THE BOOK--Playing The Percentages In Baseball

Is it possible there is a reverse effect too? The better your team is in Year X, the more you have to pay them in Year X+1, Year X+2 to retain the players.

It’s an interesting thought. 

I think I’ve shown how fairly efficient each league is in paying players in a thread a year or two ago (can’t find it now).  I would guess that because of multi-year deals and the way the arb process is laid out, that what you are positing doesn’t really come into play.

Myth or No Myth…

1) AL teams and NL teams are composed differently due to the inherit nature of the DH.

2) The AL teams carry a DH and the NL teams do not.  Therefore the AL teams have an offensive advantage while playing in an AL park.

3) Playing in an NL park the advantage in #2 disappears as the AL teams are forced to either sit their DH or one of their other players.  But in games played in an NL park the advantage the NL has, which is namely that pitchers bat is negligible.

4) On top of that the $10M in salary difference should be worth 2-3 wins assuming the money was apportioned evenly talent wise.

5) The rest could be noise (SSS).

vr, Xei

Interleague history (total of 3207 games): the AL has won 52.2%.

If we limit it by home park, here’s how the AL did:
AL park: .573 (1604 G)
NL park: .470 (1603 G)

What should we have expected?  Well, in that same time period, the average team wins .539 at home and .461 on the road, or a 78 point gap.

The AL shows a 103 point gap, which means they have the “home league advantage”.

If how they performed in the NL (DH rendered obsolete) is the “real” test, then the AL was .470 on the road, and we add 78 points to that for their “true” AL home win% of .548.

They actually win .573 at home, which is .025 wins per game more than expected.  Can we give this to the DH?

Well, the DH is worth roughly 2 wins per 162 G, which is .012 wins per game.

So, I think that we can give part of that “home league advantage” to the AL for their use of the DH.

That leaves .013 wins at AL home parks unaccounted for.  Given 3200 games, and given how I should not necessarily treat the road records as the real baseline, that could be small sample size.

All to say the following:
- the AL did in fact win .522 of the interleague games
- the AL did, in half those games, get a benefit of roughly +.012 wins that the NL did not have
- that the DH-adjusted AL record should be .516
- and that being +.016 wins above average is 1.8 SD above the mean

So, the AL, since interleague has started, has likely been a slightly better league than the NL, but not by much.

***

What if we repeat this for 2004-present?

AL at:
AL park: .616
NL park: .495

That’s a 121 point gap.

In that time period, the home team has an 88 point gap advantage.  So, there is a “home league advantage” of 33 points, similar to the 25 point for the historical interleague.

The AL has a .556 record against the NL in this time period (on 1511 games).  If we knock out 12 points because of the DH, that puts them at a .544 record.  That’s 3.4 SD from the mean.  So, the AL is better, even beyond the DH advantage.

The NL should not, in theory, be at an inherent structural disadvantage due to the DH. Given equal resources between the two leagues, the AL will end up with superior DHs (since DHs are worth more to AL teams), but the NL should end up with better talent everywhere else. Since NL teams do not have to commit resources to the DH position, they should have an advantage in acquiring the remaining talent. In other words, there is an opportunity cost to acquiring DH talent that the AL must pay but that the NL does not have to.

From 1997-2008, an average of 48.8% of the salaries were paid by the AL.  AL has 14/30 of the teams, or 46.7%.

Xei--

Not arguing your point overall, but what about the offensive hit AL teams take when they have a regular DH (whom they rely on) that suddenly sits? This happened with Hideki Matsui this year, for example. And what about the defensive hit that teams take when they move someone like David Ortiz into the field to keep his bat in the lineup?

How much extra injury cost to is there to NL pitchers because they have to hit?

Another thing that might come into play, though I am not sure how I’d measure it, is that the AL may have better/luckier GMs.

#7 Dan, that’s mentioned in bullet #3.

I think MGL found that the biggest difference between the two leagues is pitching.  Is it possible that the AL has an advantage for acquiring FA pitchers because the pitchers want to avoid having to hit?

"But in games played in an NL park the advantage the NL has, which is namely that pitchers bat is negligible. “

No no no no no.  The AL has to bench their DH or put him in the field and bench someone who is almost always a better fielder.  They lose production from the game.  The NL doesn’t lose anybody.  All else being equal (which it’s not because of larger payrolls in the AL) the NL should have a better team left on the field because the money it saves by not signing a DH will be put into another bullpen ace, a better starter, or a second baseman who can both hit AND field.

I read earlier today that since the AL and NL play .500 ball in games in NL stadiums that they really are equal teams.  No (no no no no) again.  The home field advantage is something like .540, meaning that if the AL is turning the home NL team into a .500 team, they are the better team in the game and the better league overall.

Sky: read Tango/4.

Shouldn’t the difference in payroll only add up to about three wins, or .520?

I’d write more but my comments seem to be disappearing into the ether ...

I mean about three wins per 162 games.

Without looking at the winning percentages, it just seems to make more sense that the NL has the overall IL advantage for reasons stated by others. I just don’t see how the difference between AL DH and NL DH (which usually means the worst defensive player goes into the DH slot and a decent hitting/better defensive player plays the field, a double positive for the NL) is larger than when the AL’s DH has to sit or play the field.

Something to possibly consider. A full-time AL DH would be getting more at bats than an NL team’s best pinch hitter, so when interleague play happens, the AL would have an added pinchhitting advantage since their DH had been getting regular at bats. Maybe a difference between AL and NL teams then is the quality of their benches.

Remember, since 2004, AL teams spend 10MM more for their teams than the NL.  That’s a huge difference.

Thanks for the very interesting breakdown, Tango.  I think they’re all good thoughts here and I to love contemplating the DH and what it does to baseball.  But I think it’s a little more simple than that.

Couldn’t the difference just be the simple fact that the American League has overall higher revenues per team?  They just buy more talent.  They do have the Yankees and Red Sox afterall?  Overall, the AL has some big market territory and teams like the Mets are second to the Yankees in their market.  Granted the Cubs and Dodgers are in the NL, but I don’t think they’re all that near the Yankee level.  And don’t forget that Detroit looks to be a ‘Win Maximizer’ rather than ‘Profit Maximizer’ more so than any other team in recent times (though I doubt they’re losing any money in the long haul...and last year they weren’t very good winners). 

Looking at the most recent Forbes data in the Revenues column (and I’m assuming this is even after revenue sharing), the AL teams average about $5 million more in revenues per year than NL teams.  I don’t put too much trust Forbes valuations reports, but they can definitely shed some light on this.  There’s more talent in the AL because the AL teams make more money.  This should give us the expectation that the AL wins more games.  As TANGO/17 states, $10 million is a lot in a single season payroll.

Even if it weren’t the case that there’s more money in AL, as JOHN/5 states, then the NL would spend the money elsewhere in which it could contribute to beating an AL team at the expected level (better pitching matchups outweighing the DH, better bullpens, etc.).  Since the AL is spending that money on the DH, they wouldn’t be able to keep up in other areas...or they’d just have to have a really bad DH.  In either case, the talent level for each team over the course of 3200 games should come somewhere close to what we expect.

Coming back to the $10 million difference, it seems that the AL teams aren’t spending all of this at the DH position.  They have talent elsewhere that the money is going to, resulting in their increased winning on the road at NL stadiums as well.

From 1997-2008, an average of 48.8% of the salaries were paid by the AL.  AL has 14/30 of the teams, or 46.7%.

If we try to put this in 2008 equivalent dollars, this would mean that the AL paid 94MM in salaries per team, in this time period and the NL was 86MM.  That’s a difference of 8MM.  The dollar/win ratio is 2.5MM (note that the free agent dollar / win ratio is 4.5MM), so that the gap between the two leagues (or rather the average team in each league) is about 3 wins, or .020 wins.

But, the actual gap in performance was 141 wins in 3207 games, or .044 wins per game.

So, the AL does have an inherent advantage in head-to-head matchups over and above how much talent they happen to have.

Thanks for that, Tango/19.  Not much I can say about those numbers, as I’m not all that experienced in that sort of game-level analysis.  I’ll have to take your word for it.  Very interesting!

All I can think of from there would be:

1) More efficient arbitration players in AL (though you say you looked at efficiency already)
2) At a certain talent concentration, the wins-to-spending ratio changes.
3) The NL spends more on an unused bench, while the AL concentrates payroll in the starting lineup (or vise versa somehow making depth more efficient than concentrated talent in the starting lineup).

Otherwise, it seems confusing.  As you state:

“From 2000-2003, each team spent around 53MM per team, in the AL and NL.  In this time period, both leagues have close to a 50/50 W/L record.”

So something seems to have changed besides the money spent (based on the dollar/win ratio that you cite), because they had the DH in that time period as well.  Any light you can shed on #2 or #3 above?  I’m very curious.

I also would not discount other things, like small ball, closers, etc.

For example, you can have two identical teams in terms of runs scored and runs allowed.  But, the run distribution of those two teams could be very different.  Enough that one team would win 52% of their games!  If you don’t believe me, run the Tango Distribution (go to my home page, last two links), and do it yourself.

So, small ball play, the deployment of the bullpen and pinch hitters, the DH, etc, all could conspire to show a non-50/50 result, even if you have two teams that are, overall, equally paid and equally talented.

I would not discount the SSS either.  3200 games means one sd is almost .010 wins per game.

I didn’t realize the SD would be that high.  And I believe you!  Your point about small ball and bullpen deployment is a good one.  From a management standpoint (which much of my interest lies), there are a number of implications for researching differences in management techniques. 

The main question I pose is: Why would we expect the management to be more efficient in the AL as opposed to the NL in terms of bullpen/PH deployment?  Would you put most of that non 50/50 difference on the ability for the extra PH on the bench thanks to the AL’s DH?  Or do AL managers know something NL managers don’t (not likely)?

Well, you could check for luck.  Pythagoras?  Linear Weights estimates?  Clutch hitting?

Shouldn’t be too hard to isolate what’s different in interleague play.

You could also check payroll in more detail.  Maybe AL teams get more for their money because they have more slaves and arbs.

Phil/23,

I was thinking about the slaves/arbs hypothesis as well above.  Tango, do you know if this is the case, or from your evaluation have you seen AL/NL to be equally efficient in this case?

Millsy: I haven’t checked too hard, or too many years, but it seems fairly efficient.  Don’t hold me to that too much though.

Here’s what bothers me about the idea that the NL has an inherent structural disadvantage against the AL because of the DH:

If we hold all factors other than the DH that could cause interleague disparity constant, including payrolls, management, marginal value of a win, etc, how would we expect talent to be distributed?

Two things immediately leap to mind:
1. AL teams will have to spend to acquire a DH. NL teams will not.
2. The NL will have a lower run environment than the AL, assuming DHs hit better than pitchers.

This means that:
1. AL teams should acquire all the best DH talent, but this will leave them with fewer resources for non-DH talent. This gives the NL an edge in acquiring the remaining players.
2. Because the run environment in the NL is lower, each marginal run scored or saved by a player will be worth more in the NL in terms of wins. Thus, we would expect the NL to offer slightly more for non-DH talent than the AL simply because it is worth more to an NL team.

Thus, NL teams should have both the resources and the incentives to outbid AL teams for the non-DH talent. Therefore, they should be at a disadvantage in an AL park where they are forced to play a worse DH than the AL team, but they should also be at an advantage in an NL park where they should have slightly better overall talent on the field. If the NL somehow does not end up with superior non-DH talent, it won’t be because of the DH. We have to look elsewhere.

I’m open to being wrong on this, but I have to be able to see what’s wrong with the above reasoning to be convinced.

John/26,

As I said above, I agree with you on that one, which is why I’m interested in this scenario we’re seeing played out.  I think Tango makes an interesting point in the managing styles.  Unfortunately, there’s no good reason to believe that AL managers are better at this than NL managers...especially in an NL environment where NL managers have more experience.

Millsy/27,

It would not surprise me to find that the effect we’re seeing is based on some effect that tends to persist over multiple seasons. For example, even if managerial quality (both on the field and front office) tended to even out over time as you suggest, that effect could easily persist for a few years simply because managers/GMs tend to stick around for a couple of years at a time. This would naturally encompass many baseball games. We may have a decent sample of games, but that doesn’t mean we have a decent sample of managers, or GMs, or whatever.

This is why I’d like to see my reasoning in #26 countered before I buy that any portion of the disparity that we are seeing is due to the mere existence of the DH in the AL (as opposed to how the DH might currently be skewing the talent distribution in a manner that we would expect to equalize over time).

I don’t think the DH should make much difference.  That is, 8 hitters vs. 9 hitters shouldn’t be a big deal.

Consider the extreme case: everyone on every team is identical except one hitter.  In Rotisserie league, Barry Bonds’ value increases; he goes for $260 (the maximum) because he guarantees you the pennant.

In real baseball, Bonds’ value goes up, but not that much.  He adds 5 wins to your team, but the SD of wins is maybe about 7.  He gives you a great shot at winning, but no guarantee.

That was the extreme case.  In the real case, having 8 hitters instead of 9 makes each a bit more valuable.  But that slight increase is so outweighed by luck that I doubt you’d notice much difference.

That’s just an intuitive argument.  It may be wrong.

I think you can argue that the salary advantage is actually much smaller, on average, than it appears.  The reason for this is that there is one very large outlier in your dataset.  If you were to exclude the Yankees from the data, then the difference between the average NL team and the average of the 13 remaining AL teams is down to about 1.6 MM.  So while the Yankees account for about 85% of the difference between the average AL and NL team salary, I don’t think they account for anywhere near that portion of difference in the head-to-head winning percentage.

Phil/29,

I’m not sure that it’s outweighed by luck really.  If the SD is 7 around an average of 81 wins, and you add Bonds to your average team with 8 hitters, and assuming the SD is still that 7, but your most likely team output is centered around 86 wins and one SD ranges from 79 to 93 wins instead of 74 to 87.

31/Millsy: right.  And that makes Bonds worth a lot.  But not infinite, because there’s still an excellent chance that Bonds’ team won’t make the postseason. 

What would he be worth?  Pick a decent number.  Then keep in mind that the way you got to that number was to reduce the roster from (say) 15 full-time (equivalent) players to 1.  When you reduce it from 15 to 14.3, by eliminating the DH, you’re talking maybe 1/20th of that effect.

Gotcha.  Wasn’t clear on the idea you were presenting before.  I would definitely agree that Bonds isn’t worth that infinite amount.  But I think having that production in a single roster spot is advantageous in the event of being at an AL park.  I tend to agree that the DH isn’t a main part of the effect of AL domination in NL parks for reasons presented by John above.

If the AL team having a DH is equal in value to the NL teams making up for that loss in value of not having the DH by improving in other areas like bullpen depth, starting pitching and the other 8 starters then in theory a NL team should be able to move to the AL and be just as good against AL teams as it was against NL teams.  With the only difference being lower payroll and noise.

But we see from the empirical data that over the last 5 years or so, the NL teams have been more inferior to the AL teams by much more than just a difference in payroll “should” be.  And the difference is great enough that it can’t be all attributed to noise.

If there is no inherit advantage of having the DH, then a team from the NL, should be able to move to the AL and perform at the same level.  The sample of interleague games played with the DH doesn’t back that up.

If an AL team were to move to the NL, it would take a hit of losing it’s DH or possible taking a defensive hit from putting their DH in the field.  But it would be more than offset from not having to face other teams with a DH.

vr, Xei

XeiFrank/34,

“If there is no inherit advantage of having the DH, then a team from the NL, should be able to move to the AL and perform at the same level.”

This is incorrect. The NL team is built for a lower scoring run environment. All else equal, moving to the AL means that their run differential will decrease: they will give up more runs to the higher powered AL offenses and not make up the difference because they have a worse DH. Thus, moving between leagues will (again, all else equal) cause the NL team to perform worse.

However, the same is true of an AL team moving to the NL. They will give up fewer runs, but because more of their run scoring was concentrated in their DH than NL teams (who don’t have one), they will see a larger decline in runs scored, also reducing their run differential. Thus, switching leagues always hurts the switching team. This means that the DH is not an inherent advantage for AL teams: it should hurt them when they visit an NL ballpark.

When I say that the DH provides no inherent structural advantage for the AL, I simply mean that the harm that it does the NL when they play in AL parks (which easy to see and thus draws a lot of attention) will be balanced by the harm it does the AL when they play in NL parks (which is subtler and therefore draws less attention).

If I may elaborate a little bit more, the existence or non-existence of a DH changes how a given team values certain players. It does not change the value of a win to a team. Thus, if each team had equal resources and was a perfect talent evaluator, they would all end up spending the same amount for the same number of wins.

Howevever, when the rules change for any team (DH added where non had been; DH removed where one was expected), this means that the roster is now valued incorrectly. The method that they would have used to evaluate their players is now incorrect. Their resources are now not value efficiently, whereas every team for whom the rules have not changed still has a correctly valued team. Thus, the team that has had the rules change on it is at a disadvantage.

Now at any point in time talent may be distributed such that AL teams have an advantage that may manifest itself through the DH position. The underlying cause, however, is not the DH.

if wonder if these factors explain why the AL spends more:
- path dependency
- market size
- incentives for organizational learning/spending
- Yankees exist

Briefly:
- Path Dependency: It seems that at some point, NL teams realized they were mediocre, and decided they were fine with that.  Except for the Mets, Cubs, and more recently the Dodgers, no other teams has committed to having a playoff team every year.

- Market Size: no theory/explanation here, but you’ve got to wonder if AL teams simply have better revenue or returns to wins.

- Incentives: Earlier on, AL teams saw division rivals overtaking them after relying on more statistical analysis.  The As, Red Sox, and Indians, and the Rays adopted the new model and won.  The Padres, Diamondbacks, and (briefly) the Dodgers adopted the new model and struggled. 

It doesn’t look like the entire AL was universally spurred to go sabermetric, but I think it’s fair to argue that without the As, the Sawx aren’t dominant, and the Jays aren’t decent, and the Rays wouldn’t have taken off.  The Rangers haven’t shown much until this year, of course. 

I guess a corollary to this is that even if organizations fail, they may not learn.  The Giants kept spending and kept failing for years. 
This would understate the effect of the payroll disparity, and of course the Orioles are the Giants of the AL, but it does show how clubs can be lose even with money to spend.

- And I wonder if this last one isn’t a bigger deal, but having the Yankees in the AL has to make a decent sized dent.  They