Equivalent Average - Unmasked

[TheGrinch]

In fact it's essentially what people say mathematicians criticize sabermetricians for: Units. People who dislike sabermetrics generally say real mathematicians would hate their "work" because they shed units completely. This really isn't true. Everything in EqA is measured in relatively precise units that in the end cancel out leaving an answer in runs.

 

Any engineer/mathematician would laugh at the statement that unit less numbers aren't allowed or are somehow bad. Excellent post. I never looked closely at how most of the stats are generated and assumed that the stat guys had a handle on this...but some of the coefficients do sometimes seem arbitrary, and maybe rightly so for the reasons stated in one of your previous replies. It seems there might still be some room for some improvement.

 

Two questions, here's the first: Has BP or anyone else done a historical statistical study to see if tinkering with coefficients used to calculate EqA can create a better correlation to runs scored?

 

Second: How did the coefficients that were chosen for the stat come to be chosen? Was there a vote at BP or did one individual decide on the weight of each outcome and everyone agreed it was pretty close?

[CubinNY]

In fact it's essentially what people say mathematicians criticize sabermetricians for: Units. People who dislike sabermetrics generally say real mathematicians would hate their "work" because they shed units completely. This really isn't true. Everything in EqA is measured in relatively precise units that in the end cancel out leaving an answer in runs.

 

Any engineer/mathematician would laugh at the statement that unit less numbers aren't allowed or are somehow bad. Excellent post. I never looked closely at how most of the stats are generated and assumed that the stat guys had a handle on this...but some of the coefficients do sometimes seem arbitrary, and maybe rightly so for the reasons stated in one of your previous replies. It seems there might still be some room for some improvement.

There's LOTS of room for improvement in the quantitative analysis of baseball, but it sure does beat the living tar out of subjective evaluations.

[TheGrinch]

In fact it's essentially what people say mathematicians criticize sabermetricians for: Units. People who dislike sabermetrics generally say real mathematicians would hate their "work" because they shed units completely. This really isn't true. Everything in EqA is measured in relatively precise units that in the end cancel out leaving an answer in runs.

 

Any engineer/mathematician would laugh at the statement that unit less numbers aren't allowed or are somehow bad. Excellent post. I never looked closely at how most of the stats are generated and assumed that the stat guys had a handle on this...but some of the coefficients do sometimes seem arbitrary, and maybe rightly so for the reasons stated in one of your previous replies. It seems there might still be some room for some improvement.

There's LOTS of room for improvement in the quantitative analysis of baseball, but it sure does beat the living tar out of subjective evaluations.

 

Agreed completely. I guess I just imagined it was closer to "truth" than it actually is.

[CubinNY]

In fact it's essentially what people say mathematicians criticize sabermetricians for: Units. People who dislike sabermetrics generally say real mathematicians would hate their "work" because they shed units completely. This really isn't true. Everything in EqA is measured in relatively precise units that in the end cancel out leaving an answer in runs.

 

Any engineer/mathematician would laugh at the statement that unit less numbers aren't allowed or are somehow bad. Excellent post. I never looked closely at how most of the stats are generated and assumed that the stat guys had a handle on this...but some of the coefficients do sometimes seem arbitrary, and maybe rightly so for the reasons stated in one of your previous replies. It seems there might still be some room for some improvement.

There's LOTS of room for improvement in the quantitative analysis of baseball, but it sure does beat the living tar out of subjective evaluations.

 

Agreed completely. I guess I just imagined it was closer to "truth" than it actually is.

That's one of the problems IMO, many are not looking for the truth. Many are trying to create models that approximate the truth then when the model disagrees with the true value they criticize reality and blame luck instead of looking for why or where the model went wrong.

[TheGrinch]

In fact it's essentially what people say mathematicians criticize sabermetricians for: Units. People who dislike sabermetrics generally say real mathematicians would hate their "work" because they shed units completely. This really isn't true. Everything in EqA is measured in relatively precise units that in the end cancel out leaving an answer in runs.

 

Any engineer/mathematician would laugh at the statement that unit less numbers aren't allowed or are somehow bad. Excellent post. I never looked closely at how most of the stats are generated and assumed that the stat guys had a handle on this...but some of the coefficients do sometimes seem arbitrary, and maybe rightly so for the reasons stated in one of your previous replies. It seems there might still be some room for some improvement.

There's LOTS of room for improvement in the quantitative analysis of baseball, but it sure does beat the living tar out of subjective evaluations.

 

Agreed completely. I guess I just imagined it was closer to "truth" than it actually is.

That's one of the problems IMO, many are not looking for the truth. Many are trying to create models that approximate the truth then when the model disagrees with the true value they criticize reality and blame luck instead of looking for why or where the model went wrong.

 

When dealing with outcomes that deal with chance or apparently partly random outcomes as well as trends and probabilities, it can be hard to tell if sampling error or model error caused the discrepancy. But it isn't impossible to distinguish between the two.

[samhainn77]

Great Post, thanks Meph!

 

Quick question (and I'll probably look stupid in the process): Instead of using a constant to make an attempt represent league avg as .260, is there a logical measurement that can be derived from the leagues in a separate formula to make this less arbitrary?

 

In other words, In your mind is there a correlation that can be drawn from cJapan = 4.9, cNL = 5.2, and cAL = 5.7 that would give us a more accurate variable to plug in for the constant?

 

Or am I clueless and missing the point? The 5 just seems like a "This hurts my head, just plug in a constant since the variance will be negligible."

 

Anyway, thanks again!

[TheGrinch]

Great Post, thanks Meph!

 

Quick question (and I'll probably look stupid in the process): Instead of using a constant to make an attempt represent league avg as .260, is there a logical measurement that can be derived from the leagues in a separate formula to make this less arbitrary?

 

In other words, In your mind is there a correlation that can be drawn from cJapan = 4.9, cNL = 5.2, and cAL = 5.7 that would give us a more accurate variable to plug in for the constant?

 

Or am I clueless and missing the point? The 5 just seems like a "This hurts my head, just plug in a constant since the variance will be negligible."

 

Anyway, thanks again!

 

The point was...the "5" isn't always a 5. If you were in the cNL, it was 5.2 and if in japan it was 4.9. So yeah, there is a more accurate variable to use than 5, and it is used. I guess we could give that variable a name instead of referring to it as a constant..even if it is constant for all players in the same league. Calling it "5" is confusing, and maybe that's how BP intended it to be.

[Mephistopheles]

Two questions, here's the first: Has BP or anyone else done a historical statistical study to see if tinkering with coefficients used to calculate EqA can create a better correlation to runs scored?

 

Second: How did the coefficients that were chosen for the stat come to be chosen? Was there a vote at BP or did one individual decide on the weight of each outcome and everyone agreed it was pretty close?

 

 

First: You can tinker with them, and other things have been developed, linear weights. Then again, EqR can be broken down into linear weights if you want to. Linear weights basically represent that each event has a specific run value. Off the top of my head it's something like this: R = .5*1B + .8*2B + 3B + 1.4*HR +.33*BB -.25 OUT. Multiplying these three by 4 results in: 4RC = 1.3 BB + 2 1B + 3.2 2B + 4 3B + 5.6 HR - Out....which is very very close to Raw without the outs.

 

Second: Basically something like OBP + SLG. If you ignore the denominator and add just the top half of the fractions of OPS you get BB + HBP + 2*1B + 3*2B + 4*3B + 5*HR. OPS is actually fit better by 1.6*OBP+SLG, but they just put all of the 1.6ish term into BB and HBP. They then added more bases to the top. So it's not all that different than the weights for OPS. Clay Davenport came up with them by himself, I believe.

[Mephistopheles]

Great Post, thanks Meph!

 

Quick question (and I'll probably look stupid in the process): Instead of using a constant to make an attempt represent league avg as .260, is there a logical measurement that can be derived from the leagues in a separate formula to make this less arbitrary?

 

In other words, In your mind is there a correlation that can be drawn from cJapan = 4.9, cNL = 5.2, and cAL = 5.7 that would give us a more accurate variable to plug in for the constant?

 

Or am I clueless and missing the point? The 5 just seems like a "This hurts my head, just plug in a constant since the variance will be negligible."

 

Anyway, thanks again!

 

I did define the constant: C =(LgR/LgOut)/.260^2.5

[samhainn77]

Great Post, thanks Meph!

 

Quick question (and I'll probably look stupid in the process): Instead of using a constant to make an attempt represent league avg as .260, is there a logical measurement that can be derived from the leagues in a separate formula to make this less arbitrary?

 

In other words, In your mind is there a correlation that can be drawn from cJapan = 4.9, cNL = 5.2, and cAL = 5.7 that would give us a more accurate variable to plug in for the constant?

 

Or am I clueless and missing the point? The 5 just seems like a "This hurts my head, just plug in a constant since the variance will be negligible."

 

Anyway, thanks again!

 

 

I did define the constant: C =(LgR/LgOut)/.260^2.5

 

Ok, it clicked. Thanks. Good lord, after rereading your original post I'm not sure how I misinterpereted.

Edited February 13, 2008 by samhainn77

[TheGrinch]

Two questions, here's the first: Has BP or anyone else done a historical statistical study to see if tinkering with coefficients used to calculate EqA can create a better correlation to runs scored?

 

Second: How did the coefficients that were chosen for the stat come to be chosen? Was there a vote at BP or did one individual decide on the weight of each outcome and everyone agreed it was pretty close?

 

 

First: You can tinker with them, and other things have been developed, linear weights. Then again, EqR can be broken down into linear weights if you want to. Linear weights basically represent that each event has a specific run value. Off the top of my head it's something like this: R = .5*1B + .8*2B + 3B + 1.4*HR +.33*BB -.25 OUT. Multiplying these three by 4 results in: 4RC = 1.3 BB + 2 1B + 3.2 2B + 4 3B + 5.6 HR - Out....which is very very close to Raw without the outs.

 

Second: Basically something like OBP + SLG. If you ignore the denominator and add just the top half of the fractions of OPS you get BB + HBP + 2*1B + 3*2B + 4*3B + 5*HR. OPS is actually fit better by 1.6*OBP+SLG, but they just put all of the 1.6ish term into BB and HBP. They then added more bases to the top. So it's not all that different than the weights for OPS. Clay Davenport came up with them by himself, I believe.

 

Thanks. Getting back to the linear weights you mentioned, I can understand the logic of choosing the weights applied to each event, but I don't understand why these weights have not been further statistically analyzed to see how accurate they really correlate to runs scored. What I mean is, is it God's honest truth that a HR is 1.4 times as valuable as a 3B? Could a study prove its closer to 1.47? They seem like a pretty logical point to start out at, but judging by the values it seems they haven't been studied in depth to find the optimum weights.

[Wes Mantooth]

At my advanced age, I was raised with batting average, rbis, and home runs were all you needed to know. It hasn't been easy getting past that. But these posts are a great help in understanding what the stats are and why they are used. Hate to stroke your ego,not that you need any help, but I do look forward to reading your posts. Thanks a lot.

[TheGrinch]

Since a HBP is worth slightly more than a BB which is worth more than an IBB, shouldn't it be separated out that way?

 

If so, have you worked on improving EqA? Is it just diminishing returns (or would it be a good thing at all) to make the values of the coefficients a little more precise?

 

Even though the 5 changes, how well does it handle different run environments considering, e.g., that the ratio of a walk to a single always stays the same?

I think this is an excellent question to ask and what could be the first step to quantifying situational hitting. Instead of weighting all ABs the same, you could weight a BB with no one on base the same as a 1B for that particular AB. Maybe a HR will have a proportionally greater coefficient applied than a 2B or 3B when there are two outs as opposed to no outs. Baseball players DO change their approach at the plate depending on the score of the game, the inning, the number of outs, whos hitting behind them, what the count is, and so on. I'd imagine how effectively someone changes their approach could also be accounted for in a catch-all WINS created stat (as opposed to runs created stat) with enough data...and an insane amount of number crunching and research.

[OleMissCub]

I just spent 20 minutes reading this post and I must say I've learned a lot. Thanks Meph.

 

 

 

You might want to fix the grammar in this sentence though, there are some words missing or something.

It tells how often a player gets hit when while deciding to throw out some times he goes up to the plate for no reason other than we feel like it.

[Rob]

Since a HBP is worth slightly more than a BB which is worth more than an IBB, shouldn't it be separated out that way?

 

If so, have you worked on improving EqA? Is it just diminishing returns (or would it be a good thing at all) to make the values of the coefficients a little more precise?

 

Even though the 5 changes, how well does it handle different run environments considering, e.g., that the ratio of a walk to a single always stays the same?

I think this is an excellent question to ask and what could be the first step to quantifying situational hitting. Instead of weighting all ABs the same, you could weight a BB with no one on base the same as a 1B for that particular AB. Maybe a HR will have a proportionally greater coefficient applied than a 2B or 3B when there are two outs as opposed to no outs. Baseball players DO change their approach at the plate depending on the score of the game, the inning, the number of outs, whos hitting behind them, what the count is, and so on. I'd imagine how effectively someone changes their approach could also be accounted for in a catch-all WINS created stat (as opposed to runs created stat) with enough data...and an insane amount of number crunching and research.

 

It's probably more effort than it's worth, in all honesty. We'd be talking about pretty slight variations.

 

I usually feel fine just looking at EqA and WPA when I'm trying to evaluate those sorts of things.

[TheGrinch]

Since a HBP is worth slightly more than a BB which is worth more than an IBB, shouldn't it be separated out that way?

 

If so, have you worked on improving EqA? Is it just diminishing returns (or would it be a good thing at all) to make the values of the coefficients a little more precise?

 

Even though the 5 changes, how well does it handle different run environments considering, e.g., that the ratio of a walk to a single always stays the same?

I think this is an excellent question to ask and what could be the first step to quantifying situational hitting. Instead of weighting all ABs the same, you could weight a BB with no one on base the same as a 1B for that particular AB. Maybe a HR will have a proportionally greater coefficient applied than a 2B or 3B when there are two outs as opposed to no outs. Baseball players DO change their approach at the plate depending on the score of the game, the inning, the number of outs, whos hitting behind them, what the count is, and so on. I'd imagine how effectively someone changes their approach could also be accounted for in a catch-all WINS created stat (as opposed to runs created stat) with enough data...and an insane amount of number crunching and research.

.

It's probably more effort than it's worth, in all honesty. We'd be talking about pretty slight variations.

 

I usually feel fine just looking at EqA and WPA when I'm trying to evaluate those sorts of things.

 

...but how do you KNOW you should feel fine? And how fine should you feel? :P

 

In all seriousness, I think that if you are not accounting for the fact that a HR is more valuable with two outs than with no outs, or that in some situations a walk is exactly the same as single when in others it is not...you are missing something. And I'd rather prove that what I'm missing is insignificant rather than just assume so. The more accurate and inclusive you become the more the stat as a whole improves, sometimes by magnitudes would wouldn't imagine. ...and what is WPA? I guess I'll look it up.

[Butterscup1679666578]

So when are you going to release a baseball statistics book?

[Ding Dong Johnson]

So I tried reading this at work and while the kids are at home with me and failed miserably. Now that I've finally gotten through it...

 

Terrific post.

[third eye]

EqR = (Raw/LgRaw )^2* PA * LgR/LgPA

 

So what is EqR doing? It's measuring the relative production of the team divided by what an average team does squaring and multiplying it by PA and the runs per PA an average team scores. The squared term is based on the idea that the relationship between Raw/LgRaw and runs is not linear. This makes sense because when you add good hitters your other good hitters get more guys on base and each of their hits cause more runs. Now since we're looking at EqR on a team level and we want it on the player level let's look at that.

 

 

 

Thanks for the post. Very informative. Quick question about assumptions here (and my bad if you answered this in your post and I just didn’t get it) - Is there a specific reason for using 2 as the exponent here? I can understand if the relationship is nonlinear that you would want some factor to correct for it. But is the squared term based on anything, or just a simple way to represent a nonlinear relationship? Was there some sort of study to show that it is a quadratic and not a cubic or < 2 exponential relationship? If I reach way back into the college math toolbox (and I admit it is way rusty), could a cubic spline interpolation not more accurately represent a relationship that may not hold as x increases? I don’t know if that is even possible based on the info available.

[Mephistopheles]

why would you want to do a cubic spine interpolation. Once you start interpolating data (in ANY fashion) you're going to wind up losing control of certain behavioral aspects of the function. Ie... in this case you'll lose a positive slope. If you increase your offensive out put you'll increase your runs output, it's only logical. interpolating it may not result in that. interpolating data isn't effective in something like this

 

Thanks. Getting back to the linear weights you mentioned, I can understand the logic of choosing the weights applied to each event, but I don't understand why these weights have not been further statistically analyzed to see how accurate they really correlate to runs scored. What I mean is, is it God's honest truth that a HR is 1.4 times as valuable as a 3B? Could a study prove its closer to 1.47? They seem like a pretty logical point to start out at, but judging by the values it seems they haven't been studied in depth to find the optimum weights.

 

There are more digits, I just don't have them memorized off the top of my head. Besides, does a difference is .05 of a run make much of a difference? If you hit 50 HRs we're underestimating your run production by 2.5 runs. Who cares? There's no reason to go any further than two decimal places on a team basis much less an individual basis.

 

Baseball players DO change their approach at the plate depending on the score of the game, the inning, the number of outs, whos hitting behind them, what the count is, and so on.

 

As noble as it may sound, that's not really true. The only difference in approach is a sacrifice bunt.

 

I'd imagine how effectively someone changes their approach could also be accounted for in a catch-all WINS created stat (as opposed to runs created stat) with enough data...and an insane amount of number crunching and research.

 

This is done, WPA (win probability added). The problem is that the year to year correlation of these variables is virtually non-existent...so we should use runs (which can then also be converted into wins if we feel like it). All production should be measured in runs.

[TheGrinch]

 

Baseball players DO change their approach at the plate depending on the score of the game, the inning, the number of outs, whos hitting behind them, what the count is, and so on.

 

As noble as it may sound, that's not really true. The only difference in approach is a sacrifice bunt.

I feel as if I'm being forced into taking up a Deuce Baseman stance, but what stat or observation or information makes you think batters (at least some of them) don't change their approach? What about hit & run situations? Sac Flies? Taking pitches for SB or getting balls from pitch outs? Don't some hitters shorten their swing (or even choke up on the bat!) with two strikes with men on base but not otherwise? Don't some batters try to just put the ball in play with a man on third and one out? Now whether or not these changes in approach are smart, or whether the differences significantly change their run production for better or for worse I don't know...but how can you state so positively that at least some batters don't?

 

 

I'd imagine how effectively someone changes their approach could also be accounted for in a catch-all WINS created stat (as opposed to runs created stat) with enough data...and an insane amount of number crunching and research.

 

 

This is done, WPA (win probability added). The problem is that the year to year correlation of these variables is virtually non-existent...so we should use runs (which can then also be converted into wins if we feel like it). All production should be measured in runs.

That's the kind of stuff I like to hear. If there is no correlation, then the stat either doesn't have enough data to constrain the model, or the model isn't any good. Either way, I can then dismiss it. Thanks for the responces.

[OleMissCub]

Meph are you not going to fix that sentence?

[imb]

Meph are you not going to fix that sentence?

 

I know I can't wait to find out!

[Mephistopheles]

Meph are you not going to fix that sentence?

 

 

nope

[WrigleyField 22]

Ugh, I made it about half way through. I need to read this sober.