The Myth Of Defensive Diminishing Returns
This was written before the Kotchman deal became public. I published it, then took it down when the Gutierrez news broke (so it wouldn’t get lost in the shuffle). This is not written to justify the Kotchman acquisition, which I’m lukewarm about. But it’s still true.
One of the popular phrases you’ll hear people spout is that the M’s “have enough” defense and now need to focus on adding some offense. The idea behind this is that adding another good defensive player will have less of an impact on the team’s overall record, because they are already a good defensive team. This is basically the theory of diminishing returns, where the next unit of something is worth less than the prior unit you acquired.
There are a lot of areas where diminishing returns are an important concept to understand. When stores try to up-sell you into an 84 ounce drink because its the best “value”, diminishing returns helps you realize that the actual value of the liquid beyond what you should consume is actually zero, so you’re paying for something you simply don’t need, and in reality, you should just order the human sized version.
This even applies in roster construction for baseball teams. The Mariners have four power right-handed relief pitchers on the roster right now, with David Aardsma, Mark Lowe, Brandon League, and Shawn Kelley. The marginal value of adding another reliever to the bullpen is diminished from their true talent level, because there are only so many high leverage innings to go around. If the team signed a guy like Jose Valverde, his innings would come at the expense of one of the relievers already here, so the actual value they’d get from Valverde would be less than what he would add to a team with a more shallow bullpen.
Since this is a valid theory, and it works in other parts of roster construction, a lot of people have no problem transferring it over to the defensive side of the game. The assumption is made that a quality defensive team will face diminishing returns from adding another quality defensive player, resulting in a value add that is less than the player’s actual abilities.
This assumption is wrong.
Put simply, almost every single ball in play that matters is only catchable by one player. On a line drive to left field, the quality of the defender at second base is completely irrelevant. That the team already has Franklin Gutierrez and Jack Wilson doesn’t matter when the hitter smashes a line drive down the first base line – the only variable on the defensive side is the quality of the first baseman. If he’s lousy, then the play isn’t getting made, regardless of how good his teammates are defensively.
Now, I know there are plays where two defenders converge on the ball, but those balls in play are going to be outs 99.9 percent of the time even if the second guy doesn’t get there. Even the worst defensive teams in baseball turn 65% of their balls in play into outs. Nearly two-thirds of all non-HR contact is fairly routine for the defense, and those plays are going to be outs whether you have Adam Dunn or Endy Chavez playing defense.
The plays that matter, though, where the runs are saved and wins are earned, are on balls that are smoked. Hot shots up the middle, sinking liners in the gap – this is where the difference in defensive ability comes into play, and on nearly all of those types of plays, there is only one guy who has a chance to convert the out. His defensive quality matters, and that’s it.
History has shown this to be true. When you put a good defensive SS next to a good defensive 3B, their individual numbers do not take a significant hit. Ichiro’s UZR did not go down when the Mariners replaced Jeremy Reed with Franklin Gutierrez, despite Death To Flying Things covering more ground than any outfielder in baseball. Adrian Beltre’s UZR didn’t crash when the team went from Yuniesky Betancourt to Ronny Cedeno and then to Jack Wilson. There just aren’t enough plays that matter where two guys both can convert the out for there to be significant diminishing returns in playing quality defenders side by side.
If the Mariners add a good defensive first baseman, they will get the full value from his glove, regardless of the fact that they already have good defenders around the field. If they upgrade their second base defense, it will improve the run prevention, even though they already have Jack Wilson playing shortstop. There is no evidence that there are significant diminishing returns from adding another good defender to a team that already plays good defense.
Run difference matters. Whether you create another 20 runs with an offensive first baseman or save another 20 runs with a defensive first baseman doesn’t matter. 20 runs are 20 runs, and those 20 defensive runs saved are not dependent on the skills of the other guys on the field.
Now, it’s certainly easier to find a +20 hitter than a +20 fielder at first base, so there’s a pretty solid argument to be made that the team will likely add a guy who is more of an offensive player at the position, but don’t buy into the hype that the team “needs a hitter and already has enough defense”. It’s not true.
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Doing some playing with Pythag, and it looks like a small positive run differential is far more valuable to a team with great defense than to a team with poor defense. (The sword cuts both ways, though–a team with poor offense is hurt far more by a small negative run differential.)
Runs RA Pythag win%
324 162 0.8
486 324 0.692307692
648 486 0.64
810 648 0.609756098
972 810 0.590163934
1134 972 0.576470588
1296 1134 0.566371681
1458 1296 0.55862069
1620 1458 0.552486188
I’ve put the semi-realistic range (based on last year’s actual min/max runs scored/runs allowed) in italics, but when I do that, it becomes pretty clear that we’re never, ever going to see a season where the “extreme endpoint” analyses suggested by prior commenters will have any relevance, and so in practice, a run saved will always be equal to a run scored.
Put simply, almost every single ball in play that matters is only catchable by one player.
Infield groundouts require coordination between the infielder and the 1st baseman. It would seem to me that first base is the 1 position where there is a diminishing return on defense.
A first baseman who is adept at picking throws out of the dirt is more valuable to a team who throws a lot of balls in the dirt.
I don’t know enough about how defensive metrics are put together to know if picking throws out of the dirt is even a component of a first baseman’s defensive value, but whether it is or isn’t, I do think there is some diminishing return with regard to first baseman on any play where their play is combined with a throw from an infielder.
Also, when it comes to first base defense, picking throws in the dirt represent a significant amount of a first baseman’s defensive value.
Too extreme. More realistic: Is a team that scores that on paper scores 5 runs a game better than one that on paper scores 4 runs a game?
Given the streaky nature of offense, it’s hard to reliably construct a team that will win 4 runs or 5 runs a game. So you aim high and hope that over the course of a season the surges cancel the streaks. I.e. you aim for what should be a 5-run-per-game offense, hoping to see at least 4 runs a game when you factor in slumps and injuries.
After reading the piece, I was going to make (though probably not as well) the argument that MFAN made above very well. My understanding of the math says he’s right, that you’ll have a mostly direct/linear impact on OBP, but surrendering runs is a different beast.
Another way of thinking of it–which was in my question for Saturday on that thread — is isn’t it significantly easier to reduce a run/game surrendered from 4->3, than from 2->1? There’s some exponent on run prevention math — because it’s clearly possible to squish from 5 to 4 runs a game, but is effectively impossible to go from 1 to 0 (or even 2 to 1)
As it turns out, it doesn’t really matter who hits where. The difference between an optimal and pessimal lineup over 162 games is on the order of half a win
I’ll bear that in mind if I ever see a starting lineup for a game that has Rob Johnson batting first and Jack Wilson batting third.
There is a principle in analysis that is usually called the reasonableness test, but is often also called the “stink” test. Simply put, does the analysis fit within reasonable analysis? If not, then likely your analysis is faulty.
In this case, whatever analysis you used is faulty.
This is exactly where such a worthless, lowdown, stupid, old school stat as RBI proves that batting orders matter. Rob Johnson hitting lead off is not nearly as effective a strategy as Ichiro hitting leadoff – and if your analysis does not point that out the fault is in your analysis.
@wschroer – Actually if you read “Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong”, you’d find that Graham is right. If you took the same 9 players and rearranged them in any particular order, the difference is minimal.
Try reading it.
http://alumnus.caltech.edu/~raj/writing/BattingOrder.html
http://www.retrosheet.org/Research/SmithD/Batting%20Order%20Lineup2006.pdf
The first link is a study of batting order in which the spread was closer to 6 games than a half game.
The second link looks at run production depending on which batting order player starts the inning. This study is good to bear in mind considering that we have the best leadoff hitter in baseball.
@wschroer
Lots of things in life don’t pass the stink test, but are true. The human brain just isn’t optimized to think about certain problems the right way, so the answers seem wrong even when you can mathematically prove them to be true. The batting order is one instance, and the Monty Hall problem is another.
KaminaAyato – I assume you’re alright with Rob Johnson batting first, Jack Wilson batting third, and Ichiro batting 7th. Every day. For 162 games.
As long as those 3 are part of your best 9 OBP position players with at least some consideration given to defense and SLG, then sure I’d give it a whirl if nothing else than to test the theory IRL.
Heck, I’d even be willing to give the whole “pull lineups out of a hat” for 162 games a try as long as you have only the “best 9” in the hat.
Kamina – See, that’s the thing. No real-life team is constructed that way. Almost no real-life team could be constructed that way, unless everyone’s OBP was roughly equivalent only because everyone’s OBP was replacement-level.
So as thought exercise, yes, lineup order doesn’t matter and there’s good math to show it. But you have to have certain pre-conditions for that to exist (everyone’s OBP pretty close to each other) that almost never come up.
This is a really insightful post and one of the best in recent memory at taking an in depth look into the numbers behind baseball. There are a few things that I would like to add.
First, mfan has some very insightful analysis, but has overlooked a couple of things. Although the impact on runs saved would diminish as plus defenders are added to a team, the effect on added wins would not diminish so that there would not in fact be diminishing returns by continuing to upgrade the defense. (Example: although it is easier to reduce runs allowed from 3.5 per game to 3.0 than from 3.0 to 2.5, the added wins from going from 3.5 to 3.0 would be greatly exceeded by going from 3.0 to 2.5) Also, it must be pointed out that returns on offensive upgrades do not increase but actually stay constant the same as defensive upgrades. Sure, more runs are generated by adding a POINT of OBP to a high OBP team than to a low OBP team, but the effective runs added are greater when a high OBP PLAYER is added to a low OBP team because that PLAYER has a greater effect on the TEAM OBP and on TEAM runs on a low OBP team.
Secondly, I agree that defensive runs saved essentially are equal in value to offensive runs generated, but I would propose that there are several reasons why defensive upgrades may actually be better than offensive upgrades: 1) There is a greater likelihood that a terrific defender will have an above average year on offense than there is that a great offensive player will suddenly improve on defense, so the upside of a defensive player may be inherently higher all other things being equal. 2) The largely unquantifiable element in any game is errors and the better defensive team makes less of those which means that a great defensive team does not need to record an RBI in order to drive in the winning run, they just need to be better at defense than their opponent. You can in fact score runs on errors by the other team. 3) As stated earlier, better defensive teams experience less wear and tear on their pitchers throughout the season. 4) History has proven that you don’t need a great offense to win championships, but you do need a great defense. 5) Also as stated earlier, defense is cheaper than offense. This trade would essentially be a payroll swap with the money owed to Bill Hall going to Kotchman, which means that the team still should have about $8 to $10 million to invest in starting pitching and I am not quite convinced that we are done tinkering with 1st and 2nd base just yet.
I am very excited for 2010 and Jack Z may end up changing the way franchises look at building teams and the way defensive players are treated in the free agent market. Go Mariners!
I’m sorry, this can’t go unchallenged.
I know the mantra “Defense Wins Championships” but besides the Ozzie Guillen’s go-go White Sox, who has won title recently without a superior offense?
(sorry for straying from this original topic, but I dislike claims like this…)
I’m not sure you’re getting the point or not. If say we look at the ’09 M’s and the best OBP while taking into account for defense.
C Johjima .296
1B Branyan .347
2B Lopez .303
3B Beltre .304
SS Wilson, Jo. .294
LF Langerhans .311
CF DTFT .339
RF Ichiro! .386
DH Sweeney .335
(of course there are IMO)
If these were my best 9, and if I understand the book correctly, then shoving Ichiro to the bottom of the lineup everyday might cost me 2 wins at most compared to lining them up in descending OBP order.
The players don’t have to be replacement-level or have similar OBP numbers for the theory to work though. At least that’s what I understood from reading it.
And to clarify, the point in the book was that it didn’t really matter how you ordered your lineup, rather it mattered who you put in your lineup.
Since 1972, there have been twenty-seven teams that made the postseason in spite of having below-average offenses. Of these, seven won the World Series: the 1985 Royals, 1987 Twins, 1990 Reds, 1995 Braves, 1996 Yankees, 2000 Yankees, and 2005 White Sox. All of these teams, except the 1987 Twins, had excellent pitching staffs; it’s hard to make the playoffs with a below-average offense unless you have an excellent pitching staff.
Conversely, twenty teams have made the postseason with below-average run prevention. None of them won the World Series, and only two (the 1982 Brewers and 1993 Phillies) even played for the championship. Sixteen of the twenty lost the first playoff series in which they played.
All the more reason to have multiple above-average hitters, because hitting is streaky and you need some insurance against one or two guys slumping. The 2009 Ms are a recent example of what can happen if you build for superior defense and superior pitching, and expect just average offense will be sufficient: good, but not great.
Sorry, should have put something in there to indicate that I was quoting the linked article, not using my own words.
Superior defense, yes…
Average offense, sure…
Superior pitching… um….
Outside of King Felix, and the approximate ½ seasons out of Washburn, that Canadian guy, and oh yeah RRS, 78 games were thrown by the likes of Vargas, Snell, Olson, Morrow, Jakubauskas, French, Fister and Silva (*shudder*).
I’m not sure I could qualify that as having superior pitching.
With 640 runs scored compared to a MLB average of 747, they were not close to average offensively either.
Hmmm…
Superior defence – Yes! Definitely! Top UZR/150 in the league by a big margin!
Superior pitching – well, we only were better than 4 teams in the league in xFIP (Orioles, Indians, Rangers, and Angels) so low average at best – certainly not superior.
Average offense – well, our wOBA was the absolute worst in the league. Nuf said.
Luck in 1-run decisions (35-20) – Yes!
Results show 85 wins. It’s a good year.
This is interesting data, especially the conclusion. Even those teams you call out as WS champs which were inferior offensively, were not that far below average. And from my cursory look, none of them were Mariner-sized below average.
Certainly playoff teams can be built without screaming hot offenses, but that is not optimal – screaming hot offenses are generally going to be more successful given that the other phases of the game are not ignored.
History would say it is more likely that a team will make the playoffs due to good defense, good pitching and good offense rather than excellent defense, good pitching, and dreadful offense. Right now, we are a dreadful offense. In our case, it probably would not matter all that much if Ichiro did bat 7th, to tell you the truth.
Taking market value into consideration, I’ll gladly side with all of the defense-defenders here.
Throwing “diminished” value and “accelerating” value aside for a minute, offense and defense both have a lot of just plain value, obviously. And it is a lot easier to build a spectacular defensive 8-position roster on a ~$100M payroll than it is to build a spectacular 8/9-man lineup on the same payroll because the market value of defense is so disproportionately low.
It’s like buying 5 boxes of store brand cereal for the price of one name brand! (Breakfast of champions, anyone?)
And this, I think we can agree, is where Jack Z has been a true wizard. (or wizdurd?…)
I love going super economy when it comes to airline tickets, but not if it involves changing my destination from Hawaii to Pullman.
Kamina, georgmi, oolon – I said built for. You’re listing off the results. I’m talking about what was intended at the start of 2009.
The plan, going into 2009, was to expect average offense and have the pitching and defense be what really got the wins. When the offense fell off of a cliff and half the reliable starters in the rotation were traded away, the only things holding it together to get to a better than .500 season were luck (one-run games) and defense (top in the league).
85 wins. 12 more wins were needed to win the west, 10 more wins needed to win the wild card. Reduce that down to perhaps 10 and 9, respectively, if some of those wins were likely to have been against Anaheim or Boston. Could those 10 or so wins have come from improved #3 and #4 pitchers alone? Didn’t they need a better bat in there at some point?
Putting aside the fact that looking at WS teams to prove or disprove this argument is not probably the best method, you’re making relative arguments. An excellent defense would be consisted of a bunch of +10 defenders, while an excellent offense could consist of a bunch of +30 hitters.
There is no absolute difference between a group of 9 +10 defense/0 offense and a group of 0 defense/+10 offense.
I’m not trying to say that it is easy to win a championship without a great offense, just that it is entirely necessary to have a great defense in order to win. The Mariners may not be likely to win the World Series this year, but they do have a great chance at contending for a playoff spot and then once you get in who knows?
Also, has anyone else noticed that by pursuing players with undervalued skill sets the Mariners are putting themselves in excellent position to be able to spend some serious money over the next two years in acquiring the two rarest commodities currently in baseball, namely dominant pitching and a power-hitting left handed 1st baseman? (I think we can all think of a couple of good candidates for those positions.)
If you want to see a whole 25-man roster go to Hawaii first class, root for the Yankees.
I’ll be just fine in seat 27D eating my peanuts with all of the undervalued talent we’re getting on the cheap. There is more than one way to get to Hawaii, y’know.
I will, however, hold out hope that Jack Z can dig us up a real crown jewel: some undervalued offensive prowess. Ooooh, aaaah…
There’s no doubt that a firstbaemen that has great ability to scoop throws should have an positive impact on the other infielders. What I haven’t seen yet is whether or not Kotchman has that elevated level of ability. Has anybody seen evidence that he’s better able to handle throws from infielders such that we should assume he’s going to make our other infielders better?
No, it’s not. Win Shares would be a derivitave stat, but WAR considers the events produced by the different players and contrasts them with league average to to arrive at a value. It does not consider team context and a team’s total WAR can often be different than it’s won/lost record.
I’m pretty sure that the difference between optimal and pessimal (nice word, by the way) is much more than that. I hadn’t previously seen the link Jeremariner provided that estimated it at 6 wins, but I’ve seen many other sims put it at around 3 or 4.
Whoops, you’re totally right. I should have said that the difference between optimal and MLB standard is around a half win, and then the drop to pessimal is another 2.5-3.5, which completely invalidates my point.
Here’s why there is no minimum level of offense needed: Any time a team loses, it could’ve prevented the loss by not allowing their opponent as many runs as they did. The only scenario that could be claimed as an example of diminishing returns, where creating a more balanced roster could’ve won the game, is if a team loses a game that went into extra innings tied at zero. How many of those ever happen? If this happened a lot, it could be said that the team was already so good at preventing runs that they would’ve still shut out their opponent through nine even if they’d replaced one of their Adam Everetts with an Adam Dunn. Since this is an extreme, the minimum offense argument shouldn’t have any weight.
Milton Bradley.
Insert mandatory “games” joke here. But seriously, anything one can buy with the coin of Carlos Silva is a win.
Unfortunately my friend, you may have been sold a plane ticket to Hawaii, but you are in fact on a slow bus to the bottom of the division.
One does not have to be in first class to compete and perhaps to win, but you do need to climb out of the luggage bins and stop digging around for quarters in the upholstery.
[meta]
Huh? Since when? I will grant you that it is certainly easier to win when you have decent defense, but this years Yanks were not a particularly stunning model of defense. Even using the stats supposing to show the importance of defense, UZR, the Yanks were at -18 according to Fangraph, and as I recall, they won a little something called the World Series.
[meta]
I’ve read both posts and comments and believe I’m not repeating anyone. I did not see much direct discussion of defensive positioning. Though this post has fallen off the front page, it’s very much worthy of further discussion.
First of all, proper defensive positioning justifies one of Dave’s main arguments. Dave claimed (obvious paraphrasing) that the number of extreme, high-impact plays that can be handled by more than one defender are very rare. I agree, because teams position their players expressly to avoid such overlapping coverage.
Positioning allows the addition of a good defender to not take away high-impact opportunities from neighboring players by adding range on the other side of the neighboring positions. Examples from obvious to less so:
(a) SS and 2B with extreme range allow 1B and 3B to shade towards the lines and take away doubles and triples. The inverse is also true.
(b) Infielders with extremely good range into the outfield on flyballs allow outfielders to play deeper and take away additional doubles and triples.
(c) CF with huge range allows LF and RF to take away flyballs down the line and extend their range into foul territory.
(d) 3B with extremely good bunt-charging skills (Beltre anyone?) allow C and P to ignore the 3B side on bunts and take away the first side. Perhaps 1B don’t need to charge at all in some circumstances.
(e) Slick SS and 2B encourage P to ignore all grounders except those hit pretty much at him.
(f) Extreme range 2B reduces the positioning “penalty” paid by holding runners at 1B.
In short, if clubs make adjustments to all defenders as better individuals are added to the defense, the added range shouldn’t take away from neighboring players. The biggest impact is reduction of extra-base hits along the lines and to the wall. Otherwise ignored opportunities are added, such as more range in foul territory.
i want to address what i feel are the two most germane questions raised so far.
one, does a run saved = a run scored ?
two, given a great defender, what specific benefit will he bring to your specific team ?
i had submitted a long post on this. it seems to have disappeared (arrgh), so i’ll sum up the major points.
one, using pythagoras calculations, a run saved does equal a run scored. this varies slightly the further from average a team is. comparing runs scored and runs allowed, for a team with around a +75 run differential, run saved have a 10% bonus. for a team with around a +175 differential, runs saved have a 20% bonus. for a team with a +300 differential, runs saved have a 30% bonus. conversely, for teams that give up more runs than they score, runs scored are worth slightly more, at similar rates.
i want to emphasize – since this is a common misconception – for a team that scores and allows about the same number of runs, a run scored = a run saved. it doesnt matter if the team scores and allows 600 runs, or scores and allows 1000 runs.
two, the actual (defensive) impact of a player for your team is hard to tell. a first baseman who is good at scooping throws is valuable if your infielders are wild throwers, but not if they arent. so without play-by-play analysis, you probably have to take the known defensive value then make an educated adjustment.