How Can We Better Study Team Depth?

We know that Billy Beane has joked before that his stuff doesn’t work in the playoffs. And we know that, at least this time around, his Athletics team is built on depth and getting value out of the back end of his roster. These things seem to go hand in hand: your sixth starter and sixth infielder may mean a lot during the season, and they may not even make your post-season roster. But can we study this more rigorously in an effort to estimate the true value of depth?

My first idea was to look at ‘slots’ on a team. Do wins at the top of your roster mean more than wins on the bottom? In other words, would WAR from your top five players be better correlated with team wins than wins from your 20th through 25th men? Theoretically, they shouldn’t — runs are runs and wins are wins. But, with the help of Steve Staude, we can test that assertion.

Instead of running a straight one-to-one correlation for each, we tried to use multivariable regression. The inputs were team WAR (back to 1974) from slots one through five, the middle and the last five. The equation that came out of the beep-boop-bop machine weighted the top five 1.13 times to the bottom five’s .827! Success! Wins at the top of the team are worth almost a third more than wins at the bottom!

Not quite. First, this weighted equation’s r-squared was .738, and if you just take all team WAR, the r-squared for the relationship of WAR to wins is .736. Weighting the top wins did not really improve the relationship of WAR to wins, in other words.

There’s another issue with the approach. Matt Swartz brought up the interesting problem that this method of attack is really only testing the model we’ve built. The model of WAR suggests that runs are runs and wins are wins, no matter where you find them. If we really found something here, it might say more about WAR than it would about the true value of depth.

And, really, one aspect of the original question was if this meant more in the post-season than the regular season. But postseason samples are ridiculously small. Could we, perhaps, bucket teams into “deep,” “normal,” and “shallow” teams by the skew of their respective WAR contributions, and then see how teams in each of those buckets fairs in the postseason? That’s a ton of work… and we’re still possibly testing the model instead of getting at the heart of the problem.

Moving away from WAR opens possibilities, but also other problems. Would a team with three guys with .350 wOBAs, three with .330 and three with .300 fair better than a team with nine .330 wOBA players? Here the problem is, of course, that the best players would get more plate appearances at the top of the lineup and are therefore of course more valuable once these rates turn into counting stats. And you also lose the defensive side of the ball when you focus on wOBA, or wRC+. Not to mention pitching.

Lastly, the team’s place on the win curve seems important to this discussion. Would overpaying for a backup middle infielder make more sense for a contender looking to shore up their depth? And would that player get fewer opportunities on a deep roster, and therefore have a lower WAR, and therefore make the team look less deep than it actually was?

Depth is a difficult concept to nail down in the numbers. But when you see a team like the Athletics sign Nick Punto when they already had Alberto Callaspo and Eric Sogard, or when you see the Nationals react to 2013 by acquiring one of the better fourth outfielders in baseball, you know that the back end of the roster deserves attention. Is there another way to construct our inquiry in order to better get at the true value of team depth?




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Graphs: Baseball, Roto, Beer, brats (OK, no graphs for that...yet), repeat. Follow him on Twitter @enosarris.

45 Responses to “How Can We Better Study Team Depth?”

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  1. Kris says:

    The r-squared may not have changed, but what about the std error of the variables? Perhaps there is less variability in it’s predictive value if you weigh the WAR ‘slots’ rather than just using WAR totals.

    That would certainly be useful, if there is a difference.

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  2. here goes nothing says:

    I am really glad you bring this up. We’ve gotten *decently* good at figuring out how valuable individual players are ceteris paribus, but we know much less (IMO) about interaction effects, which *might* be one avenue for explaining the remaining 0.24 or whatever it is that the correlation between WAR and wins leaves missing. (To me that’s gold still in the ground.)

    Depth is definitely part of this. Michael Choice is a better backup for Choo because the team optimizes its results when Choo doesn’t hit lefties as much (and yes I know he’s not actually that bad at it, but I’m just talking about the principle: roster construction isn’t abstract, players are codependent, variables are endogenous). Team defense is too. Oakland’s FB/GB experiment is an interaction not just between pitcher and defense, but pitcher, defense, and park.

    Actually yeah, I’ll just say I think our future paths of analysis are going to include a lot more looks at endogeneity, interdependence; both words apply to roster construction. I want to see more of this.

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  3. The Stranger says:

    “The model of WAR suggests that runs are runs and wins are wins, no matter where you find them.”

    I think the exceptions to this rule are potentially a fertile ground for analysis. While WAR tells you a lot about an individual player, there’s a lot to be learned about how player WAR translates into team wins. For instance, let’s say you had a whole team of weak-hitting, plus-defense guys worth about 2-3 WAR each. Would that team win more or less games than a team full of bat-only guys worth 2-3 WAR each? Or a team with some of both? Or a team with the same team WAR spread between a few superstars and a few replacement-level guys? Does it matter what positions they’re at? How do certain skillsets interact to maximize team wins relative to player WAR? Is there some scenario where a right-handed power hitter has a lot of value, and giving Nelson Cruz a big contract actually makes sense?

    I don’t have answers to any of this. I don’t even know where to start looking for answers. But a smart GM like Billy Beane might be able to squeeze a few more team wins out of the same player WAR.

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    • channelclemente says:

      Like maybe the Giants?

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    • Bip says:

      WAR, especially for position players, is not park and defense independent. So if a GM knows that his home park inflates home run rates for right-handed hitters, and that his division rivals have weak defensive left-fielders, so he signs Nelson Cruz, then he may inflate Nelson Cruz’s WAR. This would be reflective of the extra team wins Cruz will contribute by having a skill set that is particularly suited to his team, compared to other player.

      Pitcher WAR may go too far in the other direction. If he signs a bunch of flyball prone right-handed pitchers, knowing home runs to lefty hitters are suppressed, and knowing he has a good defensive outfield, that will not be reflected in that pitcher’s WAR. It should be somewhat reflected in his defense’s WAR.

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    • champion88 says:

      Brian Kenny has said that having 9 hitters with an OPS+ of 100-110 is much better than having a few stars and the rest scrubs, even if their total OPS+ is the same.

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  4. badenjr says:

    I’ve been thinking a bit of late about the WAR framework. WAR values both quantity and quality. More playing time is a good thing. Better rate stats are a good thing. I think there’s still a dimension of “opportunity” missing though, and this is particularly true when it relates to bench players.

    When players have limited playing time, it is either because they are injured and unable to play or because there is a better option at the position. WAR doesn’t distinguish between those things. A 2 WAR player who is stuck behind an all-star may very well have room to produce more in another environment where he were given the opportunity to accrue more time. A 2 WAR player who is often injured would still face the same injury concerns though. Similarly, an injury-prone 3 WAR player may have the potential for a bigger season than a non-injury-prone 3 WAR player, provided the injury-prone player can stay healthy. The injury-prone player’s backup is likely to get more playing time though, so having a more dependable backup option would likely be more important in that case.

    I’m not sure how you separate out the “quantity” aspect of WAR into “health” and “opportunity”, but I think doing so is very important to determining where you intend to go with this work.

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    • Bip says:

      That begs another, more general question. What is more valuable, a player who good and durable, or a player who is outstanding and injury-prone? Say two players play the same position, and one is expected to put up 4 WAR in 600 PA, and the other is expected to manage only 400 PA, but also put up 4 WAR. Is one inherently more valuable? One would think that it would depend entirely on the quality of whoever replaces the latter when he is not playing.

      Based on what announcers say though, one would be led to believe the 400 PA guy is more valuable. They use terms like “adding a spark to the lineup” and “making his teammates better.” While I don’t necessarily believe that stuff, I wonder if team success increases linearly with individual performance. Maybe the difference between average an all-star performance means less to a team than the difference between all-star and MVP performance.

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      • champion88 says:

        @Bip: I would say the 400 PA guy is better because it will be cheaper to find a slightly above average replacement for the injured guy, whereas the excellent, consistent player will be expensive.

        Think how much you would pay for Yasiel Puig + Juan Lagares over Shin-Soo Choo.

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  5. The Stranger says:

    Another interesting concept I saw on another site some years ago was what the author called “slope.” Which was the idea that some players did very well against inferior competition but struggled against elite competition, while others performed at approximately the same level regardless. So a hitter with a high slope might struggle against opposing aces but mash against back of the rotation guys, while a hitter with a low slope would show less variance based on the opposing pitcher (still putting up better numbers against worse pitching, but less of a spread). So both of those players might be worth the same WAR over the course of the season, but you’d obviously prefer the second guy in a playoff situation. And I think the tendency was for mid-level guys to have a higher slope, because better opponents could exploit the things they couldn’t do well. If that’s true, a team built for depth rather than elite talent could struggle in the playoffs.

    Like I said, though, I just saw this briefly several years ago. I couldn’t say whether there’s been more research into this, or whether there’s actually anything to it.

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    • Milone's heater says:

      I wonder this all of the time. I believe there are some players that pad their stats better in garbage time and other players that lose focus/motivation in blow outs. It’d be interesting to see if some players disproportionately rake against lower tier pitching while others do a better job of maintaining their production against top tier competition.

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    • champion88 says:

      I saw the same concept displayed on Clubhouse Confidential with guest Vince Gennaro.

      His spotlight player was Josh Hamilton who crushes cripple pitchers with some ridiculous value like a 1.100 OPS, but withers against elite pitching, which is why he struggles in the playoffs.

      Whereas a notable player like Derek Jeter was pretty consistent in his production against any type of pitcher.

      Vince had done a more in-depth study, but those were the guys I remember. Vince is a member of SABR, but they never gave a direct link to the study on the program. You could probably e-mail Brian Kenny or Vince Gennaro about it though if you want to know more.

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  6. olethros says:

    Maybe use WAR variance across the roster as an approximation for depth, the correlate that with regular season and playoff performance.

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  7. Anon says:

    When I hear ‘depth’, I think that connotates having quality to replace injuries etc. The way I read your article seemed to not address this point directly. For example, a starter gets injured for the season, and the backup plays well; if the next man on the depth chart is bad, this team would seem to not have depth in your analysis.

    The point about hitting variance throughout the lineup is what I would refer to as balance.

    Also, the differnce in top 5 WAR vs bottom 5 WAR as correlated to team WAR is easily explained. The top 5 produce a much higher percentage of the team WAR than the bottom 5, which drives a higher correlation to the group with a larger proportion.

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    • Bip says:

      That shouldn’t affect correlation or the relationship. The idea of correlation is how does those 5 players WAR, as a rate, affect team wins, as a rate. In other words, as the WAR for those 5 players changes, how do team wins change, and how reliably. The magnitude of the variance doesn’t matter, only how reliably one influences the other.

      What that result shows is that adding 8 WAR to the top 5 WAR players actually adds about 9 team wins, while adding 8 WAR to the bottom 5 actually adds about 7 team wins, which doesn’t make immediate sense to me.

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    • champion88 says:

      @Bip: I assume that’s because if you’re trying to win a “must-game” you lean on your top guys more heavily, whereas you try to avoid putting your weaker guys in at all.

      For example, if the Red Sox play the Yankees, you probably aren’t going to see Ryan Dempster in the game, unless the Red Sox are already being blown out, at which point the outcome is not in question.

      But if it’s tied in extra innings, maybe Uehara and Tazawa stay out there for 2 innings each.

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  8. George says:

    Rather than ranking a team’s players by WAR, perhaps you could split a team’s players into three “buckets” based on plate appearances. For example, Starters (500+ PA); bench players/platoon players (250-499) and September call-ups/fill-ins (<450 PA)?

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    • champion88 says:

      A bench player won’t get 250 PA’s if he’s just pinch-hitting and the left-hand side of the platoon might not get 250 PA’s either.

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  9. Carlton Clark says:

    If the correlation between WAR and wins is only .736, you might try testing whether depth affects total team WAR rather than wins.

    Consider player A (2.25 WAR in 450 PA or 3 WAR per 600 PA) backed up by a replacement player. If player A plays 75% of the time, his team gets 2.25 WAR from position (3 X .75 + 0 X .25). If to increase depth team replaces player B with a 1 WAR player, then team gets 2.63 WAR (3 X .75 + 1.5 X .25) from position. In this tiny sample size increasing depth increases WAR. Intuitively obvious but as your work indicates, hard to prove!

    Please continue trying as I’m interested in reading the results of your research.

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  10. channelclemente says:

    What does the ANOVA tell you?

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  11. Tim A says:

    With Oak I think they are aware of the depth. The team took some tough shots to injury in 2010-11 so they depthed up hard. I think a more real reason the A’s look a little worse in the playoffs is the platoon arrangements they have don’t look as good against the type of pitchers they face in the playoffs. This is a team that can run out 7+RH or 7+LH batters in a lineup on any given night. They keep players fresher in season by having them rest more, but when you face pitchers like Verlander who don’t have much of a platoon split, then they weaken the advantage. I wouldn’t say they aren’t built for the playoffs since it’s such a crapshoot, and this team looks very different then the team 10 years ago that had similar problems. I think this will help them make the playoffs more frequently, and all you can really ask for is more tickets to that playoff lottery till its your turn for the numbers to hit.

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    • BillyF says:

      I don’t see where’s the big split for the A’s? Using Fangraphs, 2010-’11, vs.L the A’s hit .303 and .309 vs.R.

      2012-’13, vs.L the A’s knocked .321 woba, while stayed .318 vs.R.

      The M’s, meanwhile for the last two seasons, has a bigger split: .294 and .302, respectively. The Cubs have perhaps one of the bigger splits among all 30 teams: .293 and .304; the Royals have almost no splits.

      I’m just trying to show that I’m not seeing where the A’s saw this weakness and improved by increasing its advantage via split lineups?

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      • BillyF says:

        I guess what I’m questioning is, are split advantages significant? .303 woba and .309 woba? If it’s a .01 difference, say, .313 woba and .303 woba, then I see the problem for the A’s, but a 0.006 is hardly making a team from fringe to World Series contender.

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      • chris says:

        The idea is never facing the disadvantage from the hitting side, and simply increasing overall offense (wOBA in your example); not increasing the size of their platoon split.

        The difference to look for is that increased wOBA.

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        • BillyF says:

          Ok. In that sense, the A’s would have increased overall production from both sides of the plate (or pitching mound, I guess the lineup’s designed “against the opponent”) for the past four years.

          It’s hardly the result contributed from their bottom end, right? just like heater questioned above. The team had better talents now. Cespedes, Donaldson, and Moss all hit great. I doubt we can say the platoon is a significant improvement to the overall production. Just by signing better talents and play them more, the A’s improved their lineup.

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      • Milone's heater says:

        I think the A’s cover several concerns by adding depth.
        They seem to value splits (because they are a cheap way to get production), position flexibility, and being able to replace injured starters with other +WAR players.
        Gentry is a great example of this. He will get a lot of playing time subbing for Reddick and Coco because he hits lefties well, he is a A+ fourth outfielder, pinch runner in high leverage situations, and excellent defensive replacement anywhere in the outfield.
        I could make an argument that each of his wins above replacement are more valuable than the A’s starters.
        So then, is the WAR at the bottom end of A’s roster more valuable than on other teams with more rigid lineups? Or are the A’s just maximizes the WAR of every player on their roster by utilizing more fluid, situational lineups?

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        • champion88 says:

          I would say the A’s get the most out of their roster whereas other teams just have black holes on the bench.

          However, those team’s core might be better than the A’s core, so it is essential for the A’s to max out their value.

          For example, if the AL All-Star team played the A’s, you wouldn’t have much need for a deep bench because every starter would be so amazing to begin with.

          I’m not sure if that answers your question.

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    • champion88 says:

      If anything, contact hitters fare better in the playoffs than power hitters.

      The main problem for the A’s is that they just can’t hit Verlander at all. Maybe they are just susceptible to 95+ MPH fastballs.

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  12. Wally T says:

    Is there a stat for how well a player does according to his salary? For example, let’s say the average MLB hitter bats .260, hits 10 HR, has 60 RBIs and is paid 5 million. If there were a player batting .300, hitting 30 HR, and having 120 RBIs, how much should he be paid?

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    • Steven Leroud says:

      You could just take WAR/salary and compare it to the major league average. Deciding “how much should player X be paid” is different though, because the oft-mentioned $5-$6 million per WAR is for free agents only, and many players are only arbitration eligible or even pre-arbitration.

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  13. Bip says:

    I think it should be pretty obvious that WAR is going to much better at approximating a particular player’s ability than it is for approximating team success. After all, approximating a single player’s ability is exactly what it is for. It made for saying things like “How much should our team improve if we sign Player X to replace Player Y” and “How much more valuable is Player X than Player Y, when X and Y have different positions”. Usually in the case of one player, the interactions in play for a team are not going to substantially change when you substitute one player.

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  14. bob says:

    I think a large problem with accurately translating WAR into wins is that a lot of the runs don’t always end up having an effect on the outcome of a game. In the case of blowouts all the WAR accrued after a certain point really doesn’t matter to the outcome of the game. A team could win a couple of 12-4 type games yet lose a lot more 1 run games over the course of the week and end up under .500. Over the course of a season the run differential could end up being highly misleading showing great hitting and decent pitching. Unfortunately, the timing of when those runs were scored and allowed could be horrible and the results generally bad. I am sure you could switch that around too and have a team outperform their WAR but be the beneficiaries of the timing.

    I think from an offensive stand point it would be interesting to see just how much of a teams output was truly superfluous.

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    • champion88 says:

      You can do that. Look at 3rd order wins.

      It’s why we knew the Orioles weren’t going to the playoffs in 2013, because their 3rd order record from 2012 was 79-83, even though their actual record was 92-70.

      The O’s mistakenly thought they were a 92 win team, did nothing to improve, and regressed to the .500 team they actually were in 2012 during 2013.

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  15. Joel says:

    The obvious strength of depth is that player performance deteriorates when compelled to play through injuries and fatigue. How to quantify this, I have no idea.

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    • champion88 says:

      The bigger problem that Eno stated is that a great player isn’t going to want to spend an entire year on the bench.

      It’s sort of like what the Dodgers are dealing with now with their outfield. Andre Ethier would be an amazing 4th outfielder, but Ethier is not going to want that role.

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  16. Scott says:

    Fangraphs (wRC+) used to include SB/CS but does not now.
    (Off) next to WAR is now the total offensive contribution but it is hard to easily compare players to the average. (Off+) with 100 as average would do that.
    Furthurmore, a (WAR+), (Def+) and (BsR+) stat would all help see exactly where a player stands in relationship with the average at one glance.
    Does any stat site do this? How hard would it be to crunch existing numbers into these stats?
    I’m thinking it would look something like this: 2013
    Mike Trout 400 (Off+), 125 (Def+), 400 (BsR+), 500 (WAR+)
    Chris Young 85 (Off+), 90 (Def+), 110 (BsR+), 80 (WAR+)

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  17. Mac says:

    Love the idea, but the statistics used to measure “depth” in my mind need some work. Depth can mean two things:

    1) A team with no major holes. The number 4-5 starters and the 7-8-9 hitters are decent. This should really be called balance but is often confused with depth.

    2) Covering injuries. When a starting player goes down, is the replacement godawful or passable?

    Balance is important in that with balance, each individual matters less. The A’s had very few stars (Donaldson, Colon) but had 2 WAR players spread everywhere. If you’re team is balanced, the lost 2 WAR players hurts you less than if you lost a 5 WAR player. Depth is all about who replace that lost player with. Is it a AAAA scrub who might even be worth negative WAR, or does the back-up contribute meaningfully?

    Another important concept is that 6th pitchers are 4th outfielders, while not regarded as “starters”, almost always will see 20 or so pitching starts or 300+ PA’s. It’s almost inevitable, so you almost have to stop calling these people backups. They’re needed so often we should just start calling them regulars.

    From the initial article, it sounds like Mr. Sarris is more questioning what I would call balance. Is it important to get run generation/prevention from the whole roster? I would suspect the answer is that indeed there are many ways to win. As stated above, “wins are wins”.

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  18. Eric says:

    Late to the party, but had been meaning to add something for a few days now.

    First, as many have addressed, we need to figure out what we mean by depth. As Mac points out, depth can refer to quality spread across the starting roster – having a higher base level of production across the board – but it can also mean a higher base level of production among players who do not crack the starting 9.

    I’m going to ignore the first version of depth for the time being, and consider a few ways we might want to think about the latter. We can think of level production in case of injury, but this is not is as productive as might seem. If we did that, we’d need to first consider production level short term, long term, and in the face of the playoffs. If a player is injured, misses, several months, but is able to return to his previous level of production prior to the injury in time for the playoffs, the level of production that fills in needn’t be as good. If the player will miss the playoffs, the level of production to replace this player should be higher. In the latter case, we need to keep in mind the possibility of trades. Would an organization rather have good players in the wings, or decent players and the presence of mind that they can trade to replace the players lost to long term injury?

    What we need to concentrate on is games played and level of production during the games (innings or even defensive half-innings) played.

    One last thought. We might want to look into predicting the value of a player not playing. R/L splits is a pretty easy example to see how sitting one player will increase the average value they contribute on a per game basis. But another more complex example would be of rest. How might a players production level per game look if they played 152 game instead of 162? How does production level at a position in question change if it is shared by a two players? Maybe resting every outfielder 20 games a season and playing a 4th for 60 actually improves production across all three positions.

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  19. B N says:

    I’m getting the strong feeling that regression is just not a great way to handle this in general. I think Monte Carlo simulations are probably needed to really get much traction for this. The playoff “run environment” is a misnomer, as it is directly related to the interaction of exactly two teams.

    I would think that the following factors are important:
    1. Playoffs need about 4 starters, instead of ~6 across a regular season.
    2. Your playoff starting players will be a partially-random subset of your regular-season guys, due to injuries. However, these will mainly be the same guys through the playoffs.
    3. Playing in an NL field increases the value of concentrating value in fewer hitters, while AL fields decreases it (due to the DH). This impacts the WS playoffs only, however (maybe Oakland would have better luck in the NL?).
    4. Multi-position players add a different kind of depth than extra guys for a single position.

    Basically, without examining injuries, position coverage, and single-series “run-environments” I don’t see how you can ever glean much about the pros and cons of depth.

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  20. Shankbone says:

    I was thinking about depth today when the announcement of Ryan Theriot’s retirement went through. He played a minor role on two world series championships back to back and went out after scoring the winning run. Not a bad career at all from the LSU Tiger.

    Here’s what the Giants did, you have 3-4 good hitters and 3-4 good starting pitchers and a good pen. But you need a little something more…

    In 2010 it was Huff/Torres/Posey/Burrell as the heavy hitters but Juan Uribe was the glue, subbing for an injured Renteria and an out of shape Sandoval, hitting 24 HRs while putting up 248/310/440 OPS+ of 102 and a WAR of 1.2 for 3.25MM. Further he came up with big hits during the post-season, just like Jonny Gomes did. (Gomes last year incidentally 247/344/426 with a OPS+ of 111 hitting 13 HRs for 5MM and a WAR of 1.2 – great signing, I wish the Giants had gone in on that).

    In 2012 it was Posey/Pagan/suspended Melky Cabrera with Sandoval/Belt. The depth/glue guy was Gregor Blanco, who you’re familiar with Eno. He put up 244/333/334 while playing stellar defense, an OPS+ of 90, with a 2.1 WAR playing for the minimum salary. He notably took over LF duties late, and played strong through the post-season.

    Having Theriot as a stopgap for injured Freddy Sanchez and ineffective Manny Burriss was a 2nd factor, obviously replacing him with a red-hot Marco Scutaro sure helped the bottom line of those Lucky Gigantes. Theriot’s final stats don’t stand out, his defense was bad enough to make his overall WAR negative, but he was a good stopgap. He ended up hitting 270/316/321 for an OPS+ of 83 and a WAR of -0.3 (0.9 oWAR and -1.0 dWAR)

    I’m not as familiar with the 2011 Cards or 2013 Red Sox as the Giants teams, but I’d venture Ryan Theriot/Skip Schumaker helped out (especially with Furcal going down) as well as their Descalso/Freese set up). The Sox I think Jonny Gomes is a huge part, not only for the HR that changed the series but his contributions during the year, no matter how defensively challenged he might be. The Red Sox had amazing hitting depth last year, with only Middlebrooks and David Ross below league average.

    In short – I wouldn’t look to the big stats guys for depth, I’d look to vets who know how to influence games. Juan Uribe had a much better stat year in 2009, but he was extremely valuable in the flesh for 2010. I’d venture that the Dodgers would agree, he was their best player during the playoffs, and they just gave him another shiny two years.

    If the Giants had Juan Uribe and Jonny Gomes going into this year I’d feel pretty good. They’re more expensive now, and they are obviously locked into their contracts. I think they are two of the best role players/team depth guys in baseball, partly because of their ability to give tough at-bats and hit home runs. Laugh all you want at the low BA/OBP and the bad WAR scores, when the chips are down, those are the guys I’d want up. Ryan Theriot? Well, I think there’s always room on a team to have a scrappy at-bat guy who can wear a pitcher down. The Cards just signed up Mark Ellis, that looks like a stellar move.

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