Oh my God what are you talking about now?

“Well, jeez louise, man, I said in my first comment to you that was correct! We haven’t been arguing about whether they’re averages or not, but about whether they’re percentages or not. So what exactly is it that I don’t get?”

Wrong.

This is what you first said to me:
“They can also be considered to be “averages” in a mathematical sense, but only as a sum of all numbers in a set (the numbers being either “1? or “0?, and the set being the results of each AB or PA) divided by the quantity of numbers in the set (i.e., arithmetic mean). Insofar as we do not view a hitter’s statistics as a series of ones and zeros, but as a whole number divided by another whole number… well, the argument that “average” is the wrong term has merit in mathematical terms. Linguistically, what’s actually being said is that “Joe averages a hit 33.3% of the time,” but that meaning of “average” is subtly different from the mathematical connotation.”

In saying Hits per AB, Mathematically and Linguistically the stats are calling for an average. Linguistically it is asking for the number of Hits “for each” AB (as if the definition of “per”) – the number of hits will vary from 0 to 1 for each AB, and is easiest to calculate as the H/AB we are told to use. Mathematically they are averages which could eventually be altered into percentages or per-mille’s or parts-per-billion or whatever else a person may choose. But mathematically and linguistically they are not percentages or per-millies or parts-per-billion or whatever because neither the definition nor calculation specifically calls for that; the definition and calculation solely calls for the average.

And here:
“My main reason for preferring percentage here is that for all intents and purposes, knowing “how many hits a batter gets per AB” is useless since he either gets one or none in each individual AB.”

Here you admit what we have all known the entire time – that it is your preference but not necessarily the “intended” or “called for” or all the other things you have claimed BA implied. And there is the problem, and the reason we have been arguing – as if your preference for something somehow makes it a fact. Yes, we realize you personally want to say BA is a “percentage” and it is that imaginary intent of the stat you claim exists (“The only and absolute intent of the number, by itself, is to indicate “33.3% of the time.”) because you like to think of it as showing how many hits he gets over 100 AB or whatever. But that is just you and it doesn’t make it the case any more then my thinking it should be factored to “per every 3” or “per ever 600” or “per-mille” or whatever else I could come up with. That is why we had the entire conversation. You were arguing that your personal preference is fact and makes the definition of the stats something they just are not at all.

.
“Does my thought process at least make sense there?”

But yes, I read you perfectly clear now. You know you have been wrong the entire time so you are trying to backtrack to cover your bases. Unfortunately you obviously end up contradicting yourself in doing this; but whatever – you already proved my being correct the whole time so we can leave it at that…

“That was always my entire point – the ‘average’. Making something a percentage at a later time doesn’t remove the ‘average’.”

Well, jeez louise, man, I said in my first comment to you that was correct! We haven’t been arguing about whether they’re averages or not, but about whether they’re percentages or not. So what exactly is it that I don’t get?

My point, lost amidst all this froofroo: they ARE averages and they ARE percentages. Really, it’s just a semantic argument, because one answer presumes that you’re trying to determine the average number of hits a batter gets per at-bat (average), whereas the other answer presumes that you’re trying to express the rate at which the batter gets a hit (percentage). My main reason for preferring percentage here is that for all intents and purposes, knowing “how many hits a batter gets per AB” is useless since he either gets one or none in each individual AB. We’re interested in how often he gets a hit (or gets on), even though they’re functionally the same thing.

Does my thought process at least make sense there?

Anyway.

Richard: Hang on there; I didn’t mean that differences in runners were the only reason. Your example is a pretty viable exception, although there’s one respect in which it’s probably not all that workable: a hitter of Pierre’s profile with similar stats to someone who gets their XBH via power are very, very unlikely to have similar HR totals. (Not saying it can’t happen, and I’d even support you in noting that it’s fairly common for younger players with power potential to hit a lot of doubles and hardly any homers until their power develops a little more.)

But then, that’s a very specific kind of exception, and if there’s one thing I’ll argue tooth-and-nail with even stat guys about is that you can’t figure anything out solely with stats; it’s a complex game with nuances which require a knowledge of the actual bags of meat playing the game. You have to know what kind of hitter a Juan Pierre is, divorced from the actual results of his hitting, to truly understand what those results are telling you.

Now if anyone wants clarification of where it was intended to go and ultimately try to explain, then here. (and I will take this all the way to explaining completely why BA, OBP, SLG and others are always averages)

If saying 1 for that specific 4, then 1/4 does not mean 1 for every 4. If you say “25%” regarding that specific 4, then one would take you as saying a rate of 25 for every hundred calculated to that specific series of 4, or 1 for that 4. Could be taken as something else though and will explain in the next.

If saying he gets a hit for every 4 AB because of an overall 5/20, then you are technically saying 5 series of 1 for 4. Saying 25% because of those 20 would generally be taken as saying the overall 5 for that 20 but can be taken as anything between that 5 for 20 down to 1 for 4 and technically even a hit value of .250 for 1 (or a complex fraction of ¼ /1) if you didn’t specify.

If saying he gets 1 hit for every 4 AB with regards to an overall 100/400, then you are technically saying that 1 for every 4 rate shows up 100 times. Just like saying 25 for every hundred for an overall 100/400 generally means exactly what it says – 25 for every hundred. Now without specification it too can even be open to the same interpretation as above though (100/400 down to .250/1). As you said, “33.3% of 1” – which means you are giving a %/1 or a complex fraction of X/100 /1

Also, if saying “25% of the time” without specifying what “the time” is at all, your “25 for every 100” technically has to hold up under all possibly outcomes of “the time”. Meaning the first time he goes 0 for 4 your “25% of the time” is shot to hell – or if a person wanted to take it to that extreme you left an opening for, the player should be getting a hit value of .250 every time he comes to the plate or you statement is proved invalid.

It’s the problems you are going to run into by not specifying when creating a percentage off an original calculation presenting the arithmetic mean. And you get an arithmetic mean every time you calculate an outcome per opportunity for outcome. That’s why BA and others will always be averages no matter what is eventually done to them. Even BB% is an average expressed as a percentage.

By the way, whoever was looking at NL MVP above for 2004 without considering Bonds did the #2 MVP guy, Beltre, a MAJOR disservice by leaving him off the list. Especially in context of Dodger Stadium, Beltre led the league and set a franchise record for single season homers without a great supporting cast. Rolen, Pujols, and Edmonds right there reinforce each other, making it easier for pitchers to pitch under stress and allow one of the three to do something good. I won’t argue that all three Cardinals didn’t have great seasons, but I think Beltre should have been included in the list.

So yes, I’m a big fan of what the Mariners are doing. Defense can help make teams.

Juan Pierre is batting .318 this season. He has no power, so the outfield plays shallow against him. But he has great speed, so he gets a lot of leg doubles and triples.

A slower more normal player might have comparable total numbers, but would achieve them with an outfield playing deeper. Thus, runners would be likelier to grab the extra base (and the run scored) just because the outfielder would have to make a longer throw.

The beauty of baseball, IMO, is that it is impossible to generalize. I’m a big fan of many modern stats. But I also recognize that as long as they get on base enough, there is more value to speedsters than OPS+ measures. The fast slap hitters force infielders to hold them on, opening holes for the batters. They force the pitcher to devote some attention to them, which is unlikely to help them pitch better. They are more likely to force errors, outrun a force play, take the extra base. And I don’t think modern slugging based stats measure that.

And there is definite value to potential runs. It is more stress on the pitcher, which is likely to lead to more innings by the bullpen, which is a good thing for the offense. It is almost always more pitches thrown, since 4 for 4 used up zero outs. Having men on base generally increases the chances of batters getting hits. That man on second needs only a useful out to reach third, and then often the infield will have to play in, which increases batting averages (else the infield will always play in).

In short, I’m perfectly happy with the new stat, but it’s more work than I’m willing to do. When I was playing Strat-O-Matic, I used something similar: every card was ranked with 3 points for a walk or HBP, 4 for a single, 6 for a double, 8 for a triple, and 10 for a homer. Since each card was trued to 216 chances (rolling 3 dice) I could compare the total points of all cards. I could do this in my head. I can also calculate OPS in my head from all web sites, as listed above. I cannot do this new stat in my head. So I won’t use it much.

(since you will jump on it, this paragraph experienced an editing problem. Please read the “fractions” as “an independent fraction or outcome”)

(re: BA) “The only and absolute intent of the number, by itself, is to indicate “33.3% of the time.””

“%”
Definition: for every hundred

“the time”
Definition: when something happens

Without a numeral given for “the time”, “33.3% of the time” specifically means “33.3 for every hundred”.

.
“It’s a part of a whole expressed as hundredths. The key word there is not “hundredths.” The key words are “part of a whole” and “expressed as”. Expressed as,”

“part of a whole” = our hits
“expressed as” = shown
“as hundredths” = for every hundred

.
“Joey. 1/4 does not mean “one out of every four” any more than 30% means “30 out of every 100.””

Correct if you are giving 1/4 as a fraction. We werent talking about fractions – we were talking about a “percent” or “per cent” or “per century” or “per 100″. 30% specifically means “30 for every hundred”.

“Especially not in the mind-bogglingly idiotic sense that you argued that stating a player gets a hit 33% of the time implies he’d never go 0-4.”

You are taking a statement out of context. Putting it back into context: If you do not distinguish the “33%” as an “average” or state what “the time” represents, then 33% on a scale of 4 means Jeter must get 1.32 Hit in the 4 AB.

.
“because the 33.3% doesn’t refer to every 3 AB, but to the whole.”

and without defining the whole or giving the correct “average” distinction you are stating “33.3 in 100”. That was always my entire point – the “average”. Making something a percentage at a later time doesn’t remove the “average”. And even if a person chooses to make something into a percentage, it doesn’t alter the definition.

End result:

Batting Average is an Average even if you convert it to a percentage at a later time. It is the mathematical problem used to represent a series of outcome/opportunity rates to the arithmetic mean.

OBP is also an Average, even if you convert it to a percentage. It is the mathematical problem used to represent a series of outcome/opportunity rates to the arithmetic mean.

Slugging is an Average, even if you alter it into a percentage. It is the mathematical problem used to represent a series of outcome/opportunity rates to the arithmetic mean.

And that is what everyone should be able to grasp. (well, other then yourself for some strange reason)