However, Dave Cameron made an interesting point: the Rockies play in the National League West, where hitters seemingly face s larger proportion of stud pitchers — Dave mentioned Tim Lincecum, Matt Cain, Madison Bumgarner, Clayton Kershaw, and Mat Latos in this connection. He also pointed out that Longoria did not have to face the Rays’ own excellent pitching staff. So I decided to look at it more closely. The point is not to settle the Longoria versus Tulowitzki dispute. Rather, I am interested in whether individual hitters face (or do not face) particular pitchers enough that they require a “divisional” adjustment of some sort.

Let’s get a couple of things out of the way. First of all, I am not going to get into the overall American League versus National League dispute here. I realize that even seeing a birth certificate is not going to convince some people, so I will simply reference (again) MGL’s recent study and his more extensive 2006 study. If you want to complain about the assertion that the AL has better talent overall, please direct your complaints there or elsewhere. While the Senior Circuit has caught up and perhaps taken a slight lead in hitting talent (at least through 2011, who knows how this off-season might have changed things), the AL still had more talent overall because of a much greater lead in pitching.

Second, the best way to do this would be to take all the pitchers each hitter faced and get projections (or retro-jections) of the true talent in 2011, including all of the relevant adjustments for environment, and then compare. Well, I’m not doing a whole set of pitcher retro-jections and then matching them up per plate appearance with two hitters for one post. I am claiming that this is some super-duper rigorous study. I am simply going to look at the small group of “really good” pitchers as given by my Twitter interlocutors. There were other qualifications I could put in here, e.g., the problem of park factors and interleague comparison, but I’ve already gone on too long with prefatory remarks. Caveat lector.

Did Troy Tulowitzki face such a great proportion of NL West studs (as listed by Dave and others) such that he should get a special “adjustment” for difficulty level? For the sake of keeping things relatively simple, we will just look at 2011 matchups. (I just used MLB.com’s pages, which do not have PA listed separately, in a convenient way, so “plate appearance” should be understood as AB+BB for the purposes of this post. Yes, this probably led to an insignificant arithmetical error or two.) Tulowitzki had 596 plate appearances (AB+BB) in 2011: six versus Linceum, six versus Bumgarner, nine versus Cain, nine versus Kershaw, and 10 versus Latos. That is a total of 40, just under seven percent of his total plate appearances.

While that might be a slightly greater proportion of good pitching than hitters for other NL teams and divisions may have faced, given that 93 percent of his plate appearances came against the “rest” of the league (I know it gets complicated because of interleague, but let’s just stick with the basic premise for the sake of simplicity), I do not think that requires us to make NL West hitters like Tulo a special case. We do not take 40 plate appearances to be a significant sample for almost anything of which I am aware of off the top of my head.

How about if we expand this off-the-cuff selection of great pitchers to include the Diamondbacks’ Daniel Hudson and Ian Kennedy, as Paul Swydan suggested? (With all due respect to Paul and the great years and Hudson and Kennedy had, I am not sure who would put them on the same “true talent” level as Kershaw, Lincecum, or Cain, but let’s humor Paul. Dude’s gotta be exhausted from running all those “After Dark” chats.) That adds another 16 plate appearances to Tulo’s list of “stud” opponents. Again, without doing the math, I am pretty sure that those 16 plate appearances do not push things over into “cancel that league adjustment” territory, as the total is still under ten percent of Tulowitzki’s plate appearances.

What about Longoria not having to face the Rays’ staff? That’s a bit trickier, since we do not have the numbers for how many times Longoria would have faced individual Rays pitchers in an alternate universe. With a bit of digging, I found an AL East hitter who faced the Rays quite a bit: Dustin Pedroia. Now, I was not given a list of “official studs” on the Rays’ staff, but for 2011, I will count David Price and James Shields. Pedroia had 721 plate appearances (AB+BB) in 2011; 16 versus Price, 17 versus Shields. That comes to a total off 33, or less than 5 percent of Pedroia’s plate appearances.

Oh, I’ve forgotten one Tampa Stud: Pedroia also faced Matt Moore twice, pushing things all the way up to… 4.8 percent. Obviously, if I am no inclined to accept that Tulowitzki’s proportion of stud pitchers faced should change the way we thing of his “difficulty adjustment,” I am not going to be doing the same for Longoria based on an even smaller proportion of hypothetical plate appearances.

[Side note: Longoria faced CC Sabathia 16 times, more than Tulowitzki faced any one of the NL West pitchers listed above.]

The 2011 National League West (and the San Francisco Giants in particular) did feature a number of tremendous pitchers, and it is understandable that one would be tempted to judge the hitters in their division on a different grading curve. However, even taking both those pitchers that Tulowitzki faced (including Hudson and Kennedy) and that Longoria did not face together, we are talking about less than 80 plate appearances between two players versus more than 1000 PA versus of all the other pitchers they collectively faced during the season. If someone wants to do a more detailed and mathematically rigorous account of that proves otherwise, that would be both great. Until then, I do not think Tulowitzki and other NL West hitters get bonus points, or at least not a significant number of them.

Our current measures of opponent strength are imperfect and somewhat crude, and can probably be improved upon. I can understand the why Dave and others want to note that hitters in the 2011 NL West faced a great number of excellent starters. But as we have seen, a hitter like Tulowitzki faces a group of seven starters less than 60 or 70 times a season, and given all the other evidence about the league-wide skill level of the far greater proportion of hitters he faces, those league-wide evaluations likely come closer to the truth about the difficulty level faced by a individual hitters. In any case, Tulo is a great player, he doesn’t need the extra credit.

Prince Fielder and Albert Pujols signed huge deals this offseason, which pays the sluggers into 2020 and 2021, respectively. The rate of salary inflation over the next decade will play a big part in how those contracts work out. The most common assumptions are $5 million per WAR and a 5% inflation rate, which would mean Fielder would have to produce 36.9 WAR over the life of the contract in order for the Tigers to “break even.” The break-even number for Pujols’ back-loaded contract is 37.8 WAR:

If we instead assume inflation slows to 3% per year, those break-even levels change to 39.7 and 41.4. It might not sound like much — 3.7 WAR over ten years in Pujols’ case — but that translates to $18 million of contract value.

Everyone knows that baseball players are well compensated for their skills. The gap between baseball salaries and the rest of us massive, and it’s increasing over time. In 1992, the average MLB salary was 32-times the annual income of an American household. By 2010, baseball salaries were 66-times higher.

Is it possible for this trend to continue? Yes and no.

The difference in salaries between Major-Leaguers and the rest of us will continue to increase, but not at its current rate. In the long run, U.S. households will make about 3% more per year, but baseball salaries will increase at about 4% per year, meaning the gap between the average baseball player and the average American will widen by about 1% per year.

On a couple of occasions, I attempted to create a model which would predict salary inflation in baseball for the upcoming season. Both of those attempts looked at short-term predictions — the expected salary inflation given the current state of baseball revenue and the current economic health of the country.

If we pull back and look at the issue in the long term, the new perspective leads to the new 4% conclusion.

The first step is to trace where the money for players’ salaries comes from:

The above chart does not, under any circumstance, represent every nuance of this very complicated system. However, hopefully it shows the source of most of the money behind teams’ payroll.

Let’s start at the top. Households make money. Part of that money is taxed, some money is saved, and everything else is used for consumption. If you multiply the amount of household consumption by the number of households, you get the total pool of money being spent on goods and services.

Some percentage of that pool is spent directly on purchases from a team. That money is revenue for the team. Most of the total consumption money goes for non-baseball goods and services, but some of that trickles down to baseball as well.

As corporations earn money, they have money to spend on advertising, which is a significant income stream for both individual teams and the MLB as a whole. Advertising dollars are what drive the MLB’s contracts with television networks, and thus revenue which is split between the 30 clubs.

So, teams get money from direct sales, team-specific ads and licensing contracts, and a cut of the MLB pie. Yes, this is an over-simplification, but I am trying to keep it easy.

When teams earn revenue, it gets allocated to various parts of the organization, with a large hunk going to pay for player contracts. When teams have more money to spend on players, the supply of players is (presumably) fixed, and thus $/WAR inflation.

What does all of that mean, and how does that lead to a 4% per year conclusion? Well, the two boxes that start the whole process are always increasing. Household income increases by about 3% per year — which leads to 3% more consumption per household. The U.S. population increases by about 1% per year. Therefore, 1% more people and 3% more money yield a 4.03% increase in the pool of total consumption dollars available. As long as all of channels maintain a constant flow to the proceeding step, on a percentage basis, that 4.03% makes it way all the way to the bottom.

But wait a second, if the above is true, then why have baseball salaries risen by 5% on average, and by double digits in some years? Well, the flow chart assumes that the percentage going from one level to the next remains constant. For example, the percentage of income used for consumption or the percentage of team revenue dedicated to payrolls. If any of those increase, then everything below increases, and the amount of salary inflation increases.

For that reason, this is a long-term analysis. I would not be surprised to see salary inflation continue on its current 5% path for a number of years. Eventually, whatever channel that extra inflation is coming from will have to hit a ceiling. Things like the share of income spent on tickets or the percentage of advertising dollars spend on baseball simply cannot increase without bounds.

Whenever the percentage of cash flow from one step to the next is constant, salary inflation will be driven solely by the increases in nominal income and population, which should yield about 4% market inflation.

As stated earlier, this means the gap between baseball players and average Americans will continue to increase. The reason this exists in baseball (and other sports) is that the number of jobs is a constant. Increasing payroll means either increasing the average wage or hiring new employees, and in baseball there are only 750 major league roster spots, so the average wage has to carry all of the inflation.

When will the short-term become the long-term? One can only speculate, but on a 10-year contract, using the long-term estimate seems like a good educated guess.

But what about the state of the ground in baseball today?

Since FanGraphs started tracking ground-ball rate in 2002, there haven’t ever more ground balls in the game. Home runs per game hit an eighteen-year low. ERA was at a twenty-year nadir. That’s it, six more weeks of winter for power hitters — our pitchers are learning how to get more ground balls and we’re in for some more offensive winter, right? Phil has seen his shadow and returned to his hole.

Wait, let’s do this again, says Bill Murray. Yes, ground-ball rate was at a ten-year high last year… by one-tenth of a percentage point. Here’s the relevant ten-year stretch:

	G	K/9	BB/9	HR/9	BABIP	LOB%	GB%	HR/FB	ERA
2002	17611	6.53	3.38	1.05	0.289	71.70%	43.30%	10.70%	4.28
2003	17817	6.4	3.3	1.08	0.291	71.20%	43.30%	11.20%	4.4
2004	18272	6.6	3.36	1.13	0.293	71.40%	44.20%	10.90%	4.46
2005	18035	6.38	3.17	1.04	0.292	71.70%	44.20%	10.60%	4.29
2006	18694	6.59	3.3	1.12	0.298	70.90%	43.70%	10.80%	4.53
2007	19294	6.67	3.33	1.03	0.299	70.70%	43.50%	9.60%	4.47
2008	19013	6.83	3.39	1.01	0.296	71.40%	43.90%	10.10%	4.32
2009	19097	6.99	3.46	1.05	0.295	71.90%	43.30%	10.10%	4.32
2010	18786	7.13	3.28	0.96	0.293	72.20%	44.30%	9.40%	4.08
2011	18754	7.13	3.11	0.94	0.291	72.50%	44.40%	9.70%	3.94

Allright, let’s just ignore the fact that ground balls have oscillated that one full percentage point over the last decade (and therefore a tenth of a percentage point is probably not a big deal) — hey, we ignore the fact that groundhogs have a three-to-six year life expectancy and we’ve been calling this one ‘hog “Phil” for decades. This shouldn’t be a problem. We’ve been ignoring Ned Ryerson for years.

Did anything *really* change last year?

It doesn’t seem like it. Pitchers did not throw more sinkers — the ratio of four-seamers to sinkers was 1.74 in both 2010 and 2011 according to Pitch F/x guru Harry Pavlidis. So no dice on pitching mix. How about pitch location in the zone? Thanks to Jeff Zimmerman, we have some knowledge. Look at the percentage of pitches that ended up flying high versus hitting kneecaps:

Whoo-hoo, that first step is a doozy. Case closed! Pitchers are pitching more in the bottom of the zone and that’s inducing more grounders and that’s why we had a Major League record in ground-balls last year. Phil would be proud of us. Six more weeks of winter for the sluggers!

Hold up. Hit the alarm and let’s do this again. Look at the numbers for the each zone, in half-foot increments:

Yes, there might be a trend here. More ground balls — especially when combined with a ten-year low in BABIP — are good for the pitchers, and hence the nice 2011 ERA. But we shouldn’t expect this to continue, because the trend (if it’s there) is tiny. Putting too much stock in a seven-year sample in which the combined change in “high” versus “low” pitches might be two percent is like, well, asking an animal in Gobbler’s Knob about the weather in Philadelphia. If the trend does continue, though, we’ll have Punxsutawney Phil to blame, at least as much as pitch placement in the zone.

Happy Groundhog Day!

There is something of interest in the Teixeira report, though. Sure, we do not know whether he is actually going to do it or not. Remember, this is the time of year when players say things like “I’m going to steal 20 bags this year” even if they have never stolen more than 10 in any season. Still, it is not a crazy idea. While sabermetric writing on the internet went through a phase of arguing that bunts are counterproductive to scoring and winning, research has progressed to show that bunts are not as bad as all that. In certain situations, they can be a good idea in terms of getting the win in a close game or simply “keeping the fielders honest” (also known as “game theory,” a term I am pretty sure Bruce Bochy uses frequently).

But what about power hitter like Teixeira? Isn’t bunting always a bad idea for them? To answer this properly would require a great deal of complex thinking and programming. For now, let’s take a simple approach by looking at some data from 2011 to see whether Teixeira is simply blowing smoke or making sense.

One approach would be to look at different situations in which bunts might be advisable or not advisable for particular hitters, and that is obviously the way that the hitter and his team should approach it. However, I want to take a more general, introductory approach to looking at the productivity of bunts by sluggers in general. It is important to keep in mind that many the background assumptions regarding good bunting situations, as I will briefly mention again at the end.

I have posted seasonal reviews of bunting in the past, but those were primarily focused on the managerial-strategic value of particular bunts, so I used Win Probability Added in those cases. My intent here is different. I want to see how a particular subclass of hitters did when bunting in 2011. I will use RE24, or the average change in run expectancy on bunts. Without getting into a long-winded explanation of RE24, I will simply recommend this entry on linear weights) from the Sabermetric Library.

In short, based on the expected runs scored by the end of the inning for each of the 24 base/out states, RE24 measures the change in run expectancy for each plate appearance — that is, the base/outs state’s run expectancy at the beginning of the plate appearance, after the plate appearance, and including any runs scored. This is also the empirical basis for commonly used metrics such as offensive linear weights (the basis for wOBA). The average RE24 of an event is its “linear weight,” e.g., the average RE24 of a home run is usually around 1.4 runs in modern baseball. Like WPA, RE24 helps us getting a better perspective on particular bunts than by simply repeating “making outs is bad.”

Let’s check the database (with my iffy SQL skills in mind) to see what some different kinds of bunts were worth in 2011. (Ideally, yes, I would use multiple years of data and make other adjustments, but I am trying to keep this simple for the purposes of this post.)

The average run value of a bunt in 2011 was -.0571 runs, or less than one-tenth of a run worse than the average plate appearance. That includes all bunts, not just sacrifices, and also includes pitchers bunting. (The average value of a sacrifice bunt in 2011 was -0.1153.)

Let’s narrow things down to something closer to Teixeira’s actual population. For non-pitchers, the average bunt in 2011 was worth -.0083 runs. (The average sacrifice bunt by non-pitchers in 2011 was worth -.0890 runs.) You may have noticed (without me doing a separate query) that the average value of a pitcher bunt is lower than that of non-pitcher bunts. Does this mean that pitchers are bunted too often or in the wrong situations in 2011? Well, maybe, but not necessarily. While pitchers probably are bunting in situations that are less bunt-friendly compared to the average, keep in mind that the vast majority pitchers are far, far, worse than non-pitchers when hitting, so bunting is acceptable and even advisable for pitchers in a wider variety of situations than it is for non-pitchers.

That digression aside, what about power hitters bunting in 2011?

[In case I did not make is clear before, I am not doing this the "best" way. Ideally, I would have the probabilities (estimated from true talent in 2011) for each individual hitter's potential events (strikeout, ground out, walk, single, home run, etc.) for each batter to compare those to the change that came from bunting in those situations. More simply, one might at least want a sub-Marcel true-talent wOBA estimation to compare the average expected change in run expectancy for each plate appearance compared to a bunt. Moreover, multiple years of data would be better, too. All of that is simply to acknowledge that what I am doing -- using observed performance from one season of data -- is obviously limited. However, I think it is interesting at the very least as a spur to further work in this area.]

What I did was simply to look at the average run-value of bunts for two groups of non-pitchers in 2011: those who had an isolated power of .200 or greater, and everyone else. I limited the query to hitters with at least 300 plate appearances in 2011. (Note that the earlier queries did not set plate appearance minimums, so these values are not going to add up to those given earlier).

The sluggers’ (those with an observed ISO of .200 or greater in 2011) average bunt was worth +.0376 runs. The sample was only 102 bunts, as one might expect.

(As an aside, I realize that .200 is an arbitrary figure. A .180 ISO is still good power and would have made the sample larger, but on the other hand .200 and better reflects Teixeira’s population of power hitters.)

How about the non-sluggers, those non-pitchers with 300 or more plate appearances in 2011 and an ISO under .200? They bunted 1476 times according to my query, with an average run value of -.0023.

Does this mean that the sluggers are better bunters? Should they be bunting more often? To the first question I would say that I do not know, but I seriously doubt it. As for whether they should be bunting more often, that would require a more work. This is where the previously-mentioned “background assumptions” come into play. Sample size aside, and without looking at individual plays, I think it is fair to assume that the typical “slugger bunt” comes as more of a surprise than the non-slugger bunts, and that teams were playing back or had a shift on for the power-hitter.

That is not to say that teams should not continue to shift or play back — after all, it was just 102 bunts, and while it might be frustrating to have a power hitter reach on a surprise bunt once or twice a season, it beats playing in and/or without a shift and giving up several more doubles.

Like many other fans, in the past I have wondered why more power hitters do not try to bunt to the opposite field more often to beat the shift. And, of course, like so many others, I needed to be reminded that if it was that easy, they probably would. I would imagine that Mark Teixeira is not the only one of his homer-heavy peers who has not bunted since high school. Moreover, they probably are not going to be able to do it often enough to get teams to play in or give up the shift.

However, while one might chuckle at the idea of Teixeira being a “$180 million bunter,” our little foray into recent data shows that whether or not having a slugger lay down a bunt now and then is good from a game-theoretical perspective, it can actually help teams score runs.

Consider the most recent big signing, Yu Darvish. He most likely would have made more money had he stayed in Japan for three years and come over as a free agent. Through the arbitration process in Japan, he was due around $27 million over the next three years, and his deal with the Rangers only pays him $25 million over the same time frame. Had he continued his dominance, and come over in three years, it seems likely he would have made more than $30 million over three years. He would have had the leverage of the unrestricted free agent.

But Darvish’ plight resembled that of the arbitration-eligible pitcher here in the states. He could only talk to one team, which should sound familiar. And he probably valued some non-monetary benefits that a long-term contract offered: security and the ability to compete against the best in the world. How prevalent is this sort of give-and-take in the normal process here in the states? How many pitchers have given up free agent years at below the going rate?

More than you might think. Below is a listing of all the currently active players that signed deals before they were free agents that will pay them through free agency years. Most of these players are being paid below the going rate for a player of their ilk.

	Description	Service*	$/yr (m)	3yr avg WAR
Justin Verlander	FA1 – FA3	4.002	20.1	7.2
Felix Hernandez	FA1 – FA3	4.06	20.1	6.2
Jered Weaver	FA1 – FA4	5.129	17.7	5.1
John Danks	FA1 – FA4	5	15.8	3.1
Matt Cain	FA1	4.038	15.3	4.1
Josh Johnson	FA1, FA2	4.026	13.75	4.5
Dan Haren	FA1, FA2 + option FA3	4.154	13.7	5.6
Zack Greinke	FA1, FA2	4.057	13.5	6.4
Trevor Cahill	FA1 + club option FA2, FA3	2	12.8	2.4
Clay Buchholz	FA1 + club option FA2	3.059	12.5	2.1
Jon Lester	FA1 + club option FA2	2.075	12.3	5.3
Ervin Santana	FA1 + club option FA2	3.104	12.1	2.9
Gio Gonzalez	FA1 + club option FA2	2.162	12	3.3
Brett Anderson	club option FA1	2.039	12	2.5
Yovani Gallardo	FA1	2.108	11.5	3.5
Fausto Carmona	club option FA1, FA2	1.125	11	1.6
Jaime Garcia	FA1 + club option FA2, FA3	3.047	10.9	3.4
James Shields	club option FA1, FA2	1.125	10.5	3.5
Adam Wainwright	FA1, FA2	2.027	10.5	3.9
Joe Blanton	FA1, FA2	5.016	10.5	1.5
Ricky Romero	FA1 + club option FA2	2	10.3	3.3
Yu Darvish	FA1 – FA3		10.3	n/a
Johnny Cueto	FA1	3	10	2.3
Carlos Marmol	FA1	4.084	9.8	1.5
Matt Moore	club option FA1, FA2	0.017	9.5	n/a
Gavin Floyd	club option FA1	2.045	9.5	4.1
Scott Baker	club option for FA1	2.128	9.25	2.9
Wade Davis	club option FA1, FA2	1.032	9	0.9
Brandon Morrow	FA1 + club option FA2	4.091	9	2.4
Joakim Soria	club option FA1, FA2	2	8.375	1.6
Sergio Santos	club option FA1, FA2	2	8.375	1.3
Nick Blackburn	club option for FA1	2.017	8	1.3
Jake Peavy	FA1	2.101	8	2.4
Ubaldo Jimenez	club option FA1	1.087	8	5.3
Ryan Vogelsong	FA1 + club option FA2	5.02	5.6	2.4
R.A. Dickey	FA1 + club option FA2	5.007	4.6	1.7

Description = description of free agency years bought out; Service* = service time at time of contract signing; $/yr is an average of the free agency portions of the contract.

Seen in this light, the Darvish contract takes on a new hue. Now he’s given up his three free agency years for a price that sits between Joe Blanton and Ricky Romero. It might be unfair to separate out his contract, given the posting fee, but it’s only six and 60 that show up on the player payroll portion of the Rangers’ budget, and this chart can also provide some information from the player’s perspective. Yu might have left money on the table, but not much more than Ricky Romero. That seems about right.

By the crude measure of comparing salary to three-year WAR averages, Zack Greinke might be giving away the most money on his first free agent year. Or it’s Ubaldo Jimenez, who ended up signing a long-term contract a little over a year into his Major League career. That contract gave his team a good deal on that first year of free agency (eight million dollars) in return for six years of security for the player.

Jimenez’ contract does actually point to a trend on this list. Sort the list for the average value of the free agency years, and you’ll notice something about the service time. As Steve Slowinski posited when discussing a possible Derek Holland extension, teams pay more for the free agency years for pitchers that have accrued more service time. That makes sense.

The top eight values on this list were all signed by players that had four or more years of Major League experience when they signed their contract. They signed shorter contracts and had less of a reason to give up money for security — they were only two years away from free agency on average. Perhaps for some of these more seasoned pitchers, the exchange was not security for money, but wins for money — at least in the case of Justin Verlander and Jered Weaver, it seems like they might have traded some average annual value for staying on a competitive team. Still, all of them but John Danks look like below-market deals.

That might be the most impressive fact about this list. It only includes about three guys that have contracts that may be end up being tough on their teams: Fausto Carmona, Joe Blanton, and Wade Davis. Obviously, the Rays are comfortable handing out their cookie-cutter contract to young starters (team options for the final year of arbitration and the first two years of free agency), and it seems like there’s a good reason why. The value they’ll get from Shields and (probably) Moore will pay for many many Wade Davises. Judging from this list, the Jays and Red Sox are implementing a slightly more conservative Rays philosophy — pay for a year of free agency and get one option on the player. Why more teams aren’t doing this is surprising, but not all the teams have young pitchers worth locking up like this.

This isn’t necessarily a recent thing. The Indians locked up their position players to similar contracts in the 90s. C.C. Sabathia, Jeremy Bonderman, Scott Kazmir, Jon Garland, Doug Davis, Ben Sheets and even Brandon Webb gave away free agency years when they signed long-term contract in their arbitration years.

This also isn’t necessarily a bad move for the player. Chien-Ming Wang and Jeff Niemann had opportunities to sign similar contracts, went year-to-year, and probably lost money because of it.

Perhaps what this phenomenon mostly represents is that we shouldn’t be too quick to denigrate long-term contracts that lock up the player through a few below-market years. Not only is it more common than we might think but there are also lessons from the past that teach us how quickly a pitcher’s career can fall apart. If you were less than a quarter of the a year into your first season in the league, and your team offered you a five-year deal worth $14 million, and oh, hey they’ll need a few option years tacked on the end in order to make it worthwhile for them — would you say no?

Last year David Roher at Deadspin/Harvard Sports Analysis Collective noted that over the 2000s the average number of votes per HoF ballot was fairly constant, between 6.6 and 5.35. This would suggest that in years with strong first-year candidates there would be fewer votes for returning candidates and vice versa. I wanted to more explicitly test this relationship and see whether it extended further back than just the 2000s.

I looked at every Hall of Fame vote from 1967, when the current voting rules were put in place. Along the x-axis is the average number of first-year candidates voted for. Along the y-axis is the average change in vote share for returning candidates compared to the previous year (here an increase from 60% to 65% would be denoted by 0.05).

There is quite a strong, and significant, relationship. In years when ballots have about zero first-year players the returning pool sees about a 5% increase. On the other hand when there are over three first-year players on the average ballot returning players see a 5% drop in their vote. This suggests that voters — consciously or not — do have a rough number of players they want to include on their ballot, and thus the number of first-year candidates they vote for affects the rest of their ballot.

Obviously this could spell trouble for the current ballot as the 2013 first-year pool is loaded (Barry Bonds, Roger Clemens, Sammy Sosa, Mike Piazza, Craig Biggio, Curt Schilling), and could receive higher vote share than the 1989 (Johnny Bench, Carl Yastrzemski, Gaylord Perry, Fergie Jenkins) or 1999 (Nolan Ryan, George Brett, Robin Yount, Carlton Fisk) pools, thought the PED issue could complicate things. Going from a historically poor first-year pool to a historically great one, returning candidates could see double-digit drops in their vote totals.

Power, patience and contact are the components of a delectable (productive) hitter. And yet, like wine and cheese, it turns out that these different skills age differently. Ages 26 through 28 are often used to represent a hitter’s peak, but not all of their different faculties are at their apex in that age range. Let’s check the aging curves, once again courtesy stat guru Jeff Zimmerman.

Zimmerman used the delta method to weight the work of players in each age bracket.
These aging curves go back to 2002.

The flat peaks of all three curves are good indicators: It’s hard to nail down a distinct peak age when a hitter’s ground-ball, strikeout, and walk percentages all hit a plateau from around 26 to 29 years old.

Let’s take the curves and see what they tell us. As a blanket statement, though, we can say that each of these curves do not represent huge swings in results — take 5% off of a 12% walk rate, and you still have an 11.4% walk rate. Still, in the aggregate, these aging curves can tell us about the tendencies of most batters.

Walk rate performs just about as you might expect. Hitters peak from 26 to 29 years old. They improve their walk rate when they first hit the league, and then as their skills erode, so does their patience. It might be the flattest curve — until 35 they still haven’t lost 1% off their peak walk rate — but it’s a curve nonetheless. Patience is nice and stable, relatively.

Strikeouts improve sort of drastically, but not for long. Your average hitter might improve his strikeout percentage until he turns 24 or 25 and enjoy a nice long peak. But then by 34 he’s already lost more off his peak strikeout rate than he did off his peak walk rate. Look at age 31, and you’ll see that’s where the first significant decline in both strikeouts and walks come. It’s more pronounced and detectable than any age-27 peak — perhaps we should be talking about age 31 seasons being critical in a negative way instead of focusing on the 27-year-old peak performer.

Since fewer ground balls lead to more power, we’ll call that nadir at 24 years old a peak. The ground-ball curve may be the most interesting one — it’s the most volatile and it shows the shortest and earliest peak. If you want to ignore that hiccup at 27 years old, you can give it a short peak from 24 to 28. Or you can say ground ball rate peaks at 24 to 25 years old. This has power implications, so let’s check out an aging curve for isolated power before we go further.

Surprised? That’s a pretty definitive peak for power, and it might be a little earlier than most would think. The fact that ground ball rate bottoms out (peaks) at the same age — 24 — suggests to me that there is a magic age range for power, and it’s earlier than we might have thought.

Perhaps this makes sense from an athleticism stand point. Bodies may peak earlier than skills. If repetition can improve a batter’s sense of the strike zone and make him a better hitter overall as he approaches 30, he might still be falling off a pure muscle-bound power apex.

Take a player like Mike Stanton as an example. We used comps to show that, at 22 years old, he’s likely to improve his strikeout rate going forward, so this research doesn’t add too much of a wrinkle upon that finding. If it’s possible, though, this last graph could suggest that we should be even more excited about his future. He’s got his power peak in front of him still.

But other players take a (tiny) hit under this light. Matt Kemp had an awesome year this year, obviously, and at 26 it’s tempting to continue drawing a straight line through his ISOs — he’ll hit more than 40 out next year, right? This research suggests that it’s likely the 26-year-old is on the wrong side of his power peak. 27-year-old Ryan Braun may see a power dip, and it might not have anything to do with his recent positive test. Look up and down last year’s qualified ISO leaderboard, and you’ll only see Stanton and the 23-year-old Justin Upton definitively on the correct side of their power peaks.

Some aspects of a hitter’s game do age like wine — he’ll walk more and strikeout less every year until he’s close to 30 years old at least. But power? Power ages like cheese. Don’t leave your slugger in the fridge past 26 years old, or you’ll see the mold spores beginning to form. Don’t throw it out (all cheese has some mold in it anyway), but remember these curves when projecting performance.

Turns out Johnny and Frost know a little something about pitchers and strikeout rates. Thanks to the inestimable Jeff Zimmerman, we have strikeout aging curves for both starters and relievers. As dawn turns to day, it seems, pitchers also lose their gold.

Here is a more detailed explanation of how Zimmerman did his hitter aging curves.
He repeated a similar process for this graph, and the sample goes back to 2002.

What a stark graph. Zero is the peak, so your average pitcher’s strikeout rate pretty much peaks when he debuts, or shortly afterward. Starters might be able to maintain that peak until 25 years old, or so, but they never really improve the rate. Relievers? Let’s just say you better smoke ‘em while you got ‘em (and then let ‘em walk).

That’s probably the biggest take-away from this graph: If a pitcher’s strikeout rate naturally declines from day one, you probably don’t want to build your team on free-agent pitchers. Despite the high attrition rates for pitching prospects, it seems to make sense that you’d develop your own pitching, rather than aquire — by definition — post-peak free-agents. This also might put a little tiny check mark in Yu Darvish‘s corner, considering the fact that he’s 25 — but that’s a story for another time.

This graph is yet another reason to avoid signing free-agent relievers to multi-year deals. You’re not going to like the third year of that Brandon Lyon deal, Houston. And we told you so. It’s not like he was falling off a nice peak.

Remember this effect when evaluating similar young pitchers, too. Do you like Brandon Beachy and Vance Worley? They pitched a similar number of innings last year, are a year apart and had decent control. Neither was a top prospect, so both were pleasant finds for their teams and are under team control for a good chunk of time. But the Braves should be less willing to trade their young starter. Beachy is coming off a 28.6% strikeout rate, which might represent his peak. Worley, on the other hand, debuted with a 21.5% rate. Even if Worley has a marginally better ground-ball rate, his strikeout rate is statistically likely to get worse — and it’s coming off a lower peak.

But, of course, there’s true talent and then there are results. Someone like Mike Minor, in particular, could see a true-talent decline and still have better results in the future. No one is is suggesting that every pitcher in the league last year will show worse overall results going forward. The bouncing ball knows no master.

Still, when it comes to those fascist strikeouts, we know that you’ll probably never be as good as you just were.

Of all the candidates eligible for the hall of fame in 2012, Williams had the most postseason plate appearances — and by a large margin. He had 545 of them, which is more than twice as many as any other hall-eligible player. Javy Lopez is second with 225, and Fred McGriff comes in at 218. Impressively, 141 of Williams’ 545 plate appearances came during the World Series. For reference, Williams’ World Series total is nearly three times as many as  Mark McGwire, who had 53.

The extra PAs should lend some extra weight when determining if Williams gets into the hall of fame — especially when you consider that his postseason plate appearances amount to nearly an entire additional season.

To get a weighting of postseason games, I calculated all the hitters’ lifetime WAR, per 650 PA. It would have been too complicated to figure out the postseason stats, adjust them for the difficulty of the postseason play and then determine a true WAR. By using this simple method, I assumed that a player’s postseason production would be reasonably close to what they accomplished during the regular season. Williams’ production was actually very similar in that he had a regular season triple-slash of .297/.381/.477 and postseason triple-slash of .275/.371/.480.

With the WAR/650 calculated, I multiplied it times the hitter’s post season PAs. Since the postseason PAs are more important than the ones during the regular season, I added a weighting to those plate appearances. I doubled the WAR for all postseason games, and I also created another value that gave World Series games a weight of four times a regular season game. Other postseason games got a two-times weighting. Here are the results:

Initially, Williams was 10th overall in WAR among hitters. He’s grouped closely with Don Mattingly and Dale Murphy. And they’re behind Fred McGriff by more than 12 WAR.

Williams had the most postseason WAR of any player. Mark McGwire was next with about half of Williams’ WAR production. McGwire made up some ground on all the games Williams played by having a higher career WAR/650 (6.0 vs. 3.4). After adding a weighted amount of postseason WAR to Williams’ career total, it still wasn’t enough to get his WAR value into the hall of fame.

Certainly, Williams had an impressive career. But even with all those postseason appearances, his career falls short of getting his name enshrined in Cooperstown.

Relievers cannot directly decide the situations they pitch in — that is up to management — but is there some sort of innate characteristic of relievers which tends to decide when they enter games?

I decided to take a look at four different measures to see which best predict the gmLI — the average leverage at which a pitcher enters a game — of relievers the next year. The first three are measures of performance — the prior year’s WAR, the prior year’s WPA, and the prior year’s “deserved leverage index,” a concept introduced by Sky Kalkman back in 2009. Sky’s version of “deLI” is defined as (lgFIP/FIP)^1.5; to smooth out park factors, here I use (1/FIP-)^1.5. The fourth measure is the pitcher’s gmLI from the past season — sort of a check to see if there is inertia in pitcher roles.

Click on the image to go to the interactive visualization (much embiggened, of course).

Perhaps unsurprisingly given the piles of uncertainty surrounding relief roles on a yearly basis, none of the four has much to offer on a predictive level. The highest year-to-year correlation (dating back to the 2008 season) is a mere 0.249 with gmLI, just above 0.248 with prior season WAR. Teams don’t seem to respond much at all to either WPA or deLI, with both checking in under 0.15. It seems like some inertia exists, but not an obscene amount — clearly, players will be shifted between roles based on performance should they fail to produce in their designated role in the prior season. Prior year performance matters roughly as much in determining roles as the role in the previous season, according to this analysis.

But there’s one factor we haven’t looked at which we’ve seen as a deciding factor all-too-often as fans: money As a Milwaukee Brewers fan, I could call this either the Eric Gagne Corollary or perhaps the Trevor Hoffman Corollary, but every team has their own name for it. Teams simply don’t spend in the high millions for relievers to pitch in typical situations — looking at the past two seasons of free agent spending on relievers, only two pitchers have earned $3 million or more and had a gmLI below 1.0 — John Grabow, a $3.8 million LOOGY for the Cubs in 2010, and Dan Wheeler, a $3.0 million mop-up righty for Boston in 2011. Overall, though, when management spends on relievers, they spend to put them in high-leverage spots:

Again, click for the full, embiggened visualization.

The correlation of yearly salary to gmLI is 0.36, nearly 1.5 times higher than any of the other measure tested. When grouped by season (to cancel the effects of inflation), the correlation rises to 0.42. Players can still pitch their ways into or out of roles, but there is no question what kind of leverage Jonathan Papelbon or Heath Bell will see this season (regardless of what their performance says they should actually see). At the very least, this means managers and general managers are putting their high-priced relievers in the best positions to actually impact games. Whether or not they deserve these opportunities is another question (for another post).

For those interested in the data used for this post, it can be downloaded on the visualization pages by clicking on the button with an arrow on it.