having one or two studs and no big holes seems the most successful approach, perhaps unsurprisingly (that's the 97, 98, 99 teams basically). But they never had a team like the 2006 Sox, with a couple studs and then duds.

2006 Red Sox: Ramirez 168, Ortiz 164, Youkilis 108. Regulars under 100: 5 (Varitek, Loretta, Gonzalez, Crisp, Nixon (barely)). RS/RA 820/825. Won 86 games.

It's an interesting topic -- I remember trying to explore something like this in the Live Nude Girls thread from a year or two ago. Then it was a question of team offense consistency but I think the questions are related at some level. It's about distribution versus concentration. In that same thread, philly took a great look at Sox's reliance on Manny and David for offense.

One project I've had on the back burner for a long time is a look at variance in lineup position performance, and relate that to both post-season and regular season success. The teams would need to be grouped into equivalent quality bins, but then divided by variance measures to see if there's a pattern. I guess just average standard deviations of lineup position numbers for equivalent quality offenses. It's a pain collecting the data for that.

My personal theory is that depth kills ultimately and I've been worried the Sox have become too dependent on Manny and David, but maybe there's something to the better hitter hits better pitcher better thing. I know EV has shown some nice stuff comparing ARod and Manny (I think), where there does seem to be a difference in their ability to handle quality pitching. But there, it's two huge stars with that variance, not a star and a scrub. On the other hand, I always liked Mueller against a good pitcher. It's a problem.

Of course, even if it's true the Sox have become too dependent on Manny and David, trading Manny isn't exactly the obvious way to deal with that -- getting additional talent around him is. But maybe they've decided that if they can get enough pieces back, it's worth it. It's looking more like we'll find out.

The missing factor that has a lot to do with post-season success is defense. Preventing runs is slightly higher in explaining post-season success.

So, a team with 3 DH-types would need to really destroy pitchers vs. a more balanced team.

But, strictly looking at offense, it would be good to run some simualtions of a team with an average of 800 team OPS with a median of 700 vs. one with a median of 750. My prior is that the deeper line-up would be better, all else being equal.

(Fris: Maybe can ask Glassko this on Friday?)

I'm at work -- anyone have a copy of Tango's Book handy? Do they look at this? Hard to tell from his page.

It's important to keep in mind that a straight OPS analysis won't handle this...

If you got two lineups:

.350/.450
.350/.450
.400/.600
.400/.600
.350/.550
.350/.450
.350/.350
.300/.300
.300/.300
(Composite line: .350/.450)

and

.350/.450
.350/.450
.350/.450
.350/.450
.350/.450
.350/.450
.350/.450
.350/.450
.350/.450
(Composite line: .350/.450)

That the first one will score more runs in the first place. You want your offense bunched(for fairly intuitive reasons). So for the question to be interesting, the "smoother" lineup needs to have a better composite line in order to have equal runs scoring ability during the regular season.

The right way to do it is probably to use EQA, which adjusts for both context and the OBP/SLG difference. But BP doesn't have the handy team-pages by year that baseballreference does. At least, I'm pretty sure they don't (even though it's just a database sort, really).

Another way to look at the problem generally (and specifically to the SS-less 2007 Sox) would be to ask if having 1-2 really bad hitters....OPS sub-700 or so....has a significantly more negative impact than just 'below average' guys. It wouldn't shock me if guys at the poles---either really good or really, really bad---have a greater impact because those guys change the approach to other hitters around them, imo.

I also want to add, Baseball Prospectus looked at something like this a while back. While it's not the exact same question, it is related. What they were looking at there was evidence of "mistake" hitters. To quote their basic methodology for those who don't feel like reading:



Ultimately, they found no evidence to support the mistake hitter idea.

This doesn't answer the question entirely, but it does address at least one major mechanism via which a possible "bunching' superiority would manifest itself in the playoffs.

I took Bowiac's quote from the Trade Manny thread. In that thread, I have argued a few times that a team is probably more suited to win in the playoffs with better run production from 2 or 3 hitters than if that production was theoretically spread over the 1-9 hitters. The theory is that exceptional hitters have a better probability of hitting very good pitching. This theory is far from fact. Frequently, as the 2006 post season highlighted, very good pitching will beat even exceptional hitters in the playoffs (st. louis over the mets, tigers over yanks). As far as evidence, the playoffs produce such small sample sizes that I'm not sure there is any way to accurately validate such a theory. Maybe one method would be to predict run production against elite pitching (Zito, Santana, Liriano, etc.) for a concentrated line up (such as the 2005 or 2006 Sox) vs. a hypothetical line up that substitutes Manny's production with players over which that production is spread out.

As leeharris notes, constructing rosters for the regular season and playoffs require different analysis. In 2007, the Red Sox should have better starting pitching and hopefully rebound seasons from Coco and Tek. Whether the team keeps Manny or deals him for prospects/pitching and signs Drew and Lugo, the Sox will have a realistic shot at the division or wild card. I would rather see a lineup that can make it to the World Series than a lineup that will probably make the playoffs but has little chance of winning it all (a la the Oakland A's).

They actually do have team pages, they just hide them for some reason. What you need to do is go to a player on that team, and click the hyperlink to their team page. For instance, Mike Lowell's DT card, you click on "2006 BOS-A", and you get a complete list of Boston's stats for 2006.

Those Yankees teams won with pitching. A lineup like that can only work if you have Rivera at the back end of your ridiculous bullpen (Wickman, Nelson, Rivera BEFORE Wetland in 96...are you kidding me!!!???) and Pettitte, Cone, Wells etc starting games for you. Look at the ERA's of the starting pitching in 98, I rest my case.

AND they didn't have to compete with the 2003-2004 Red Sox. They also didn't have to compete with the 2007 Yankees. Lineups like Yankees and Red Sox have now would have made that pitching look much less great. Why??? Because teams were more conservative then...there weren't many teams with multiple offensive superstars, especially in the AL East then. It was easier for them to get to the playoffs than against the Red SOx teams now, and their pitching was the key in those playoff runs because Paul M is right about preventing runs being more important come the postseason.

You can run all the numbers you want, but you are going to miss out on the biggest factors when determining which lineups will be successful. Just look at where those slightly above average guys get their slightly above averg"ness" from. Its usually from hitting around guys like Manny and Ortiz (who were the biggest reasons those other guys 2002-2006 were successful) or feasting off poor pitching as has been mentioned.

I'm not completely hostile to this idea, e.g. that some guys impact the ability of those around them to hit a bit by changing pitching approaches. But it's a theory, and a tough one to prove or disprove, rather than a fact I think.

And however imperfect the approach to solving this may be, we have to have some way to value the contribution of stud hitters other than "you simply can't live without them" I think. So, how would we quantify the impact having Manny/Ortiz in the middle of the lineup in your view?

Not sure if this is what you're going for, but Baseball Prospectus also looked at this somewhat, and found that indeed, certain combinations did lead to greater postseason success beyond what you would expect on the basis of overall team strength(as in, the teams that have these qualities are going to be good teams in the first place, but they'll do better than equally good regular season teams without these qualities...)

The postseason "Secret Sauce" as BPro termed it, is:



To emphasize, the point isn't merely that strikeouts, a good closer, and a good defense are good. It's that they're even more meaningful in the playoffs than in the regular season.

I haven't read Mind Game, but while explaining why strikeouts for pitchers are so important, Silver mentions:

A couple years ago, I was briefly obsessed with the question of whether the ability to hit good pitching exists. That is, presuming that all hitters have a performance curve in which they decline as the quality of their opponent improves, are there some hitters who have a relatively flat curve or a relatively steep curve. I remember particularly focusing on players like Soriano, hackers who always seem to me to be overwhelmed by expert starting pitching. But despite my best efforts, I couldn't find any evidence that any player is able to produce a significantly different performance curve. Much to my surprise, every player I looked at, from great hitters to good hitters to mediocre ones, seemed to have a pretty comparable curve, with a pretty comparable decline as pitching opponents improved. The few examples I found of players who seemed to do "well" at that in one season didn't repeat from season to season, and nobody had a strong enough effect for me to believe that it was anything but a random distribution. I wish I had access to the numbers, although my informal study wasn't nearly scientific enough to be taken seriously as a sabermetric study. But I was left feeling that this skill probably doesn't exist.

A peek at the Sox:


I don't know how this compares to other teams. It's time-consuming to do, but maybe later. I used cbssportsline to get the lineup position numbers, but realized they've already assigned Alex Gonzalex to the Reds, so I had to manually add his numbers back in to the 8th and 9th positions. I'm probably missing someone, but it's pretty close. Doing this for enough other teams including movements is pretty much out. Does anyone have a better source for lineup position data?

I could just take the 10 guys with the most ABs for each team, but that doesn't seem like quite the same thing.

Anyway, some things do stand out, but no real surprises I guess. We're very unbalanced, but especially with regard to slugging. Didn't need to do this to see that I guess. Oh well. The +/- column is just the distance between a player and the player following him in the lineup (so for the ninth hitter, it's between him and the first).

Odd random fact: Alex Cora certainly preferred the 9th spot (766 ops) to the 7th spot (419 ops).

Decided to pursue this a little.

I got all data from the B-P team DT cards, dumped it into Excel and did a little parsing.

-For each team, I took the players with the 10 most plate appearances.
-For that list of players for each team, I generated a standard deviation of EQA. (I'm assuming via Tom Ruane's article, that lineup doesn't make much difference.)
-For the list of teams, I compared that standard deviation to team EQA, both directly, and with standard deviation expressed as a percent of team EQA.

The resulting chart is presented below, with team EQA mapped against percent standard deviation. High on the y-axis is an unbalanced lineup; far on the x-axis is a better lineup. Sorry, my graphics skills suck (how the hell do you get nice charts OUT of Excel?). The table is sorted by the % column, where high is an unbalanced lineup and low is balanced.



The data are here:


Doesn't look like there's any real correlation. I'm sure there are issues with the method (why the top 10 PA guys? sort order affects results? etc), but it's a sketch of a test.

By this method, the most unbalanced lineup is STL, which makes sense. The Yankees are pretty balanced, we're not the worst but near that group. Toronto is surprisingly balanced. The better lineups, measured by team EQA, don't seem to care much about the distribution, which I guess makes sense.

I'm beat -- maybe someone else can make more sense of this. My bottom line interpretation is that it doesn't much matter how your lineup talent is distributed -- it's the overall talent that's the issue. I guess by cold pythagoran logic that was always the expectation.

One improvement would be to get the 10 guys with the highest PA as seperate group, and then also a weighted EQA for all the rest of the offense, which is ignored in this group. Then get the standard deviation for that set for each team.

I realize I'm stating the obvious here, but that 5-hole is FUGLY.

Who was mostly responsible for that? Nixon, Tek, and Hinske?

Here's the breakdown:


Trot was okay -- excellent obp, lousy slugging. The real problems were Varitek and Lowell, and pretty much everyone else who hit there.

I have this data for each lineup spot, if people are interested. Have to say I'm not 100% certain about it, after discovering Gonzalez had already been bumped. If I'm missing someone, let me know.

Jesus H. Christ. To think Nixon's pathetic production out of there (Good OBP, shitty slugging) was only HALF of it. No wonder the Sox could score only 825 runs.

Something tells me Drew's gonna see a lot of time in that five spot.

Check out Lowell's double play rate: at that level of double plays, he's giving Jim Rice a run for his money. And that's with two .600 sluggers in front of him moving people around, though I guess Lowell was batting 5th mostly when Manny was gone? Dunno.

For a lefty, Nixon isn't doing so great on the gidps himself.

This was my initial reason for the argument that Ortiz/Drew/WMP would be preferable over Manny/Ortiz/Zilch in the middle of the order. Obviously, if the Red Sox can keep Manny, Drew, and still sign a suitable replacement SS (maybe Lugo, maybe a cheaper option or visit a trade ala Bill Hall or JJ Hardy), then the offense could downright mash next season. And the 03 lineup was a bit underrated once I went back and looked up the OPS numbers. Bill Mueller was well over 900, as was Nomar, Ortiz, Manny, and several others clocked in the mid to high 800s (interestingly enough, the one player who left and caused the most uproar, Johnny Damon, fired off a 750 OPS that season). Manny/Ortiz/Drew could be devastating, but my initial point was that if you lose Manny, the drop off from Manny to WMP would be less than the upgrade from Nixon to Drew, and A-Gon to Lugo. And this dual upgrade would balance out the lineup a bit more.

This was one thing I was surprised wasn't brought up more last season. Was it just me, or was Trot Nixon CONSTANTLY hitting groundballs. His ability to drive the baseball seemed to fall of a cliff last season. Every time he was up, I'd wager 5 bucks with my pal that he'd hit a groundball right side. I swear, more often than not he'd top a ball right to the 2B, or one would find the hole. I'm shocked he batted 5th as often as he did. Seems his skill set would have been preferable in the 2-hole.

He maybe hit into a smidge more grounders than usual, but look at his career ground ball/fly ball ratio:

1999: 1.14
2000: .84
2001: .83
2002: .86
2003: .52 <- ?
2004: .82
2005. .81
2006. .86

So up a tick this year, but 2003 is the real oddity.

Interesting numbers, I guess my eyes decieved me. In '03 his higher FB totals led to more HRs, but perhaps his chronic back problems led to Nixon swinging for contact instead of from the heels a bit more.

What we want to know is whether there's a correlation between standard deviation of the principal hitters, and two things:

Actual Runs - Calculated Runs according to EqA, CR, RC or other formula

Actual Wins - Pyth Wins

IOW, do consistent lineups score more or less runs than expected? Given however many runs they score, do consistent lineups win more or less games than expected?

Another great question: what is the relationship of "top-to-bottom lineup consistency" with "game-to-game consistency"? One would think they correlate, i.e., the teams getting shut out one day and scoring 14 the next are more likely to be the teams with a couple of mashers plus a couple of black holes.

In a study like this, a large database (10 years, say) is preferable to an exact metric, if you have to choose one or the other. So it could be done with baseball-Reference data, OPS or 1.7 * OBP + SA.

Thanks for the comments Eric. I know this thread isn't going to get a lot of attention, but I thought I'd add a little bit more.

The first step above was trying to show there's no relation between good offenses (defined by EQA) and the consistency of the principal hitters.

Another step is to look at team consistency in general. This was done a while ago in the Live Nude Girls thread, but revisited here. What this does is take, by team, the runs scored for every game, and then get a standard deviation from that.

Here are the data



stdev = the standard deviation of the runs scored in every game played by a team that year

r/g = the average number of runs scored per game

"Consistency" = relative consistency of the team's performance overall. Basically, the standard deviation of the runs they scored in every game, divided by the average number of runs per game

"Balance" = the relative consistency of the team's principal hitters. The standard deviation of the the EQAs of the 10 players with most plate appearances, divided by average EQA. Derived from post above.

EQR = expected runs for the team based on component batting lines (from B-P)

R diff = difference between actual runs and expected runs. A measure of over/under offensive performance

The table is reverse sorted by "Balance", with more unbalanced teams (eg. St. Louis) at the top and balanced teams (eg. Toronto and Cincinnati) at the bottom.

Results: in the AL less consistent teams tend to outperform, while in the NL less consistent teams tend to underperform. On average, no particular relationship is visible.

While "balanced" doesn't have any strong relation with "consistency" (a little, maybe), it does seem to have some relation to worse performance judged by R-Diff, where negative numbers indicate possible under-performance. The correlation is slightly positive, but my "balanced" is in reverse order (smaller numbers = more balanced). More balanced teams tend to do worse with regard to R diff.

I'm sure the study is too small, and I'm probably just seeing sample effects (though there are 30 teams and thousands of games involved). Is there an interleague play issue here? I wish I could subtract all interleague games, but that would be a total pita. Maybe the DH is a factor.

Here are some charts of team consistency. Haven't charted with the principal hitter variance data yet, but this is what I have:

AL Volatility vs. Relative Offensive Performance

NL Volatility vs. Relative Offensive Performance

Anyway, just a sketch of a study I guess, but at least within this study, consistent offenses overall (on a game to game run-scoring basis) might not do better, but "balanced" teams do a bit worse, overall, or at least they did in 2006.

Here's the chart with combined NL and AL data for 2006 with a scatterplot of "Balance" against R-Diff. The downward slope of the trend line suggests that more balanced teams did relatively worse than a metric like B-Ps EQR indicated they would. The trend is not strong, and obviously subject to small sample skew. Cincinnati and Toronto were both very balanced lineups that distinctly under-performed by EQR.



edit: fixed errors
edit2: I wonder if we aren't seeing here the effect of lineup? In an unbalanced lineup, the better hitters will tend to get more at bats by being higher up in the order, so that more balanced lineups need better offense on average to counterweight the greater leverage of the better players.

I took a shot at one of Eric's questions: do teams with a mixture of good-and-bad hitters score more (or fewer) runs than an equivalent team of identically average hitters? My method was pretty simple. I grabbed statistics for all American League teams from 1995 to 2006, fit linear models to (runs scored) as a function of OPS, then looked for patterns in the residuals from that fit. If there really is an effect of lineup inhomogeneity on scoring, we would expect teams with a mixture of hitters to have larger (or smaller) residuals from the linear relationship than teams with nearly identically average hitters.

You can find my report, with some graphs, at

http://spiff.rit.edu/richmond/baseball/order/order.html

I'll repeat one of the graphs below: it shows the residuals from a simple linear fit to runs scored as a function of the standard deviation in OPS of the "main starting 9 hitters" of each team.



As you can see, there is no significant correlation in these residuals. As far as this very simple analysis can show, the inhomogeneity of the hitters in a lineup has no real effect on team scoring.

Stupendous start, but I think the noise in OPS linear estimated runs is likely to swamp any effect you're looking for.

The best estimate of team scoring is my own Contextual Runs, whose formula is in the Wiki. I actually have the spreadsheet with the differentials (but not the last few years); if you're inteested, PM me.

Tremendous stuff, WTE.

First, while EqR is in the ballpark, it the past it hasn't been nearly as accurate as CR, which crucially includes Reached on Error and Out on Base. (The difference in accuracy between CR and EqR has been bigger than that between EqR and OPS).

Now, this year EqA was actually a bit more accurate than CR, which suggests that it's time to recalibrate the coefficients for the CR formula (CR recognizes that the coefficients in a linear run formula should not be not fixed but rather must vary across eras according to style of play, especially baserunning). In the meantime, though, most or all of the specific differences of opinion between EqR and CR are meaningful and reflect ROE - OOB, which ranged last year from +48 for the Cubs to -4 for the Indians.

Here's a table with a very different and possibly better set of R diff numbers. I'd be very interested in seeing if your correlations change with these values rather than the ones based on EqR.


Next, are you using Excel? Can you use Tools, Data Analysis, Regression on that r^2 = .0759 relationship, and whatever you get with CR values rather than EqR? I'm curious to know what the p value.



Five years of data would make this study really rock.

We also want to regress all of these numbers against Pyth differential.

I just did my own study based on 30 years worth of data, and found no correlation whatsoever (r = .016, p = .739) between line-up balance and Runs, BaseRuns differential. I'll write up my study on THT or my blog in the coming days.

EDIT: Also no relationship between Pyth Differential and line-up balance, though the relationship is somewhat interesting (r = -.066, p = .178).

Or we could use my Team Runs Created (TRC):




Seriously, whichever theoretical runs system you use, understand that there is a fair amount of run-scoring entropy that obscure teams that score runs at around their expected values, so the middle ground is all noise. If you want to analyze this, I would recommend looking at the outlier teams throughout history. I would start with the 1914 Philadelphia Athletics who overachieved by an incredible 116 runs over their expected runs (using TRC). Deadball is a great place to start a lineup dynamic study, because there were almost no home runs - nearly all runs were manufactured.

There were five teams in the past six years who overachieved expected runs by more than 50 runs:

2001 Oakland A's
2002 Anaheim Angels
2003 Kansas City Royals
2004 Chicago White Sox
2005 Toronto Blue Jays

Of those teams, only the '04 White Sox were a big home run team, the others overachieved - I believe, through lineup depth and other factors. Those would be interesting teams to analyze.

Another fly in the ointment of this analysis is run clustering. I'd be willing to bet that there is an inverse relationship between the percentage of runs a team scores via home runs and their pythagorean run performance. I've seen glimpses of it, but haven't really tried to prove it. Home/Road performance is also a qualifying factor, especially with home runs.

This is a great thread and a great study, WTE. There's an awful lot of cool stuff in here, and even cooler stuff out there to be discovered about lineups. One thing I think is almost certain is that if you have a nice deep hitting team, it really doesn't matter what your batting order is.

Here's a quick look at p-values. I'm using the mean EqA and stdev EqA numbers provided by WTE to predict the R, CR and Diff numbers from Eric. Running them through a generalized linear model to find significant effects of EqA and stdev in predicting each of those three. The model is essential (R, CR or DIFF) = f(mean EqA, stdev EqA). *Edit: also, I'm allowing the intercept to be a parameter. The intercept is significantly different than 0 only for the CR model (p=0.0005). Not real important to the question at hand, though it seems interesting in evaluating CR (0 EqA does not mean 0 runs).

Predicting R:
EqA p<0.0001
stdev p=.29

Predicting CR:
EqA p<0.0001
stdev p=0.62

Predicting DIFF:
EqA p=0.49
stdev p=0.33

So basically, mean EqA is a significant factor in predicting R and CR (as would be obvious), but doesn't predict the Diff. The standard deviation doesn't seem to be a significant factor of anything. Perhaps with a larger sample it could get there, but it's pretty far off.

Let me know if there's anything done obviously wrong... This was a pretty quick look at significances.

Actually, the correlation is positive and marginally significant (r = .085, p = .081). (I'm assuming that you were saying that teams that score a large percentage of their runs on home runs are going to underperform their Pythagorean record.) Actually, this makes sense, because a team that hits a lot of home runs is much less likely to get shut out, which is the one thing that really hurts a team's Pythagorean win differential, as Sal Baxamusa has shown on The Hardball Times.

Thanks to you, however, I did discover two very cool things, which I will keep under wraps until my article runs Thursday.

EDIT: Actually, I'll attribute the idea to you, so if you want to be referred to by your real name, feel free to shoot me a PM. Whatever your prefer.

Looking forward to DSG's article.

I've still been wondering if there isn't another element here that the principal hitter variance doesn't get at, which is actual lineup order variance. It's probably pretty close, especially sorted by plate appearance. A case where this might be an issue is if there's a giant hole in the middle of some lineup, so that while the average is good and even the total variance relatively even, the positional variance might be higher. The 2006 Sox are a good example, where we got bupkis from the #2 and the #5 slots, while #3 and #4 were monsters. The contrast would be with the 2003 Sox or 2006 Blue Jays or something -- a more balanced lineup.

Here's one chart with a quickie illustration of 10 years of Sox team data:


I didn't even bother running stats since there's only 10 years here, but it's interesting to see the change in profile over time. Our lineup last year was the most internally variant lineup we've had recently, including the Nomar years.

I don't think there's anything significant here, but it's a little bit of a different question, it seems to me. I guess I should get sets of sorted principal hitter variance and sets of actual lineup order variance and see if there's a difference. But retrosheet has the only lineup position order information that I can find, and seems way too cumbersome and slow to get that data. Is it somewhere else? Is it even worth bothering with? I guess really just pythagoras rules, and we just need to min-max overall run differential.

By the way, why do the Sox underperform their run expectations (by B-P expected runs) nearly every single year, and sometimes by a lot? Are we that sucky at running the bases or reaching on errors? Apparently that underperformance doesn't have much to do with lineup construction, since it occurs both when relatively balanced or relatively unbalanced.

Your wish is my command :-)

I went grabbed another set of historical team data, this time over the period 1997-2006 in the American League, which included almost every term needed to compute the Contextual Runs (as given on the Wiki page). The only term I couldn't get was LOB, so I just set that to zero and kept going. I know, I know, it's not the right thing to do. Sorry.

I ended up with CR values which were very nearly half of the actual number of runs scored. Over the entire period, the ratio (actual runs / CR) was 2.03. So, I multiplied all the CR values by this factor before comparing the CR to the actual runs.

I've revised my earlier report on the results to use the predictions from scaled CR, rather than from team OPS. As Eric suggested, the scaled CR (even without LOB) does a better job of predicting actual runs scored than OPS. The new report can be read at

Does the uniformity of a lineup affect its scoring significantly? (revised version)

The conclusion remains the same: the residuals from the predicted number of runs do NOT correlate with the inhomogeneity of the "main" batters in the lineup, as far as I can tell. The only pattern that I found mildly suggestive was that the recent Detroit Tigers appeared 3 times in the list of "Top 10 Teams which overperformed their CR prediction." It could be random chance, but is there some feature of these teams (1999, 2002, 2003 DET) which might modify their performance relative to the CR formula? I dunno.

The Red Sox did not show up in the "Top 10 List of Underperformers," by the way. Plenty of other teams didn't show up in that list, either, so it doesn't mean anything.

Are we all violently agreeing?

No details to speak of but I threw together some mean/stdev type things on a couple of statistical measures (OPS and EQA I think) a couple years back for teams over a couple of seasons back after the 04 WS. And while there was noise in both of those stats' correlations to runs, it didn't fit with the stdev in any way that I could detect.

Glad to see that those with better math skills agree.

All questions in this thread answered here.

That was a great piece David, but if I'd known that you were going to attribute me only to point out that I was wrong, I would have told you that my real name was Eric Van.

One thing I would like to see is an expanded data set. You chose A.L. teams with DH's for your data set, and it seems as if in doing that, you may have created a lot of noise for your study. I'd be curious if the same tendencies apply to N.L. teams over the same period. As a general rule, N.L. teams underachieve expected runs as a league by quite a bit more than the A.L. teams since the DH rule was enacted, which is what got me thinking that there was a relationship between lineups and run efficiency in the first place.

It also would be interesting to look at teams from the 1960's - which often had extremes in their lineups - a couple of monster HR hitters surrounded by a bunch of weak defensive/speed types, perhaps teams from the 1930's, and of course the interesting 1913-14 Philadelphia A's

I made a small mistake in my calculations, so the article has been updated.

Interesting stuff DSG. Nice to see coefficient of variation getting it's due. ;p

I'm still interested in a few things though, if you or someone are up for a few questions:

1. Real lineup positional variation (as opposed to variation of the principal hitters).

Here's a abstracted version of this:


The "Smooth" team has an even curve minimizing differences between lineup spots. The stdev of distance between lineup positions in 47, which is low.

The "Rough" team has the exact same set of OPS numbers, but arranged in a pretty random distribution maximizing some of the differences between lineup spots. Both teams have the same average OPS and the same stdev of the principal hitters. But the stdev of distance between lineup positions here is 129 -- nearly 3 times as large.

Will this have an effect? Doesn't a high lineup positional stdev suggest a failure to cluster offensive events, which is inefficient? I think this is a little different than just getting coefficient of variation of baseruns for principal hiters, or whatever.

I'm probably missing something in Tom Ruane's article at Retrosheet, but it does seem like his "best" lineups not only have the better hitters up top, but also minimize relative stdev, while the "worst" lineups did the opposite.

2. Even more interestingly, to me, is individual hitter consistency through time. I'm pretty sure that some hitters have less game-to-game variation in performance than other hitters. I would guess those hitters are somewhat more valuable, in that fewer of their offensive outputs would be in blow-out type games, since their very inconsistency might contribute to a higher percentage of relative blow-out games. Should teams track for hitter consistency through time within a season? Does it matter?

I'm sure retrosheet can provide the data for this, but I can't really do this project. Was wondering if DSG or anyone has some ideas.

So far, though, it seems like the bottom line of all these studies is that it just doesn't matter much. Get good hitters, stick them wherever, and that's that.

1. I don't think it'll really have an effect, because c'mon, who's going to bat Manny second and Ortiz eighth? Teams construct their lineups in a pretty similar fashion, so I don't think this should be a big deal.

2. I've written about this for pitchers here and Sal Baxamusa has written about this for offenses here and here. In short, I don't think there really are consistent and inconsistent players, and if there are, the effect is very small, so I don't really think this will matter.