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BASEBALL STATISTICS PART 1

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OUT WITH THE OLD, IN WITH THE NUCLEUS

I got a little off my notes in writing this...
I got a little off my notes in writing this...

Baseball was my first true love when it comes to sports.  Part of that was growing up in the Northeast, where baseball was king, part of it is having many great memories playing it as a young boy.  Baseball is much more of a thinking man's game than any of the other American "big four".  That's no disrespect to football, which has probably (shamefully) replaced baseball as our national pastime.  Football has a lot more strategy in it than most people realize, but in terms of pure spectating, baseball requires a different mentality to watch.

Baseball is a game of patience, and a game of cunning.  If you can't enjoy the pitcher - batter matchup and all the mental battle that is going on there, you'll not enjoy the game.  In addition, baseball is just a perfect way to spend a spring/summer day, or to just have on as you're relaxing on a Sunday afternoon.  Baseball also ties us to our childhoods and our elders in a way football doesn't.  Watch a game live if you can, you'll soon have a discussion about who had the better slider between two players who haven't played in 30+ years.  Football has a history, but football fans don't care about it.

It's hardly surprising that baseball fans have come up all manners of nonsense to measure the players of the game.  A lot of the people who come up with these measurements are very smart people.  There's two types of "bad" statistics in my mind.  The first is the kind that even the statistically illiterate can understand are badVT when they hear them, the kind of statistic I will refer to as the "mindless media tid-bit" (MMTB).  The MMTB is something like "Swanson is batting 0.160 when there are RISP and two outs" or "Batters against Ferguson are .360 when there is a man on third and a full count".  Virtually anyone can understand that the sample size of those situations is probably small and therefore meaningless.  MMTB statistics are also things like "Vandy hasn't won a three games in a row against the Volunteers since 19xx".  Again, something that really doesn't mean jack shit, because the chances to do that are fairly low.

The other kind of statistic that hacks me off are harder to identify.  These are the ones that are made by smart people to identify very specific skills of a player and are not just strange facts.  Many sabermetrics fall into this category, and I'd argue often are overthinking things.  Statistics "purists" will argue that everything is calculable and "this is all we have" or "you just don't understand the math" and generally start to sound like a Hollywood scientist caricature.  I'd argue there is indeed a big "intangible" element to baseball that cannot be measured.  It is bigger than sabermatricians admit to, and smaller than the statistically-naïve want to believe.

The other issue with many sabermetrics is one of misuse.  If I hear one more layperson start talking about the batters' BABIP to me one month into the season, I'm going to throw him off the back of the stadium.  Another common one is to start waxing prophetic over the WAR for a RP in the middle of a meltdown.  WAR (Wins above replacement) isn't even a standardized statistic, which makes it all the more laughable and worthless.  It also doesn't cover certain oh, you know, minor things, like HOW THE DAMNED TEAM ALIGNS THEIR DEFENSE.

That said, throughout the season, I will visit one particular crazy baseball statistic, and either praise or deride it.  Make your suggestions below for the next target!

For now, however, I'd like to address the statement made by AoG baseball guy VU04.  In his preview, he stated, "anyone shouting "SMALL SAMPLE SIZE!!!" when I bemoan the slump of a guy hitting .125 who has made no hard contact will be immediately taken outside and shot."  This is an interesting comment on many levels.  One of the bigger issues here is why would shouting "small sample size!" be valid for some crazy metrics, but not for batting average?

Well, let's start with a very simple example.  Let us consider a range of ballplayers, who have AVG ranging from .200 to .450.  Yes, .450, this is college where that happens often.  If you're any sort of baseball fan, you know it is a game of streaks and slumps.  A batter could be a .350 batter, but go say .425 one week and then .275 the next.  Let us refer to a batter's consistency as the standard deviation he has about his "true" average on a week-to-week basis.

Yes, ladies and germs, I'm going to go with the good old normal distribution to describe a batter's performance week-to-week over the course of the season.  I've not bothered actually determining the "true" distribution, but it's probably close enough to that.  Besides, I'm more hung over than Your Uncle Mike probably was when someone stole Howard's Rock from Death Valley the lesser.

So, what kind of result is it that a batter with a given average and consistency would have a week in which they slump and bat a buck and a quarter?  The answer turns out to be something even a freshman psych major could answer for you.  It's simply a matter of finding the residual about the mean and dividing by the standard deviation.  Some of you may know this as a "z-score", whereas others (like me) may refer to this as "significance". By some simple knowledge of a Gaussian/Normal/Bell curve, you can already have a good idea of what significance means.

So with these values in hand, I then computed the CDF (cumulative distribution function) up to this "measurement".  That is, what is the probability of "measuring" (playing) a week of 0.125 ball (or worse) for a given average and consistency?  The results are below:

Notes

The results are not very shocking!  Consistency is of course the biggest factor here, but even the most inconsistent players will have a low chance of batting that badly if they have a good average overall.  Keep in mind, again, we're talking college baseball, where .300 isn't what it is in MLB.

Even so, let's take something fairly reasonable - a .325 batter who has a consistency of 0.125.  That is, 68% of their weeks are between .200 and .450.  It is roughly a 1.6 sigma result for him to bat as badly as 0.125, meaning that ~5.48% of his weeks will be at that or worse.  Conversely, it also means that ~5.48% of his weeks will be .325 + .125*1.6 = .525.  Sounds insane, right?

So when our esteemed colleague complains about that .125 slump, keep this in mind - it's generally for a good reason.  It doesn't necessarily mean the player is bad, but it is something to be concerned about.  It may be an indicator of an inconsistent player.

The astute reader may be thinking now, "well, wait a minute, just how inconsistent is 0.100 or .200?"  A good question!  According to VU04, Vandy had about 3.6 ABs a game last season.  Once conference play starts, we'll be having 6 games a week, translating to about 21 ABs a week.  So each hit in a given week is equivalent to about 0.050.  It is a trap here to think that the more consistent batter is batting two more hits in the week, but that is incorrect.  That would be the difference in a given week's performance.  It would be more appropriate to say that a batter with a consistency of 0.100 has 68% of his weeks fluctuating +/- two hits off his average.  That is, a batter who is hitting .333 would be hitting on AVERAGE 7 hits a week.  If his consistency was .100, that means 68% of his weeks would vary 2 hits off of that, which is 5 - 9.

Finally, it's important to note that consistencies on the level of .200 actually don't make a lot of sense because it ultimately means you need negative hit weeks to make up for crazy high hit weeks.  That is why I argue earlier that consistency of .125 is probably "just right" (maybe even a little mean).  So we should focus on that range when talking about players.

Word informs me that I am over 1,400 words and I've not said much of anything.  So I'll cut volume one off here, and encourage y'all to ask questions below.  Next week, I'll address a new metric.

EXCELSIOR!

Disclaimer: VTPhD is a pompous blowhard who always thinks he's right.  Generally, his arguments are crap, and should be taken about as seriously as you take that car alarm going off 8am on a Sunday.  His critics enjoy making fun of the PhD in his username under some hilarious attempt to be original and make themselves feel S-M-R-T all at the same time.  If you can find him the Jade Monkey before midnight, he may allow VU04 a week off during baseball season.