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Should the Red Sox sign Josh Hamilton?
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Post by beasleyrockah on Nov 29, 2012 18:09:54 GMT -5
Fair enough, I get caught up in snark from time to time. Allow me to clarify again. Hamilton hasn't been an elite hitter against elite pitching over the cited three year sample. Hamilton has been an elite hitter against bottom third pitching. His advantage in production over the average hitter is scaled much more to his domination against the bottom feeders than his ability to transcend against elite talent.
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Post by lasershow07 on Nov 29, 2012 18:11:04 GMT -5
This conclusion doesn't logically follow from the evidence. According to this study, Hamilton has hit 12% better than league average against "good pitching" (as measured by OPS against) and 40% better than league average against "bad pitching." By virtue of the fact that it's more difficult to hit good pitching than bad pitching, it's also more difficult to hit better than league average against good pitching than bad pitching.The guy goes on to say Jeter is an example of a guy who hits good pitching well because he hits them 19% better than league average but only hits bad pitching 5% better than league average. All this shows is that Jeter didn't hit bad pitching particularly well. This looks as a graph on TV when it pops up for 10 seconds, but it really doesn't make any sense. You are missing the point, I think. The conversation in the context of this thread has revolved around "elite hitters" hitting any type of pitching (elite, average, below average) fairly consistently, while the good/mid-tier hitters feast on the average/below average guys and struggle mightily against the elite pitchers. Since Hamilton has been the talking point, he is the natural test case. He is an example of an elite hitter who produces far more against the bottom third while being just another guy against the elite pitchers...not just in a vacuum where it's obvious that you'll produce better against inferior competition, but scaled to the rest of the MLB. His total production is more heavily based on feasting against the bottom third than the average hitter. The narrative being discussed is that elite hitters can hit anyone and the Napoli's and Swisher's can't, which is why you need elite guys to win in October. The average MLB hitter has a difference of ~180 OPS pts between facing bottom third pitching and the league's best. Hamilton has an OPS difference of ~250 pts in the same categories. This means his production is more reliant on producing far better than average against the bottom third than far better than the average against the elite guys. He's marginally above average against the elite guys and elite against the poor pitchers, which is the opposite of the narrative here. I don't think this study is perfect and I don't think Hamilton represents every elite hitter, I just find the narrative in this thread is too simplistic and all-encompassing. Hitting has everything to do with the individual hitter/pitcher matchups, every elite/mid-tier player is not created equal. EDIT: I think you got caught by my intentionally hyperbolic comment. To clarify, Hamilton has hit elite pitching, just slightly above league average. He has absolutely crushed bottom third pitching, much more than the average hitter. I'm sorry I just realized I did a horrible job of explaining my point. The problem with this conclusion, which the study draws, is that it isn't supported by the evidence. He's using relative data to draw absolute conclusions. To say that Hamilton hit 40% better than league average against bad pitching by hitting 1.154 compared to a league average of .823 is a logical fallacy. What this actually shows is that he hit at a 40% better rate than league average. This could be 1000% better than league average for all we know, but the point stands that we don't know, because we can't actually compare Hamiton's rate against the rates of all other MLB players to draw that conclusion correctly. What I was trying to say earlier, is that I would suspect, without having any evidence to prove this either, that players have a smaller variance of success against better pitching than against bad pitching (by virtue of the fact that it is harder to hit good pitching than bad pitching, it is also harder to hit better pitching at a higher rate above league average than it is against bad pitching). Therefore, Hamilton's 12% rate above league average against good pitching may be close in absolute terms to his 40% rate above league average in bad pitching.
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Post by lasershow07 on Nov 29, 2012 18:19:56 GMT -5
Fair enough, I get caught up in snark from time to time. Allow me to clarify again. Hamilton hasn't been an elite hitter against elite pitching over the cited three year sample. Hamilton has been an elite hitter against bottom third pitching. His advantage in production over the average hitter is scaled much more to his domination against the bottom feeders than his ability to transcend against elite talent. I'm sorry I'm not trying to pick on you here Beasleyrockah, but just to clarify my comments in light of the debate about Hamilton helping the Sox: the study you posted doesn't support the conclusion that Hamilton, in fact, is not a good hitter against elite pitching who is incapable of helping a team in the playoffs.
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Post by beasleyrockah on Nov 29, 2012 18:21:02 GMT -5
I'm sorry I just realized I did a horrible job of explaining my point. The problem with this conclusion, which the study draws, is that it isn't supported by the evidence. He's using relative data to draw absolute conclusions. To say that Hamilton hit 40% better than league average against bad pitching by hitting 1.154 compared to a league average of .823 is a logical fallacy. What this actually shows is that he hit at a 40% better rate than league average. This could be 1000% better than league average for all we know, but the point stands that we don't know, because we can't actually compare Hamiton's rate against the rates of all other MLB players to draw that conclusion correctly.What I was trying to say earlier, is that I would suspect, without having any evidence to prove this either, that players have a smaller variance of success against better pitching than against bad pitching (by virtue of the fact that it is harder to hit good pitching than bad pitching, it is also harder to hit better pitching at a higher rate above league average than it is against bad pitching). Therefore, Hamilton's 12% rate above league average against good pitching may be close in absolute terms to his 40% rate above league average in bad pitching. Everything is scaled to the league average against the cited competition level. It's harder to hit good pitching than bad pitching, this is a fact. It's also why the offensive league average bar is set much lower against the elite pitchers than the average bar is set against the bottom third guys. In this study, when he says Hamilton hit 12% better than league average against good pitching, it's 12% better than the average hit against that same group of pitchers. When he says he hit 40% better than league average against bad pitchers, it's 40% better than league average against that same group of bad pitchers. He took all the starters and put them in tiers (top, average, bottom), and then took the average OPS against each competition level. It's not simply the league average OPS in general and then applying it to the competition level.
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Post by lasershow07 on Nov 29, 2012 18:25:29 GMT -5
I'm sorry I just realized I did a horrible job of explaining my point. The problem with this conclusion, which the study draws, is that it isn't supported by the evidence. He's using relative data to draw absolute conclusions. To say that Hamilton hit 40% better than league average against bad pitching by hitting 1.154 compared to a league average of .823 is a logical fallacy. What this actually shows is that he hit at a 40% better rate than league average. This could be 1000% better than league average for all we know, but the point stands that we don't know, because we can't actually compare Hamiton's rate against the rates of all other MLB players to draw that conclusion correctly.What I was trying to say earlier, is that I would suspect, without having any evidence to prove this either, that players have a smaller variance of success against better pitching than against bad pitching (by virtue of the fact that it is harder to hit good pitching than bad pitching, it is also harder to hit better pitching at a higher rate above league average than it is against bad pitching). Therefore, Hamilton's 12% rate above league average against good pitching may be close in absolute terms to his 40% rate above league average in bad pitching. Everything is scaled to the league average against the cited competition level. It's harder to hit good pitching than bad pitching, this is a fact. It's also why the offensive league average bar is set much lower against the elite pitchers than the average bar is set against the bottom third guys. In this study, when he says Hamilton hit 12% better than league average against good pitching, it's 12% better than the average hit against that same group of pitchers. When he says he hit 40% better than league average against bad pitchers, it's 40% better than league average against that same group of bad pitchers. He took all the starters and put them in tiers (top, average, bottom), and then took the average OPS against each competition level. It's not simply the league average OPS in general and then applying it to the competition level. The problem is that this data is not actually scaled to league average. When you compare rate stats like OPS (the rate at which a player gets on base + the rate at which a player takes a base per at bat) the side to side comparison is meaningless. The bottom line is you cannot draw absolute conclusions from relative data.
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Post by Deleted on Nov 29, 2012 18:26:21 GMT -5
I don't understand this obsession with "impact bats." I'd rather substantially upgrade two positions as opposed to a really big upgrade at one. Hamilton will probably cost more in both AAV and years than a combination of Napoli and Swisher, and I'd rather spread out the injury/underperformance risk. "Talent in baseball is not normally distributed. It is a pyramid. For every player who is 10 percent above the average player, there are probably twenty players who are 10 pecent below average. " ----Bill James This is why a six win player is worth more than three times as a two win player. There are many many more chances to acquire the latter than the former. Further, you are assuming that all players have the same injury/underperformance risk. Wouldn't better players have less underperformance risk at the very least? Diversification was basically Dan Duquette's strategy early in his Red Sox tenure and it failed miserably.
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Post by beasleyrockah on Nov 29, 2012 18:41:15 GMT -5
I'm not sure I follow. You're saying it's impossible to get a league average OPS total for each individually tiered pitching environment?
(just to make sure we're on the same page)
This study claims it separated the qualifying starters in three tiers based on their OPS against, with the lowest totals going to the elite tier and the worst going to the bottom tier. Then, each tier was assigned a league average OPS AGAINST THEM ONLY. So the elite tier's total OPS against is their own benchmark. The mid-tier's total OPS against is their benchmark, and the low-tier's total OPS is their own benchmark. Then, the study took Hamilton's OPS against each individual tier and compared it to that tier's average. It created three different offensive environments (elite, average, below average pitching) and assigned the league average OPS when facing each respective environment. How is that not scaled to league average (genuine question)?
FWIW I'm not trying to claim absolute conclusions from this at all, I think the process behind this is flawed and not very predictive. There's probably a sample size issue at play here and it would be necessary to see how many PA's he got against each tier before attaching meaning. It seems like they also ignored the middle tier in the displayed results and only focused on the two extreme tiers. Playing in a division where the only qualifying pitchers for the elite tier might've been Weaver, Felix, and another starter or two could really manipulate the results.
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Post by lasershow07 on Nov 29, 2012 18:49:16 GMT -5
I think I can best demonstrate the problem with a hypothetical:
So as here, the 50 percentile hitter had a .823 OPS against bad pitching. Assume the 60th percentile hitter had a 1.154 against bad pitching. In this scenario, Hamilton performed 10% better than league average against bad pitching.
The problem is, that we have no idea what the 60th percentile (or any other percentile) hitter did against bad pitching. So what we're left with is the meaningless statistic that Hamilton hit bad pitching at a 40% better RATE than league average. But this does not mean that he was in ABSOLUTE terms 40% better than league average against bad pitching.
Edit: What we need here is a comparison of the rates at which hitters hit bad pitching to draw meaningful conclusions. Wow, that was easier than four or five posts.
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Post by beasleyrockah on Nov 29, 2012 21:41:49 GMT -5
I think I can best demonstrate the problem with a hypothetical: So as here, the 50 percentile hitter had a .823 OPS against bad pitching. Assume the 60th percentile hitter had a 1.154 against bad pitching. In this scenario, Hamilton performed 10% better than league average against bad pitching. The problem is, that we have no idea what the 60th percentile (or any other percentile) hitter did against bad pitching. So what we're left with is the meaningless statistic that Hamilton hit bad pitching at a 40% better RATE than league average. But this does not mean that he was in ABSOLUTE terms 40% better than league average against bad pitching. Edit: What we need here is a comparison of the rates at which hitters hit bad pitching to draw meaningful conclusions. Wow, that was easier than four or five posts. I think we're both assuming this study is using different data points. By my understanding, this study isn't claiming the exact 50th percentile hitter had an exact .823 OPS against bad pitching. It isn't claiming the definitive league average hitter produced at a .823 clip against this tier. It's saying the combined OPS of all hitters against that "bad tier" is .823. It's also saying the combined OPS of all hitters against the "elite tier" is .641, which illustrates the difference in competition level. The OPS's used here take every at bat into account and don't discriminate based on playing time. Like any offensive stat, there will be tons of outliers on both sides based on plate appearances, doing percentiles like you're proposing on a stat like OPS would include tons of guys with limited at bats at the far ends of the percentiles. Your scenario doesn't seem to make practical baseball sense. If the average OPS against bad pitching is .823, there is no way Hamilton would be just the 60th percentile at 1.154. How would the average OPS be ~.350 lower than the 60th percentile? In order to compensate for the dramatic difference, the 40th percentile and below would be hitting at or below pitcher levels. When you take into account the fact that productive players tend to play more than unproductive players, it becomes even less plausible. In your scenario, the MLB would be filled with elite guys and replacement level players, with very few average hitters. There just couldn't be that much variance between the total average and the 60% percentile. I agree this study is very flawed, the baseline it sets doesn't give enough context, it should be scaled like wRC+. We need a fangraphs style leaderboard to see everyone's results and compare players. We also need to know how many at bats each player got against each tier, I'm guessing Hamilton faced mid/bottom tier pitching more than the elite tier. He also was in a division with Felix and Weaver, so the majority of his "elite tier" at bats came against the truly elite guys.
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Post by lasershow07 on Nov 29, 2012 21:51:20 GMT -5
The 60th percentile was an extreme exaggeration, meant to illustrate that you can draw any particular conclusion you'd like with the data they've provided.
The conclusion here that Hamilton "feasts" on 'bad' pitching because he hits those pitchers at a 40% better than league average rate of success and doesn't hit good pitchers because he only hits those pitchers at a 12% better than league average rate of success relies on a faulty premise. This dude is making the assumption that the distribution of rates of success against good and bad pitching is not meaningfully different so that reasonable conclusions can be drawn by comparing those two rates.
I am making the argument, essentially, that the actual rates of MLB hitters' success against the 'good' pitchers are likely to be bounded much closer together than the rates of success against the 'bad' pitchers (relative to the median in both cases). This means that even though he might only have hit good pitchers at a 12% better than league average rate, this might actually be an equal rate of success to the 40% against bad pitchers relative to all other MLB hitters.
For example his 12% better than league average rate of success against good pitchers might put Hamilton in the 80th percentile of MLB hitters against these pitchers and his 40% might put him in the 85% of MLB hitters against bad pitchers.
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Post by beasleyrockah on Nov 29, 2012 21:58:42 GMT -5
The guy only gave a few players for reference, but he claimed Hamilton had one of the largest differences in OPS from the elite tier to low tier in all of baseball. Selection bias is at play here, a guy with an elite OPS will naturally have a larger difference, but he cited Hamilton as an outlier. It would make sense for lower BB% guys with higher slugging to do poorly in this type of test. I can't speak on it without seeing everyone's results, just going off his possibly flawed findings.
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Post by lasershow07 on Nov 29, 2012 22:03:54 GMT -5
I hear ya, I just would find it hard to believe that many players hit 40% better than the rest of the league against the top 1/3 of pitchers. That Hamilton's differential in OPS in this case is so extreme is likely a testament to the fact that he's a great hitter, not that he can't hit good pitching, or at least its just as likely to be the case. Which is why I have a problem with this guy's 'study.' End of rant.
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Post by beasleyrockah on Nov 29, 2012 22:11:01 GMT -5
My jumping off point was all elite hitters don't hit every tier of pitching equally, which believe it or not became a talking point in multiple threads today. The Napoli's and Swisher's of the world were labeled as guys who just feasted on bottom feeding pitching and couldn't produce against the elite pitchers. I had MLB Network on as background noise yesterday, remembered the study, and boom...it was less a co-sign of his findings, and more to point out 3WAR position players can sometimes hit good pitchers. Also, elite hitters struggle against elite pitching too.
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Post by lasershow07 on Nov 29, 2012 22:26:10 GMT -5
I am one of those advocates of acquiring "impact bats." My use of that term applies to hitters like Ortiz, Manny, etc., guys who can hit any pitcher at any time, particularly at crucial times. The average player can't do this. The average player seldom hits the really good pitchers. They get their hits against the average pitchers. Look how the Sox teams of recent vintage have piled up a lot of runs, but usually against average, or worse, pitching, and have folded against the good pitchers. Teams without impact hitters, but full of players like Napoli, Gomes, Ross, etc., usually don't win championships unless they have tremendous pitching, or incredible luck. The Ross-type players are needed because no team can have impact bats at every position, but two of them do not replace one impact bat, not even three or four of them. Baseball-Reference has this neat split called vs. power/finesse pitchers. It figures out a player's performance versus power pitches (defined as those in the top third of the league in strikeouts plus walks) as opposed to their performance versus finesse pitchers (those in the bottom third of the league in strikeouts plus walks). This "power pitchers" category is not a perfect proxy to "good pitchers", but it's close enough for our purposes. There's then a tOPS+ stat which tells you how that player performed against that category of pitchers relative to his overall performance, with 100 meaning he hit them about the same as he hits all pitchers, more than 100 meaning he performed better against that split than he did overall, and less than 100 meaning he performed worse against that split than he did overall. The below is the tOPS+ split for some of the players you mentioned in your post, first versus power pitchers and then versus finesse pitchers: David Ortiz: 82/112 Manny Ramirez: 83/110 Josh Hamilton: 84/120 Nick Swisher: 96/108 Mike Napoli: 84/109 The data indicates that your so-called "impact bats" derive as much or more of their overall offensive value from feasting off bad pitchers and struggling (relatively speaking) against good pitchers than my non-impact bats. I'm pretty sure you're just wrong on this one. Just scrolling through this thread again and wanted to shout out jmei here because this is exactly the type of analysis that the clubhouse confidential guy was trying to do. And I think it supports your points beasley. In this SS Ortiz actually has the hardest time against good pitching relative to his normal production. I'd agree that the numbers probably will bear out that elite hitters don't hit each tier the same over a larger sample. I just wanted to point out that the clubhouse confidential guy using OPS as a comparative measure just shows that he was probably a Cabrera supporter.
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Post by jmei on Nov 29, 2012 22:38:20 GMT -5
Beasley-- we all agree, lasershow just wants a stat which is normalized to 100 like my tOPS+ stat was. Just a sticky methodological question. Fact remains that there is little evidence that "impact bats" as a whole hit good pitchers better than "non-impact bats" hitters do relative to their baseline performance levels.
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Post by Guidas on Nov 29, 2012 22:46:33 GMT -5
Then again, by the above definition, these hitters will face "finesse" pitching about 80% of the time.You have three or more guys in your line-up who Feast on that at the rates above you'd likely be looking at 103-110wins per season. That should have your own (probably) average pitching well rested for the playoffs where, you'd likely only be facing one elite pitcher per series who, at very best in the first round, would pitch twice, and three times in a seven-game series. And of course no guarantee that, this late in the year, they will perform at an elite level.
As an aside, I will take Manny Ramirez or Miguel Cabrera in their prime anytime against anyone.
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Post by jmei on Nov 29, 2012 22:51:10 GMT -5
"Talent in baseball is not normally distributed. It is a pyramid. For every player who is 10 percent above the average player, there are probably twenty players who are 10 pecent below average. " ----Bill James This is why a six win player is worth more than three times as a two win player. There are many many more chances to acquire the latter than the former. Further, you are assuming that all players have the same injury/underperformance risk. Wouldn't better players have less underperformance risk at the very least? Diversification was basically Dan Duquette's strategy early in his Red Sox tenure and it failed miserably. You're right in that in an ideal world, a six-win player is better than two three-win players because there are only so many roster spots and at bats to go around and if you can add six wins and still leave a roster spot open, you can hypothetically add another player at that second, open position and improve your team even more. The problem is that the Red Sox, like most teams, work on a budget constraint and invariably have to make tradeoffs. If you only have $25m per year available over the next four years and two roster spots to fill (RF and 1B) with basically only near-replacement-level players available to fill those spots if you don't sign a free agent (not too far from the truth, especially at 1B), I'd rather have Napoli and Swisher than just Hamilton. In theory, the higher-performing player might have lower risk, but the actual case has Hamilton as probably the free agent with the most risk in terms of the widest range of possible outcomes. Contrast that to Swisher, who is one of the lower-risk FAs (at least in the short term). Moreover, one basic tenet of risk diversification is that you invest in multiple assets, and that certainly makes sense here.
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Post by jmei on Nov 29, 2012 22:54:47 GMT -5
Then again, by the above definition, these hitters will face "finesse" pitching about 80% of the time.. Err... not true. The B-R splits explicitly divides pitchers into three tiers, with one-third as "power," one-third as "finesse," and one third in the middle, so over the course of a season you'd hypothetically hit a third of the time against each. That again means that the "power" tier does not match up perfectly with what we'd conventionally regard as good pitchers, but I believe it's the closest we can get without figuring out our own subjective list of good pitchers and adding up batter v. pitcher splits manually.
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Post by beasleyrockah on Nov 29, 2012 23:22:20 GMT -5
Beasley-- we all agree, lasershow just wants a stat which is normalized to 100 like my tOPS+ stat was. Just a sticky methodological question. Fact remains that there is little evidence that "impact bats" as a whole hit good pitchers better than "non-impact bats" hitters do relative to their baseline performance levels. Yeah, towards the end of our discussion I asked if he wanted that guy's findings scaled like wRC+, but I should've just mentioned your tOPS+, I got stuck in a discussion about the obviously flawed study trying to make the larger point. To end on a more serious note, Guidas, I'll take Pedro over Manny and have fun watching Manny put up a James Loney line over a full season.
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Post by dcri on Dec 1, 2012 3:26:01 GMT -5
From reading various sites, there seems to be a growing opinion that Hamilton will re-sign with the Rangers.
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steveofbradenton
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Post by steveofbradenton on Dec 1, 2012 8:39:50 GMT -5
From reading various sites, there seems to be a growing opinion that Hamilton will re-sign with the Rangers. I do believe he would be most comfortable there. With what he has gone through over the last 10 years, comfort may trump bucks. I go back and forth about him each day. Sometimes it happens every other hour. I know we need talent and with me not wanting to part with 90% of our prospects, this always looks like the easy solution. But.......I want the Sox to build something solid and lasting with an ongoing philosophy. That philosophy, for me, should be of balance, high OBP, excellent defense, and great pitching. I never ever liked it when our teams were primarily built to "bludgeon" an opponent one day.....and the next we lost a one or two run game.
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Post by Deleted on Dec 2, 2012 18:20:26 GMT -5
I don't see how the additional constraint of a budget constraint as opposed to a roster constraint changes the idea. The backbone of the concept is that a star and a replacement player will have a greater expected value over time than two players at half the cost. A budget doesn't change that idea, it reinforces it.
Quick question before I launch into something that just bores everyone. Do you understand the basic idea of risk diversification/Modern Portfolio as put forth by Markowitz in the 50s as well as it's limitations?
In short, I don't think there are many benefits to diversification as you think there are, especially among baseball players. First off the relationship between two assets in the baseball market is mostly zero. For instance Napoli's chance of underperforming is independent of the chance of Swisher's chance of underperforming. I'll go more into this if you want, but I'd need to see how familiar people are with the ideas I'm alluding too before I do.
What you are stating here is known information and hence should be reflected in the ultimate market value of the players. This could cause the assumption that Napoli and Swisher could be had for the same amount or less than Hamiltion to be violated.
Not completely true...especially in baseball.
I actually think that Josh Hamilton might be undervalued in this market because teams are overly valuing the risk involved and thus undervaluing his upside and the overall tradeoff. But again, we'll have to talk about that more later.
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Post by Chris Hatfield on Dec 2, 2012 19:15:40 GMT -5
Man, I missed you picking apart arguments line by line, especially when you do it with the same line twice!
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Post by wcsoxfan on Dec 2, 2012 20:42:31 GMT -5
I think I can best demonstrate the problem with a hypothetical: So as here, the 50 percentile hitter had a .823 OPS against bad pitching. Assume the 60th percentile hitter had a 1.154 against bad pitching. In this scenario, Hamilton performed 10% better than league average against bad pitching. The problem is, that we have no idea what the 60th percentile (or any other percentile) hitter did against bad pitching. So what we're left with is the meaningless statistic that Hamilton hit bad pitching at a 40% better RATE than league average. But this does not mean that he was in ABSOLUTE terms 40% better than league average against bad pitching. Edit: What we need here is a comparison of the rates at which hitters hit bad pitching to draw meaningful conclusions. Wow, that was easier than four or five posts. I was confused after reading the first couple of posts you made and I think I figured out why. Please keep in mind that 50 percentile is the median and not the average. When I replace 'average' with 'median' it seems that you are making the argument that we have no clue what percentile Hamilton rests in vs good or bad pitching - and we simply need to see all of the data to this study. Does anyone have access to the rest of the data? (sorry if i missed this in an earlier post) Btw: I like your reference that 1 6win player is more valuable than 3 2win players because a 2win player is more readily available for a team with the Red Sox resources. We must all keep in mind that next year Greinke and Hamilton level players are less likely to be available than Napoli/Swisher level players.
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Post by lasershow07 on Dec 2, 2012 21:29:36 GMT -5
I think I can best demonstrate the problem with a hypothetical: So as here, the 50 percentile hitter had a .823 OPS against bad pitching. Assume the 60th percentile hitter had a 1.154 against bad pitching. In this scenario, Hamilton performed 10% better than league average against bad pitching. The problem is, that we have no idea what the 60th percentile (or any other percentile) hitter did against bad pitching. So what we're left with is the meaningless statistic that Hamilton hit bad pitching at a 40% better RATE than league average. But this does not mean that he was in ABSOLUTE terms 40% better than league average against bad pitching. Edit: What we need here is a comparison of the rates at which hitters hit bad pitching to draw meaningful conclusions. Wow, that was easier than four or five posts. I was confused after reading the first couple of posts you made and I think I figured out why. Please keep in mind that 50 percentile is the median and not the average. When I replace 'average' with 'median' it seems that you are making the argument that we have no clue what percentile Hamilton rests in vs good or bad pitching - and we simply need to see all of the data to this study. Does anyone have access to the rest of the data? (sorry if i missed this in an earlier post) Btw: I like your reference that 1 6win player is more valuable than 3 2win players because a 2win player is more readily available for a team with the Red Sox resources. We must all keep in mind that next year Greinke and Hamilton level players are less likely to be available than Napoli/Swisher level players. Yes with respect to the first portion. The last part wasn't me. I don't have the data myself but I'd love to see it.
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