To Replacement-Level or Not?

NOTE: If you haven’t seen the poll, then click that FIRST, then come back here to read more.

***

This is a the final part of a three-parter (for today anyway).

One thing that I wanted people to consider is that adding to one guy is like subtracting to another guy.

Say we look at our two players:
Player X: 105 runs created in 105 games
Player CD: 125 runs created in 162 games

Baseline: 0.35 runs per game

And we subtract that from each player.

So, Player X goes
from 105 runs created in 105 games
to 105 – 105*.35 = 68 runs created above Baseline

And Player CD goes
from 125 runs created in 162 games
to 125 – 162*.35 = 68 runs created above Baseline

Therefore, in terms of runs above replacement, both are at 68 runs.

But, what if instead of subtracting as I’m doing here, I simply ADD 0.35 runs per MISSING game.

Now we have this:
So, Player X goes
from 105 runs created in 105 games
to 105 + (162-105)*.35 = 125 runs created WITH baseline

And Player CD, having played all 162 games, remains at: 125 runs created

See? In both cases, we get the exact same answer.

When it comes to MVP talk, I presume a fair number of readers can’t fathom giving runs to a player for missing a game. That those 57 missing games should get zero runs, and therefore, the 105 runs in 105 games must remain identical in value to 105 runs in 162 games.

And I also think that those who support replacement level don’t realize that they are giving credit for the missing games, that they are in effect adding 20 runs to our Player X here.

In the end, it all comes down to an equivalency. You have someone with 105 runs created in 105 games. Is that better or worse, for MVP talk, than someone who created 106 runs in 162 games? How about 109 runs? 112?

The average Fangraphs reader made that decision: the average is 125 runs created in 162 games is equivalent to 105 runs created in 105 games. And so, the average Fangraphs reader supports adding 0.35 runs per game, for every missing game.

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64 Responses to “To Replacement-Level or Not?”

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1. FJR says:

To be fair though, I think people were so confused that all we saw was the well known fact that people get anchored to the median value in a poll when they don’t know what they’re looking at, since it seems to be inherently the most reasonable.

• FJR says:

This is why we see that any poll where you chose from given values is biased towards the middle answer. The more confused the repondents are, the more pronounced this effect is.

• Telo says:

That’s noted, however, it you were completely correct we’d see votes split between player C and D equally, while there was a very clear tendency towards C.

• tangotiger says:

Note that I ran the poll on my blog, where there’s likely less confusion (though not completely, as noted by the readers there), and I got the exact same answer: 125.

• FJR says:

@tango

it’s not so much the actual answer that concerns me, it’s the level of agreement and the near perfect symmetry, after you take into account the obvious bad answer.

• FJR says:

@yirmiyaho

yeah, i think that was part of the issue as well. The sabr inclined made up their own replacement level FIRST, which defeated the whole purpose as Tango stated it. The non-sabr inclined just picked the middle answer.

• CBP says:

I think the average Fangraphs reader is intelligent enough to understand the poll question. If this were on Fox or ESPN, I’d have been more inclined to agree with you.

• Yirmiyahu says:

I think I cheated. I worked backwards.

First I decided that I wanted to rate MVP based on runs-above-replacement instead of runs-above average. (I’d do the opposite if we were discussing HoF). Then I decided I wanted replacement level to be 20 runs-below-average per 150 games. Then I figured out all of the players RAA and sorted.

I am apparently a saber geek.

• Yirmiyahu says:

Should’ve said “Then I figured out all of the players RAR and sorted.”

2. Mr. wOBAto says:

Interesting that the crowd source on this one is spot on, with a plurality voting on sloting the mythical 105 in 105 right behind the 130 in 162 in the poll.

• FJR says:

I think that was because whoever made the poll made the best actual answer the middle answer. In doing so the person making the poll communicated a lot of information.

• Telo says:

Except… there were two middle answers, and one of those middle answers got over twice the amount of votes as the other. So… you are just wrong. Was there some polling bias? Yes. Was there enough to dismiss the results out of hand? Of course not.

• Dan says:

There was OBVIOUSLY polling bias. Telo, how can you be sure the polling bias wasn’t enough to make a difference?

• FJR says:

@telo

yeah, but one of the answers could more or less be flat out dismissed. The one with fewer runs in more games played. I’m not saying it can be completely dismissed, but there’s probably so much noise that I don’t know how useful it is.

As someone that has been trained to observe studies and look for bias, I can tell you that looking at the graph of the answers, it perfectly fits with answer choice anchoring bias. That doesn’t mean it’s wrong, but it’s one, where if you want accurate studies, you’d definitely want to redo and see if your results are confirmed.

When people aren’t sure what the best answer is, and from teh comments on that poll, we can pretty much all agree that many people had no idea what the best answer is, they are inevitably anchored towards the middle response. The effect is somewhat lessened if you don’t put the answers in order (which shouldn’t matter, but empirical evidence unequivocally shows it does somewhat matter). The effect is at it’s most extreme when: 1) people are confused 2) the answers are in units people are unaccustomed to dealing with 3) the answers are put in order 4) the respondents have some sort of interest in being correct

I’m pretty sure we had all 4 items going on in that poll. It doesn’t make the results wrong, but it’s hard to tell how much bias is going on.

Look at the level of agreement. Do you think that respondents would agree THAT MUCH about the answer to that question naturally?

• tangotiger says:

FJR: there was much more agreement on my site, with 47% choosing C, and 18-19% choosing B, D.

The anchoring bias would mean that you’d have both Player C and Player D drawing the votes, as someone else noted. If you want to wipe out a large share of votes because of bias, then you should remove them equally from C and D. You’ll still be left with C as the winner overall.

Given that my readers, Fangraphs, and saber-wisdom all give the same answer, I doubt we have much bias.

I was more interested in the range of answers. A healthy majority, both at my site, and here, chose something other than C. And at Fangraphs, the range was much wider, which probably is based on a misunderstanding of “runs created”. I took it for granted that we all know what that means (and that’s ok at my site).

Given some of the reader responses, they don’t know what runs created means. I may have to write a future post on that.

• Telo says:

A
B
C
D
E
F

I concede that since the answers are a continuum, C and D are likely to chosen more naturally. But I still don’t see how you can ignore the fact that C got more than twice as many votes as D. What polling bias exists that favors C over D?

• FJR says:

@tango

I’m not saying they ARE VERY biased, I’m saying we have no idea how much they are. It’d be interesting if you threw out the last answer and changed them around a little so that the ‘correct’ answer was #2 or next to last and see if it was still chosen as often.

Also, like I said in another post, another issue was that most sabr inclined people did it backwards, which was come up with replacement level FIRST. This is indicated by most of them saying that this is what they did, which from what you have said in other posts, was the exact thing you designed the poll to avoid. (otherwise, you would have just asked “what do you think replacement level is?”)

Another issue was the last answer was so obviously non-sensical that if you put ANY thought into it, you could throw that out, thus providing the preference for C over D.

• tangotiger says:

FJR: it’s not that we have “no idea”. We have SOME IDEA. This is the current results:
A 15%
B 19%
C 37.5%
D 17%
E 8%
F 2.5% (the nonsensical choice)

First of all, that’s not symmetrical. It’s skewed toward the A/B side rather than the D/E/F side. If we throw out the F as an implausible choice (a junk vote), we have 34% at A/B and 25% at D/E.

In any case, how many people would be so biased as to want to choose C? We’re not going to suggest half the voters, are we? Even if you want to suggest that 45% of the voters of option C are so biased, choice C would STILL win.

You’d have to have an enormous amount of bias in order to affect the results.

• Blue says:

F is not nonsensical–you just have to assume that a player who only showed up 2/3rds of the time isn’t qualified to be in the discussion at all.

3. Scott Clarkson says:

I realize this is supposed to be viewed through the lens of the MVP debate but what about the question of which player you’d rather have manning a given position on your playoff team?

Would you rather that 110/110 guy who mostly likely missed time due to injuries/deployment/platooning or would you rather have the 125/160 guy who you can presumably count on more often?

I’m just not comfortable with having a higher probability of needing to call upon 110/110 guy’s replacement in a high leverage situation/playoff game.

• FJR says:

this brings up an interesting point as well. The answer is probably different if the player missed the games due to a platoon, which implies a higher replacement value, than if they missed them due to injury, which means a matchup independent replacement (or, perhaps two players in a platoon replacement).

• Telo says:

The truth is, it doesn’t really matter if it’s a platoon or not. They both still give you X amount of runs above replacement, and it’s up to you to determine what the equivalent 162 game player is that is interchangeable with our 105/105.

Think of it this way. If next year I told you you could have either a 105/105 (via platoon) or a 125/162, which would you take?

So, I just confused myself, because now I think the replacement level is LOWER for the 105/105. Because it’s EASIER to find someone to play 57 platoon games, than it is to find 57 random games.

I won’t delete my stream of consciousness here because I want to read it again and have to run.

So, a platoon 105/105 is more valuable than a non-platoon… that’s not passing the logic test, because it forces you to use an extra roster spot. Maybe that means that, via game theory, you should have 1 position on the field, or one bench player who is exceptionally strong from one side of the plate, but basically unusable otherwise. If you had any more than 1, you handcuff yourself roster-wise. That seems to make sense. In which case, you would want the 105/105 platoon over non-platoon, because it allows you to maximize the other 57 games more efficiently, assuming you weren’t already employing a platoon that occupied a roster spot

very ramble-y, sorry

• Telo says:

higher lower

• tangotiger says:

Telo: yes, it is an interesting question.

In the case of the injury guy being 105/105, his roster spot is taken up by someone else, and he’ll provide say 20/57 value there.

On the other hand, a platoon guy that is 105/105 (though obviously not the best example, since we don’t find that guy, but let’s continue anyway), will get someone with, say, a 25 runs /57 game value.

So the question you are asking is: would you like to have 130 runs in 162 games, knowing you have one less roster spot, or 125 runs in 162 games?

It’s probably pretty close. Just a few days ago on my blog, I reasoned that the value of a roster spot would be something like 5-10 runs. So, we’re in the ballpark here.

• Scott Clarkson says:

if 105/105 guy only played 105 games due to injuries, I think it passes the sniff test that this creates more of a roster problem than an otherwise healthy/available player who you choose to deploy or not in certain situations.

If you have made the decision to platoon you have likely done so with the time and wherewithal to acquire a competent platoon replacement that ideally would give you close to 57/57 production matching your 105/105 guy from the other side.

At the very least you would not platoon if player X’s likely platoon partner was only going to produce at replacement level.

The injury-prone 105/105 guy on the other hand probably forces you to play with 24 guys occasionally in addition to forcing teams to trot a true “replacement level” talent out there if the roster isn’t flexible enough to handle the loss internally.

• FJR says:

@tango

Yeah, it’s a really interesting question that I can’t recall being studied. Does it cost a team more to have a player not play due to platoon or injury, given the same production when playing?

One of those ‘somebody should do a study’ questions for sure.

4. Tom says:

Why Tangotiger? Every other person who rights on here gives their actual name.

• Mr. wOBAto says:

You don’t know who tangotiger is?

• FJR says:

does anybody?

• Telo says:

The mythical Tom Tango. Learn yoself some sabermetrics, son.

• Scott Clarkson says:

• tangotiger says:

I don’t blame you for ignoring posts with internet handles.

I can post as “Tom Tango”, but that’s my book pseudonym, so I don’t know that that’s any better. I can post with cool names like Trevanian or Prince or Mark Twain, but I’m not talented enough for that.

My suggestion is that you just ignore any post I make. You’ll be happier.

• Tom says:

I am not questioning the content of your posts, it’s solid stuff, I was just curious as to why the handle.

• tangotiger says:

Privacy, inertia, amusement, freedom, unique. One of those I guess.

5. AF says:

Assume that Team A has a player that creates 105 runs in 105 games, a replacement that creates 20 runs in the remaining 57 games, and a team that is otherwise league average.

Team B is the same except that it has a player that creates 125 runs in 162 games and does not need to be replaced.

Which team is likely to win more games, all else equal?

I suspect that the answer is Team B, but I’m not sure that is correct. Anybody know?

6. TK says:

If nothing else, catchers should get credit for replacement level play for some of the games they miss (perhaps 10%) because those missed games are across the board for all catchers and all MLB teams must and do make adjustments to account for those missed games (by carrying two players that are primarily catchers). Thus, it cannot be said that a catcher in any way hurts his team by not playing those games.

7. Blue says:

I wouldn’t vote for the player in any circumstance. Playing 105 games as a position player simply isn’t enough time to be qualified for MVP.

• Blue says:

Let’s say you have a player who is 50 plate appearances short of qualifying for the batting title and is hitting .420. Would it be appropriate to just give him replacement level hitting and assume a .400 season? Or let’s say you have a tight platoon of players, each playing 81 games and their combined average is .400. Would they qualify?

Individual awards are for individuals, not for multiple players.

• tangotiger says:

There’s nothing “simply” about this. You can make a fair argument on anything from B to E.

• Blue says:

Yes, it is simple. The award is not for most valuable slot on the 25-man roster–it’s for most valuable PLAYER. It is an individual award–the way you are framing your analysis turns it from an initial award into a multiple player award, and that makes no sense.

Once you go down the rabbit hole you are proposing, there’s no going back. Have one player at 150 games and one at 162? Well, you need to just add some made up counting stats to the 150 player to see what they were really worth. I’m sorry, but its a nonsensical analysis.

8. My echo and bunnymen says:

Dang, I’m outside the average. Though I most certainly understand the reasoning and logic behind adding value with the other player filling in for his time missed, I cannot bring myself (yet) to that conclusion. Maybe time will help me wrap around that, but I still only see things in results. The 105 runs created player only created 105 runs, while a player who created 110 runs over 162 games is certainly less “skilled” than the former, the fact that the latter can play 162 games helps him gain more value. I cannot vote an MVP award (once again, yet) on someone else’s contributions.

• My echo and bunnymen says:

Oh, but I do believe in about a ~5 run give, either way, in terms of runs created. Simply put, the data may be wrong or it may be 100% right but until then I’ll say that an argument could be made for either player being better, worse, or equal. Arbitrary, a little but after thinking about the math and formulas it seems good enough to decide player’s production in comparison to other players. So in the above example (unless exclusively talking about offense) they could be equal or not. I’m fine with either opinion, since I don’t believe it necessary to split that fine of a hair.

9. Greg says:

Exactly. It all comes down to equivalency. I wasn’t as precise as you were, I just said. Average is 80 runs, half that is 40, half that again is 20, so a terrible player would still get 20 runs in place of the monster who produced 105 in 105. The fact that somebody produced to such a level that they were equivalent to a 125 run player through 162 games despite only playing 105 counts greatly for the 105 run player, even though a terrible player was taking their spot for nearly a third of a season counts greatly in my opinion. Ultimately, that’s the break even point.

But really, for a player to even be considered for MVP despite playing only 105 games, they would have to put up some Bondsian numbers, basically racking up more WAR in 105 games than anybody else got in 150. That’s why WAR is such a good stat, it’s just accumulated wins. Traditional voters would never go for it, but still.

• tangotiger says:

What is bothersome about your comment is that you treat WAR as a great stat, without appreciating what the replacement level actually is.

For example, this is not true:
“so a terrible player would still get 20 runs in place of the monster who produced 105 in 105″

No, the replacement-level player would produce 37 runs in 105 games (0.35 runs per game x 105 games).

So, our 105 in 105 player is being compared to the 37 in 105 player, and is +68 runs above replacement (and ultimately +6.8 WAR).

And the 125 in 162 is compared to the 57 in 162, and is also +68 runs above replacement (and 6.8 WAR).

10. Sivart says:

While it wasn’t expressly questioned in the poll, I took the question as it applies to MVP voting seriously. I penalized the player for missing games and forcing his team to find an alternative player, since number of games played is actually part of the MVP consideration process (as far as I remember).

It seems like you failed to take that into consideration in your maths. If anybody agrees with me, they likely gave a value to the player based on their performance per game, but then penalized them for failing at the other MVP criteria. So while you can make a formula that will arrive at the same conclusion, I believe that others may have used a completely different process.

The problem is then it becomes completely subjective, and I realize that. But people all have their own ideas on how much a player should be penalized for forcing his team to make 25 and/or 40 man roster decisions, burning options on players, signing a replacement level player to player for 57 games but who takes ABs away from their prospects at AAA before and after those missed games, etc. It may be impossible to quantify how that impacts poll respondants decisions, but to ignore that variable and make a formula regardless of it is just working backwards from an answer and making up numbers that fit.

If you hadn’t brought MVP voting into the discusion and were talking purely value, this would be less important. But games played is clearly a part of the MVP voting criteria, so this is really a vital omission imo.

• tangotiger says:

There was no omission.

I was looking for the people answer’s, and what their answers IMPLIED.

Some people’s answers IMPLIED that you get 0 runs for each missing game. Some people’s answers IMPLIED that you get 0.35 runs per game. Some people IMPLIED that you get 0.50 runs per game.

There’s no right or wrong here. It’s a question of how people perceive things.

AS IT TURNS OUT: on average, people perceive things with 0.35 runs added per missing game. That is, peoples perceived replacement level. On Fangraphs anyway, and on my site as well. On ESPN? I don’t know. I can ask them to run the same poll…

• Sivart says:

Yes, I see how you quantify what people answered, but you’re implying that it has anything to do with replacement level or average production.

What I’m saying is person A could really be saying the 105 runs in 105 games is worth the same as 150 runs in 162 games, but then they’re penalizing them a purely arbitrary number that nobody is able to quantify due to the reasons I listed (roster moves, options spent, major league service time implications to prospects).

Person B may not take roster implications into account at all (as you seem to only be concerned with minor league contract free agents that magically appear on the 40 man roster without any other changes needing to be made). So averaging two totals that are measuring different things isn’t really drawing a conclusion. From reading the Fangraphs responses, it appears most people have ignored the rules of MVP voting that state games played should be credited as a bonus for players (or as a penalty for games missed). Everybody is focused on the 105 game player, and what that’s actually worth ccompared to 162 games, when the MVP voting is actually concerned with something slightly different, the value that that 162 run player added over those games. MVP voting is not “How valuable you and your replacement are to your team”, it’s “How valuable you are to your team”. You can interpret value in many different ways, but ignoring the MVP rules entirely to make this about replacement players is a completely different discussion.

So what’s the point of averaging two different perspectives? I just don’t get it.

• Sivart says:

To clarify: The MVP vote is not about the value a team derives from a position, but from a single player. What other players do while that player is not in the lineup isn’t something that player can control and isn’t something the MVP voting rules indicate they should be credited for in any sense. There’s no basis for that line of thought at all.

• tangotiger says:

The ONLY thing the poll asked is where you would rank this 105/105 player with respect to a whole bunch of other players who all played 162 games.

*Why* a person chose what he chose was not asked. As it turns out, we can *approximate* the various decisions made by the people by simply *adding* 0.35 runs per game for each game missed. (On average.)

You may not like that the people chose to put the 105/105 player in between the 130/162 and 120/165 player. You can take comfort in the fact that while that was the popular choice, it was hardly a decisive choice. People ran the gamut from adding 0 runs per missing game all the way to adding 0.7 runs per missing game (even if the average player was only 0.5 runs per game).

Your objections seem to be rooted in the fact that people chose an answer that you didn’t like they chose.

• Sivart says:

Actually, that’s the answer I chose….

I’m just saying that the poll is more “What rules do you think apply to MVP voting” than anything else, and drawing any other conclusions is pointless and inaccurate.

Because person A feels that the number of fans a superior player brings to the ballpark makes him an appropriate choice for C and another person thinks that doesn’t matter but that his replacement level player’s value drives his value to a choice C is significant how?

We’re all measuring different terms of value, some people are taking TV contracts, jersey sales, attendance, trade value, or any host of other things into consideration while others aren’t. You’re just asking us what we think “value” means in the MVP vote. It’s a tired argument, and any poll that doesn’t clearly state what aspect of value should be measured is so inaccurate that it’s a waste of time.

• tangotiger says:

I agree that the conclusion is with respect to MVP. And wrt to MVP (which is right there in the title of the poll), you add 0.35 runs per game.

As it turns out, for things like salary, you ALSO add 0.35 runs per missing game.

So, how a player should be perceived for MVP voting is the same as for salaries. And you do that by using a replacement level of around -0.15 runs per game relative to average.

• Sivart says:

So what you’ve actually concluded is:

X% of people take Y number of factors in to account.
A% of people take B number of factors in to account.
C% of people take Y number of factors in to account but measure Y number of factors differently than X% of people.

And so on, and so forth.

That does not give us any insight into replacement level or replacement value in my opinion.

If you want a poll about value, say value. If you want a poll about intangibles, how people interpret MVP voting, and the implications of playing time in respect to clearly stated rules for an award, don’t say that the answers from people offering different perspectives implies anything beyond “More people chose answer X”

• Sivart says:

You talk about the average run production of players, which means it’s the first thing people will consider.

Had you left that out, but said “Since 105 runs in 105 games makes the player a superstar caliber player that will increase fan attendence by 4,000 per game at an average value of 12 dollars per ticket and with a marginal win worth 4.8 million dollars and a win worth 10.1 runs” then people would have converted it all to dollars first and used that information given.

• tangotiger says:

Dude, that last post makes no sense whatsoever. But, whatever, you’ve made your point(s) and your mind, and there’s nothing I can do to illuminate you otherwise. The rest of your posts where otherwise well thought-out.

• Sivart says:

What part made no sense? You lead the voters to the answer you wanted by giving them only the information on an average player’s runs/162 games to measure value.

You did not give them any other information to measure value. I shall break it down for you.

Your example player was worth 105 runs in 105 games. We can assume that a player worth 105 runs in 162 games is a worse player. We can assume that more fans will show up to see better players. Fans cannot know a player will be injured all the time before going to a game, so we can assume that more people will show up to see the better player, and that effect will be evident even in some of the games he’s not there.

Are you with me so far?

The revenue that player generates is value for his team. In a discussion of the MOST *VALUABLE* PLAYER, then value is surely important, isn’t it? If you broke down that revenue and gave people that information first, they would tend to use that information first to make their selection on the poll. Instead, you gave people the average runs per game, and so the majority tended to use that.

There are ethics in statistics, and what you did was not ethical. You asked a question, but provided only the information that would logically lead someone to come to the conclusion you desired.

If you wanted to do this properly, you would ask the question without any notes, and let people do their own research and come to their own conclusions. Highlighing a specific aspect of value will cause people to focus on that aspect. The people that see through your manipulation though, will be in effect responding to a completely different question, and measuring value in many different ways. Your data is worthless, because not everybody was answering the same question.

I hope you are able to understand this.

• Blue says:

“You lead the voters to the answer you wanted by giving them only the information on an average player’s runs/162 games to measure value.”

That’s exactly right. The poll answers would have been FAR more interesting if Tango would have selected six real players and placed the five benchmarks in random order within the question. Of course, that would have the chance of invalidating his belief that MVP voters should add a bunch of counting stats to players who don’t play a full season.

• Sivart says:

In case you’re still confused, I wikied some of these introductory concepts for you:

“Response bias is a type of cognitive bias which can affect the results of a statistical survey if respondents answer questions in the way they think the questioner wants them to answer rather than according to their true beliefs. This may occur if the questioner is obviously angling for a particular answer (as in push polling) or if the respondent wishes to please the questioner by answering what appears to be the “morally right” answer…. This occurs most often in the wording of the question. Response bias is present when a question contains a leading opinion. ”

“It is well established that the wording of the questions, the order in which they are asked and the number and form of alternative answers offered can influence results of polls. For instance, the public is more likely to indicate support for a person who is described by the operator as one of the “leading candidates”. ”

Again, I hope you were able to follow this, and understand how giving partial information will lead people to answer a poll in a certain way (or cluster around a certain set of similar answers). What you did is asked who someone would vote for on an award that has several aspects to it, then slanted your entire question and answer set to highlight only some of those aspects.

Best of luck avoiding this common pitfall in your next attempt!

• tangotiger says:

“There are ethics in statistics, and what you did was not ethical. You asked a question, but provided only the information that would logically lead someone to come to the conclusion you desired.”

Stop being a jerk by questioning my ethics.

And given the answers were far-ranging, no one was led to anything.

I presume you need to have the last word, so have at it, as long as you don’t talk about me, my character or my thought-process.

• Blue says:

“So, how a player should be perceived for MVP voting is the same as for salaries. And you do that by using a replacement level of around -0.15 runs per game relative to average.”

Note the presence of the word “should.” That’s hardly the same as claiming “[t]here’s no right or wrong here.” You clearly think there is a right answer and you slanted your poll to generate it.

• tangotiger says:

Oh brother. Now, we’re going to parse every single sentence I write like a Zapruder film.

ON AVERAGE…. ON AVERAGE… people use replacement level for their MVP voting. Do I have to keep repeating ON AVERAGE?

Some people think you give 0 runs per missing game. Some people gave 0.70 runs per game (70% of his 105 runs per 105 games). Others gave league average (0.50 runs per game).

There’s no right or wrong. There’s no slanting. There’s no ulterior motive.

This method was a way for each person to imply their own replacement level for MVP purposes.

ON AVERAGE.

• Blue says:

NO.

YOUR POLL DOESN’T ALLOW YOU TO MAKE THAT ASSERTION. Indeed, making that assertion is WHY this poll, structured this way, is so ill-conceived.

It is a slanted measurement device that essentially requested people to conduct a mathematical calculation and report the result. This generates a response bias, as Sivart points out, and slants all of the responses to the poll.

• Sivart says:

This should not get personal, and I didn’t mean it that way. I did not mean to attack you Tom, only your work.

I’m sure you never ment to lead people with the poll, and it was just your bias showing through unintentionally – it happens to the best of us. I didn’t mean to imply that you are unethical, just that what you did was.

At this point, it’s best to just admit you made an error and accept that the poll is deeply flawed. It’s only your continued insistence that your process and conclusions are valid that makes your motives seem suspect.

• tangotiger says: