I played HS baseball, and no one ever showered in the gym. We all just went home. I mean we were going home anyway, why change out of your uni at school?

I played on a couple high school teams, and of course took gym every year. Our school had showers, but I don't recall ever seeing a person use them.

I played on a couple high school teams, and of course took gym every year. Our school had showers, but I don't recall ever seeing a person use them.

same

At a sample size of 162, that 95% confidence interval is about +/- 8 percentage points or +/- 13 wins.

I'm having a little bit of a hard time buying this, but its possible that I'm not smart enough and/or educated enough on this topic. But it sounds like you're saying that we can't tell if an 81-81 team is a .500 team, or a really lucky 68 win team, or a really unlucky 94 win team? That doesn't sound right, but I'm willing to be educated :)

I know we showered after 7th-grade basketball practice, but if the coach (or Bill James) had walked in & joined, we'd have been pretty taken aback.

This was (& of course still is) a very small, very poor town; I suspect that for some of those kids, this was the only hot shower they were going to get. Hell, it was for me, too; we had a bathtub, but no shower.

Yeah, I played on my HS baseball team too. Nobody used the showers. We just went home after practice or a game.

I play tennis now at a club in NYC. I'm not a member, but have access to the facilities. (FYI, the locker room doesn't even have a door.) Sometimes -- always before 7pm or 8pm and never late at night -- there are kids in the locker room with their father or with their father milling about in the lounge outside waiting for the kid. The kids are never alone per se, and never use the showers. The men use the showers, but the kids don't.

"Come watch the MS Excel World Series, where 30 spreadsheets duke it out for supremacy! Follow the riveting action as we take a weighted, age-adjusted average of each player's last three and current seasons and project team WAR totals!"

Funny, but I bet at least a dozen Primates read this with one hand under the desk.

Our school had showers, but I don't recall ever seeing a person use them.

Showers were a mandatory part of our gym class from 7th grade through high school. That was back in the day when there was (occasional) vigorous exercise, and we also had a swimming pool. And the YMCA had just a bank of showers used by all the males of whatever age were present. Of course, as noted above, the fact that was common doesn't mean the Penn State shower scene wouldn't have raised suspicions.

I played HS baseball, and no one ever showered in the gym. We all just went home. I mean we were going home anyway, why change out of your uni at school?

Ditto for high school cross-country. And in the spring I played golf, and usually we didn't even go back to school after practices or matches. We were "required" to take showers after P.E. in junior high, but that basically consisted of putting a towel around your waist, walking into the shower area, and walking directly back out.

I've read Rickey was named for Ricky Nelson, not Branch Rickey, right? Nelson is his middle name.

Henderson was a travelin' man who made a lot of stops all over the world.

If there was a Primey for "Threads you absolutely, positively must read from the top down, rather than bottom up" -- this one would win....

I think it depends on when your gym period is. In junior high, our gym period was immediately after lunch (not good timing) and most of us (occasionally) showered before going back to class. In high school, it was last period, practice (if you were on a team) went long and everyone just went home. As stated above, if you're just going home, why shower? But if you're going back to class, it's not a bad idea.

And, along with everyone else, it was always a group. Adults may be around and maybe infrequently showering, but no kid was ever alone with an adult in the shower.

But if you're going back to class, it's not a bad idea.

I don't know, but we all did it. Even with gym in the morning, we just got dressed and went back to class.

The logistics alone made showering impractical. There were no towels or supplies provided, so you'd have to schlep your own towel, soap, shampoo. And then, what do yo do with all the wet towels afterwards? Really don't want to leave them in your locker all day.

I think a lot of us who favor "best record" wins fail to acknowledge that there isn't a whole lot of difference between a 99-63 team and a 97-65 team.

And most of the time, the top teams are tightly bunched at the top of the standings. Over the past decade, only three teams have led MLB in wins by more than three: The 2004 Cardinals, the 2009 Yankees, and the 2011 Phillies.

The whole nonsense about communal showers being common or uncommon is meaningless. We had them at school at the Y and in the military. Doesn't matter. Rule number one is key your eyes to yourself (not to mention your hands). Sanduskey was an old guy naked wrestling (and then some) with pre-teen boys. No where is this or has this been acceptable.

Rule number one is key your eyes to yourself

That's just silly. How else am I supposed to keep up to speed on all the new showering techniques?

That's just silly. How else am I supposed to keep up to speed on all the new showering techniques?

That's what the internet is for -- as I constantly have to remind my boss whenever he shows up at my desk unannounced.

[Stan Javier] may be the best outfielder in the history of baseball who was never a regular.

The premise is not literally true. Javier qualified for the batting title in 1994, 95 and 97. He played in 130+ games in five seasons. In 1994 he was the A's everyday CF, the starter there in 97 of their 114 games that year. Again in 1995 Javier started 111 of the team's 144 games in the OF (CF/LF).

You'd have to have an extreme definition of "regular" to say that Stan Javier was never one in his career.

In 1994 he was the A's everyday CF, the starter there in 97 of their 114 games that year. Again in 1995 Javier started 111 of the team's 144 games in the OF (CF/LF).

Eh, we all get thrown off by the strike years. Outside of that ... Javier did indeed qualify for the batting title twice ... with 504 and 510 PAs. One of those was 95 and you could add 94 when he would have hit 600+ but, like I said, we often forget that the totals in those years will be low.

Given 502 PA is a pretty low threshold for "qualified", requiring only about 2/3 of a season, I wouldn't hold that strict a guideline for a statement like the one James made, especially since Javier barely cleared it. (The strike year objections, especially 94, are legit.)

I'm having a little bit of a hard time buying this

It's the binomial distribution if you want to go searching further. There's an excel function =binomdist if you want to play around with it.

Remove baseball and make it coin flipping and assume that it's a fair coin tossed in a fair way (50% probability of heads on every flip).

You are going to toss this coin 162 times. You expect to get 81 heads. But, of course, you usually won't get exactly 81 heads -- that's the randomness. About 2.5% of the time, you will toss 68 or fewer heads; about 2.5% of the time you will toss 94 or more heads. The "95% confidence interval" is the bit in-between. About 2/3 of the outcomes (assuming you had an infinite number of sets of 162 flips) will be within one standard deviation which is about 6.5 heads, so 2/3 of the time our 500 team should finish with roughly 75-87 wins.

It gets more complicated in trying to determine how likely it is that one set of flips (with say a 55% chance of being heads) will be beaten by a set of flips from a 50% coin. That requires a "joint" confidence interval but I just guesstimated. Also, the sets of flips aren't completely independent -- i.e. when the Yanks beat the Red Sox, the Red Sox lose to the Yanks. The standard deviation on the difference probably is less than 9 wins but not by much I'd guess.

Anyway, the binomial is pretty easy to figure out:

p = probability of "success" (heads, win)
n = number of trial (flips, games)

expected successes (or average over an infinite number of sets of n flips) = p*n
variance of the number of successes = p*(1-p)*n

The standard deviation (SD) is the square root of that variance and an approximate 95% confidence interval is:

p*n +/- 2*SD

If you want to do it in terms of proportions, there are related formulas or just take the SD and divide it by n.

So for p=.5 and n=162

expected = 81 wins
variance = .5*.5*162 = .25*162 = 40.8 (the unit here is technically wins-squared which is useless)
SD = 6.4 wins

A nice thing about the binomial in baseball. See the p*(1-p) part. That reaches its maximum a .5 -- i.e. .25 -- but note its value when p=.6 (or .4) ... then it's .24 which is nearly identical to .25. So for any reasonable range of "true" team winning percentages, the variance and SD are going to be essentially the same.

Now, the assumptions. The binomial distribution assumes that the probability is constant with each flip. It also assumes that the outcome of one flip has no effect on the outcome of the next flip. The first certainly does not hold (today you're facing Verlander, tomorrow you're facing Volstad or just home/road). The second may not hold (i.e. yesterday's win created momentum). But that first one isn't going to matter very much -- as long as the p of any game is in the range of about .3 to .7 (see the equal variance statement above)* and as long as the overall mean probability is p, the standard formula will provide an excellent approximation. Similarly, unless there is a strong relationship between yesterday's outcome and today's, adjusting for that lack of independence is not going to matter very much.

What does potentially matter is injuries. Let's say Miguel Cabrera probably adds a true 5 wins above an average player but that otherwise the Tigers are a true 500 team. So we expect them to win 86 games coming into the season (p=.530) and he's healthy for the first half of the year. Then he gets hurt and they have to replace him with a replacement level player. Now they've lost his 5 wins above average plus his 2 wins to get to average and are now a "true 79 win (.490 WP)" team for the second half. Now, obviously, any projection that assumed they'd be a p=.530 team for the whole season is likely to overestimate their number of wins. In replaying the season, you would simulate them as a true .51 team.

The binomial is probably a better approximation to something like OBP than team records because the independence assumption, both within a batter's PAs and between batters, is probably quite close to being true (esp if you controlled for pitcher). So a "true 350 OBP" hitter in 600 PA:

expected times on base = .35 * 600 = 210
variance = (.35)(.65)600 = 136.5
SD = 11.7

expressed in OBP terms, the 95% confidence interval is 311 to 389. That's all purely due to randomness, nothing to do with injuries, PEDs, being in the best/worst shape of his life. That's strictly God rolling dice with the universe.

This is why one season of 600 PAs is not enough to base accurate projections on. Well, if 600 PA is not enough to do accurate projections, wouldn't 162 be even less accurate?

If you didn't understand any of the previous, then think of it in those terms. You know it's a "given" in baseball analysis that last year really doesn't tell you too much about this year because of "small sample size". Well, that small sample size is 600. 162 is a lot smaller than 600. That's the point I was trying to make about election polls. 1000 respondents gets you +/- 3 percentage points. 162 respondents obviously gets you nowhere close to that level of accuracy but even 3 percentage points is still 5 wins in a 162 season.

So, alas, to say with 95% confidence that a team is truly better than a 500 team, you need about 94 wins. Now, there's no law that says you need 95% confidence. For 80% confidence, you might only need 8-9 wins.

* In terms of single games. a true 600 team vs a true 400 team is probably something like a 70% chance of victory for the true 600 team -- who would have about a 50% chance against the other top teams in the league. A true 600 team at home against a 400 team might even get to 75-80%. But even when the occasional game is greater than .7, that won't have too much impact on the variance across the whole season.

"Ken Phelps !! Ken Phelps!!

Walt's excellent and clear post in #69 helps explain my enjoyment of playoffs and title games, and my distrust of metrics that attempt to state with confidence that a given team is superior over a regular season in most sports. Unless you get to the point of the '72 Lakers or the '96 Bulls – indeed, the NBA seems to be the only major sport where the regular season is truly "long enough" to produce such teams semi-regularly – even a very long regular season is not long enough to produce a single definitively superior team. (Well, maybe the '27 Yankees, but as noted, baseball produces such teams very, very rarely.)

So my philosophy is, accept that. Live with it, love it. Stop feeling betrayed when an 88-win team beats a 95-win team in a short series to win a pennant. It's just a game, after all; they play them for the fun of seeing who will win.

This also helps explain my bewilderment at people who tell me that the current BCS system is ideal because it clearly identifies the two strongest college football teams, as if two given 12-0 and 11-1 teams from a pack of ten or twelve 12-0, 11-1, and 10-2 teams have miraculously distinguished themselves thanks to the power of mathematical analysis. I'm for more meaningful football games! If they are not definitive either (no single game can be), they become meaningful by virtue of having meaning assigned to them: i.e., this game is for the right to play in a national semifinal, rather than the right to have your name inscribed on the Meineke Car Care Trophy.

I played on a couple high school teams, and of course took gym every year. Our school had showers, but I don't recall ever seeing a person use them.

Man, am I glad I didn't go to your school, unless all you did in gym was sit around and analyze baseball statistics. What's the point in having showers if nobody uses them?

I played HS baseball, and no one ever showered in the gym. We all just went home. I mean we were going home anyway, why change out of your uni at school?

You wore your uniforms home? What about after an away game? Did the team bus just drop you off at home as if it were the end of the school day? Or did your transportation to games consist of 25 players, 25 cars?

And if these showers weren't used after practice, after games, or after gym classes, then who did use them? The faculty skank? The resident Sanduskys? Anyone else?

And if these showers weren't used after practice, after games, or after gym classes, then who did use them? The faculty skank? The resident Sanduskys? Anyone else?

Well, I do know of at least two people who lost their virginity in the gym shower. So, they had some use.


And, yeah, where I lived it was 25 players, 25 cars (or, rather, 11 players, 10 cars, as we only had 11 players and two were brothers). Actually, make it 9 cars as I lived a block from the field.

I suspect some generation gap here. I'm 54; I know Andy is d'un certain âge :) There were showers in my high-school gym in the early 1970s, and we showered after gym, after cross-country runs. And as I've noted before, there was not the slightest chance in hell that any teacher or coach would ever shower along with us. There was no need, anyway; those guys notoriously did nothing but stand around looking at clipboards. Perhaps there was some earlier generation where men bathed with boys, maybe in the time of Cato the Elder, but it wasn't in the United States in the mid-20th-century. That's the main point here. God knows what Bill James is remembering.

That's all purely due to randomness, nothing to do with injuries, PEDs, being in the best/worst shape of his life. That's strictly God rolling dice with the universe.

If He's rolling them independently, which He likely isn't. However, I'm not sure if the dependence on outcomes in baseball should be negative or positive.

Case for positive dependence (which means actual variance is actually higher than you've calculated): You tend to see clusters of lineups in a season, teams play series against other teams in close temporal sequence, hitters typically have at bats against the same starting pitcher / pitchers are seeing the same batters multiple times through the lineup.

Case for negative dependence (which means the actual variance is lower than you've calculated): Team strategy in adjusting to hot / cold streaks, teams swapping out players for better players, teams trying to improve during the season. The negative dependence would force the observed winning percentage to cluster more tightly around the true ability of the team.

And of course all of this assumes that a team has constant ability over the course of the season, which is likely to be not true (which would mean the variance is even bigger than you would expect). In other words, trying to use the data from baseball for anything but prediction is hard, e.g. trying to estimate the true ability of a team or player. It's much easier (although not necessarily easy) to simply try to predict what they'll do next year than estimating their true ability in a given season, because in some sense you don't care what their true ability is if you're interested in prediction (and you can readily evaluate the performance of your model).

bdc

i have worked to be restrained because i want to think that james has some basis for this contention but as someone who did manual labor from age 5 on up including working on threshing crews as a lad of 12-16 i don't have a d8mn clue what the h8ll he is using as reference

i lived in the midwest (and still do). group showering is and has been a very foreign concept save perhaps in the depression or lice outbreak (or similar)

It's still somewhat common at community pools and YMCAs, probably those with older showering facilities. It happens primarily by accident, as a young boy enters the communal facility when an older man is there, or vice versa. These are places with wide-open bathrooms, with other pool users and staff members regularly walking through the facility. Frequently, one or more of the individuals is in full bathing suit.

Yeah, this. I was on the swim team all through school, and the coach would sometimes shower in the same communal shower that we used after practice. No big deal. Swimming has, as you would expect, the sort of culture where nobody really thinks much about being half-naked around lots of other people - it's just the way things work.

It's the specific circumstances (after hours, locked, nobody else there, etc.) that make Sandusky's shower hinky, not the mere fact that he was showering with a kid.

I suspect some generation gap here. I'm 54; I know Andy is d'un certain âge :) There were showers in my high-school gym in the early 1970s, and we showered after gym, after cross-country runs. And as I've noted before, there was not the slightest chance in hell that any teacher or coach would ever shower along with us. There was no need, anyway; those guys notoriously did nothing but stand around looking at clipboards.

Just to be clear, that was the case in my school, too. Their biggest form of physical exertion was to shout "200 BURPEES, HERSH!" at the top of their lungs, which mostly seemed to be an exercise of the veins in their necks.

You wore your uniforms home? What about after an away game? Did the team bus just drop you off at home as if it were the end of the school day? Or did your transportation to games consist of 25 players, 25 cars?

The bus dropped us off at the HS, where we either had our cars parked, or someone came to pick us up. We had to wash our own unis, so no reason not to wear them home.

I was driving a '79 Chevy Nova, so wasn't concerned about getting sweat on my lovely vinyl seats.

And if these showers weren't used after practice, after games, or after gym classes, then who did use them? The faculty skank? The resident Sanduskys? Anyone else?

Don't ask me, I didn't put them there. I went to HS in the mid-90's and as far as I know this was universal. Every gym had a locker room and showers, no one knew anyone who had ever used them - not after practice, definitely not after games, and certainly not after gym class. I'd guess the ones at my school didn't even work. Swim team was probably different, but they swam at the pool, not at school.

Yeah, the only use the showers got in PE classes in my middle or high school was after swimming, where people could wash the chlorine off themselves without actually undressing. (I believe many of the athletes actually did use the showers regularly after practice.) I think it's the kind of thing where a culture gets established and either everybody showers after gym class, or nobody does. Our school was definitely the latter - at that age, we were all too shy and/or worried about taunting to undress completely. And the sweat was really never a problem; that's what deodorant and a change of clothes are for, right? I don't remember ever detecting B.O. from anybody, which in retrospect is fairly remarkable.

There was no need, anyway; those guys notoriously did nothing but stand around looking at clipboards.

Lucky. My high school gym teachers were either
A) the current captain of a World Championship lacrosse team
or
B) Insane long-distance runners

Every class started with a few miles of running. After that they more or less ignored us. The gym was divided in two and half of us played floor hockey the other half basketball. Come to think of it, I very rarely saw the teacher after the run.

I suspect some generation gap here.

I suspect the same. Never in my life would I have thought that trends in group showering among adolescent males would be interesting...but the fact that the experiences related in this thread seem to suggest a generational shift in (to use the dreaded term) cultural norms, I find at least mildly interesting. (Perhaps a 0.5 out of 10 on the fascination scale)

[69] Thanks for the explanation, Walt. I was a math major in college, but I skipped the entire statistics side of the curriculum (Calculus rules! Stats droolz!) Anyway, I suspect what's not sitting right are my own assumptions -- mainly that I'm inferring a "true talent level" from results, which as you've pointed out, is flawed.

[81] This was my experience with high school as well.

Also, unless the school is providing towel service, nobody wants middle/high school students dealing with their own damp towels. I'm picturing rows of lockers encased in mildew.

Also, re: showers, nudity, as I grew older, I was shocked to find out that semi-casual nudity wasn't the norm among families. Its not like we would hang out with our bits out but neither did anybody really worry about walking naked from the shower to the bedroom after drying off.

Yeah, the shower issue definitely has a generational aspect to it. I graduated from (a small-town) high school in 1973, and both in junior high and in high school, you were expected to shower after gym class. Many kids had vinyl "gym bags" (with the school mascot/logo) that you carried around with you, or just a bag that you chucked into your locker until the end of the day.

And the baseball team generally showered together after home games and then went our separate ways. Probably at least half of the guys walked home afterwards, but the school washed your uni, so it wouldn't make a huge amount of sense to walk home (or be driven home) still wearing it.

I believe that the coaches would also often take showers along with the team, because between hitting fungos before the game and getting worked up like raving lunatics during the game, by the end they were pretty sweaty also. But nobody thought much about it.

Also, re: showers, nudity, as I grew older, I was shocked to find out that semi-casual nudity wasn't the norm among families. Its not like we would hang out with our bits out but neither did anybody really worry about walking naked from the shower to the bedroom after drying off.

We didn't all grow up on communes, you filthy hippie.

No showers at my tiny high school, but there were definitely showers in junior high (late 70's). We were supposed to shower after gym class, and some did but others avoided it (like me).

Never, ever saw a teacher in there while we were in there. That would've been weird.

Also, re: showers, nudity, as I grew older, I was shocked to find out that semi-casual nudity wasn't the norm among families. Its not like we would hang out with our bits out but neither did anybody really worry about walking naked from the shower to the bedroom after drying off.

Definitely haven't seen that before. Those who have to walk from shower to bedroom (meaning: the kids, since we have a master bath w/shower) either get dressed in the bathroom prior to exit or wrap up in a towel. Was the same when I was growing up.

Also, re: showers, nudity, as I grew older, I was shocked to find out that semi-casual nudity wasn't the norm among families. Its not like we would hang out with our bits out but neither did anybody really worry about walking naked from the shower to the bedroom after drying off.

More fascinating stuff! In that this is something I imagine rarely gets talked about outside of a family. We're really narrowing down here, from school ethnography to family ethnography.

If it's any consolation smileyy my family sounds the same as yours.

Born in '73, showered communally in school (where we had no pool/swimming), at the Y, etc..., felt weird about it as I grew up in a family where you would get dressed or wear a towel post showering. Didn't realize that wasn't the way everyone lived 'til my mid-20s. Don't remember where I stored the towel, think it was my locker in a plastic grocery bag.

Interesting discussion. At my school career (Kansas City in the '90s), middle schoolers and high schoolers showered after gym class. Towels were ratty white things provided by the school that smelled strongly of chlorine, and you tossed them in a hamper after you were finished. Worrying about how you would deal with being naked around a group of guys was a fairly standard anxiety in 6th or 7th grade, but died down as people figured out there was absolutely nothing sexual about it. Teachers were not present, and it would have been extremely weird if they were.

The only time I ever showered around adults was after bike rides like the MS 150, when the destination school would often open up a locker room. As there were 20-30 people present at any given time, this was more akin to showering in the proximity of adults than showering with them, and could not possibly be mistaken for anything else.

Born in '67. Grew up in the Midwest. Community showers at the pool and gym would not infrequently have naked adults and children. Thought nothing of it even as the Village People's song still popular 35 years later made glamorous the sexual highjinx of adolescent boys in public gymnasiums.

Heck, I'm naked right now!

However, I'm getting some strange looks here in the office so perhaps I'd better put my clothes back on...

Come to think of it, an ex-gf of mine who grew up in NW Arkansas had a friend whose stepdad was Benjamin Spock, of all people. I gather he thought nothing of walking around in the buff after a shower, or perhaps at any other time, including during the stepdaughter's slumber parties. That would've been ... the mid-'70s, maybe? She's 5 years younger than me, & I was born in '59.

Maybe that's who Bill James used to shower with in the days of yore; Spock was from New England, it seems to me, but if he was living in the Fayetteville area, that's not too terribly far from Kansas.

but if he was living in the Fayetteville area, that's not too terribly far from Kansas.

It is, however, a long way to walk naked.

Perhaps he bicycled.

Showers in a school were always just a weird thing. I went to Jr high and high school in the early to mid 90's and I can't recall a single person taking a shower after gym class outside of a few times in the beginning of the school year in 6th grade when they tried to make kids take showers. One, who had the time, and two, who was getting so sweaty and dirty from 30 minutes of light activity that they needed to take a shower? It simply didn't happen.

Also, re: showers, nudity, as I grew older, I was shocked to find out that semi-casual nudity wasn't the norm among families. Its not like we would hang out with our bits out but neither did anybody really worry about walking naked from the shower to the bedroom after drying off.

I see no reason why anyone besides your wife or girlfriend, and your doctor ever needs to see you naked.

Not in my case, at least.