To put that standard deviation into context - does the GPA data look remotely normal? It's an easy assumption that it would be, but in practice I have found the central limit theorem to be misleading in the extreme! Then, perhaps at the end of the month, we can compute the significance of his current form.

(If you don't know how to test for normality I'd be happy to advise.)

Carlos says he isn't hurt. According to ESPN's news and notes for the Jays Carlos says his knee is actually getting better because, as he states "It only bothers me when I have to run and when you don't make contact you don't have to run."

At least he's maintaining a good sense of humour about it.

Robert: Great stuff! Thanks for doing the legwork on this. It's quite interesting.

Andrew K: Here's something that has been rattling around in my brain for awhile, and I thought I'd get your take on it as you're probably better versed in statistics than I am.

It seems to me that it would make sense to model these things as Poisson. That is, treat each plate appearance as a distinct period, and the probability of an event happening (getting on base) during that period is simply the player's OBP (or some expectation of OBP or whatever). Seems to me that this would be easy enough to test the accuracy of, since all the moments are functions of one parameter.

Am I completely out in left field, or does this make sense?

Andrew K,

I'd be happy for you to advise.

The distribution does look fairly normal to me. Here is the distribution of GPA according to STDEV below/above the median:

greater than +2.0: 2 months
+1.0 to +2.0: 7 months
+0.5 to +1.0: 4 months
zero to +0.5: 9 months
median: 1 month
-0.5 to zero: 10 months
-1.0 to -0.5: 7 months
-2.0 to -1.0: 4 months
less than -2.0: 1 month

31 of 45 months (69%) are less than 1 standard deviation from the median. 42 of 45 (93%) are less than 2 standard deviations away from the median. The simple average (unweighted by PA) was higher than the median (.321 GPA versus .316 GPA): 24 of 45 months were below the simple average.

Mike,

Re Poisson distribution. I see what you mean, but (off the top of my head) it's false. Poisson distributions arise from Poisson processes which are specifically continuous time in which the chance of an event occuring in a time interval is proportion to the interval. An important detail is that this is only true as the interval tends to zero. The problem with treating each PA as an interval is that you really can only get on base once per PA(!) - and a Poisson process has a small probability of each event happening more than once in any positive interval.

[Note that for small incidence rates the Poission distribution approximates the binomial anyway - this is intuitive because the chance of two events per unit becomes impossibly small. But for probabilities like OBP or AVG, that's too high.]

Getting on base is a classic binomial distribution because there are finitely many chances for something to happen, so long as we believe that the event (getting a hit, on base, a home run, whatever) happens independently of others and with a fixed probability. I have to admit that this scenario is not too great either (which is a good motiviation for analysing various splits). It would be interesting to model slumps as a Markov chain, where the longer the slump the (slightly) smaller chance of getting a hit (because of nerves or whatever). But I doubt there is enough information to get interesting results, and indeed whether the results are all that interesting.

Another possible model would be to model balls, strikes-without-hits, hbp, hits, etc. i.e. each event is one *pitch*. But this is so horribly confounded by the pitcher's characteristics. On the other hand it might give interesting results about various hitters. Bonds - and probably Delgado pre-slump - would look a whole lot better, and patience at the plate would probably be rewarded. (Why don't we quote average number of pitches faces per PA, by the way? As a pure measure of patience don't we think this would be a good stat?)

Enough rambling, I'm supposed to be at work!

"(Why don't we quote average number of pitches faces per PA, by the way? As a pure measure of patience don't we think this would be a good stat?)"

It's a very good stat. But it isn't close to a pure measure of patience. Players who are good at fouling off two-strike pitches do well, and guys who get hit by a lot of pitches tend to do worse than they ought to.

I think percentage of pitches taken on non two strike counts is better, but we don't have that data unless we have access to pitch-by-pitch logs.

Interesting stuff. Thanks. Since you're at work, I won't ask you about the Weibull or Gamma distributions. ;)

Robert,

That looks pretty normal. I used to know a web page which did very handy Shapiro-Wilks tests for normality (you entered the data on a form and it gave you back the p-value) but I can't find it now. Anyway, the discretized data you listed makes it look close enough. (I'm actually quite surprised at this.)

There's no doubt, then, that 2.5 standard deviations below mean (his present month) is very low. But we should bear in mind that this is off about half a month. Roughly speaking the standard deviation of a sample half as big should be about sqrt(2) times bigger, so the true significance is the tail probability after 2.5/sqrt(2)=1.76. This is somewhere around 4%. We do have to be a bit careful about what that really means though.

Robert,

Point taken about pitches per PA. Pitches per out perhaps? But as you say, we don't have access to the data. I'd love to see JPs data... but it would be guarded as closely as a trade secret.

I really do need to get back to work. I won't be reading the box for a day or so because I want to watch the red sox game, it's too late at night in the UK, so I will watch it tomorrow. and I don't want to know the score - so I won't come here until after I've caught up.

(By the way, that reminds me of last year's ALCS. I couldn't watch game 7 live because of the time of day, so I was saving it until the next afternoon. I carefully avoided any web site which might have the result. I even avoided reading a newspaper just in case the UK press decided that the ALCS was important enough to report on. I opened up the mlb.tv website very carefully, not allowing myself to see any parts of the page with the result on. I was just set to start watching when my inbox chimed so I looked to see what it was and lo and behold an email from mlb.com entitled "Yankees win!". Bugger.)

Most of the math sails over my head, but I trust you guys to enlighten me with your conclusions. I agree that pitch-by-pitch logs could teach everyone a great deal, but I'd want more than just balls and strikes recorded; location is just as important. To me, "patience" is best demonstrated by taking strike one (or strike two) when they are not in the optimum hitting zone. In other words, give the pitcher the high-and-tight strike and concede the one knee-high on the outside corner. Foul those off as long as possible with two strikes, and wait for him to make a mistake: down-and-in, belt-high on the outer half, or the always-yummy cookie.

From a purely observational standpoint, I've said it before -- Carlos appears to be trying to blast his way out of this funk, when a couple of timely opposite-field singles or doubles would do the trick. Maybe tonight, Pedro will hang a curveball and we'll see some fireworks.

I've seen Carlos for several years when he's at his best and when he's at his worst. Right now he's as bad as he's ever been and that includes that period of time when the league adjusted to him as a rookie.

I think the explanation, health concerns aside, is pretty simple. Right now Delgado is trying to pull almost every single ball. He gets into these funks almost every year where he has a spell in which he's pressing or forgets himself and they tend to last quite a while. It's just at the beginning of the season for once.

Facing Ainsworth the other day he worked a 3-1 count and got a fairly hittable outside fastball, a pitch that when he's going good he would have deposited deep into the first deck somewhere between left and centerfield. Instead he hit a weak grounder to second, though with the shift on it was the shortstop who fielded it.

Delgado has as much as anyone in the game as his four homer game last season demonstrated. He doesn't need to pull the ball or develop a loop in his swing as he has now...he can clear any part of any park. I think he'll be fine but I also think he should be a little too experienced and talented to fall into bad habits for this long of a stretch. Maybe his having a good spring training was a bad omen afterall.

Delgado has as much as anyone

that should say as much power as

http://redrival.com/rlb/links.html
Because of time difference, I'm always late to any thread, but I hope the post below doesn't go unnoticed.

Coach said: "I agree that pitch-by-pitch logs could teach everyone a great deal, but I'd want more than just balls and strikes recorded; location is just as important. To me, "patience" is best demonstrated by taking strike one (or strike two) when they are not in the optimum hitting zone."

I don't know to what degree my Russian League data is relevant as far as major league baseball is concerned, but what I see is that LOCATION and PITCH TYPE combined is the MOST IMPORTANT thing.

What it means is that you just can't treat every PA equal without knowlegde of pitch/location distribution.

IMO, using the binomial distribution to measure confidence intervals for, say, a hitter's BA based just on the number of ABs, while ignoring what happened whithin the at-bats, is somewhat problematic.

Each and every PA is not an ideally constructed test of a hitter's ability. It is not something like measuring your raw hitting skills against a pitching machine delivering balls with the same location/movement/velocity in your optimum zone.

There're at-bats when the batter sees only one pitch in his ZONE or none at all, especially with no one on base when the batter wants to take the first strike most of the time regardless of what a cookie it is. At the same time, there're at-bats when the pitcher throws several good pitches to hit. The probability of the hitter's success in the latter case is bigger to a certain degree.

For some reason, most of the Russian hitters have developed strong tendencies in their approach at the plate. The most typical hitter's profile being: high stance, bat held shoulder high, looking for stuff high and high and above the strike zone, taking anything low until two strikes; the center of the hitter's strike zone is thus above the belt.
Some hitters of that profile can't even hit the standard 'down the middle' pitch without bending their knees.

You can check a couple of 100k zip arhives with GIFS and a couple of articles on advance scouting (COMN and download Archives #1 & #2) - right now that's all I have available online. Of special interest are 'full.gif'and 'final.gif' images. Notice all the takes (green-colored) on low balls, that RH hitter Valery Platonov made diring the 2003 Russian Series.

If anybody is interested, I will demonstrate some more complete and up-to-date graphics.

Sergei, that was an interesting setup you show there. I didn't understand all of the graphs, but from what I see you've got some quite sophisticated tools. Nicely done.

What's most interesting is that unlike the Russian hitters you are talking about, in the majors an evolution has taken place over the last 30 years to the point where almost all hitters at the big-league level, even at the professional level altogether (majors and minors) are low-ball hitters. That doesn't mean that want the pitch at the knees; but the thigh-high pitch has essentially becomethe pitch of choice.

Does the strike zone that is called in the Russian league extend above the belt? In MLB, of course, nothing above the belt of the uniform pants is ever called a strike despite the rule-book strike zone. I'm wondering if a different strike zone causes this change in style. The style of hitting you describe (upright, bat held at/above the shoulders) has almost died out in the majors, as hitters have developed various knee-bends and crouches to deal with pitchers who can keep the ball on the knees.

It seems that in Russia pitching the ball a the knees is going to be the royal road to success. Looking at Platonov's chart, he didn't even do anything with the down-and-in stuff that good hitters here eat for lunch, but it looks like he did very well up-and-in, where hitters over here are taught to be very careful of.

http://www.geocities.com/s_borisov/profiles/nizov_vsrhp_ahead_behind.gif
Craig,

Sergei, that was an interesting setup you show there. I didn't understand all of the graphs, but from what I see you've got some quite sophisticated tools. Nicely done.

To help you read the graphs, here are the basics:

Pitch types:

circles designate fastballs of different variety,
upward-lookind triangles go for curves,
triangles that look sideways are for sliders and cutters,
squares - forkballs,
rhombus is for change-ups, knucklers, etc.

Pitch outcomes:

Red - hits,
Black - outs (non-hits),
Blue - foul balls,
White - balls,
Green - called strikes,
Yellow - swinging strikes.

I borrowed the designations from renowned Japanese scouting company/sports software maker Asobous, that published complete live pitch-by-pitch accounts of Pro Yakyu games on internet with their elegant Java applet since at least 1997. Currently the firm is known as Datastadium (datastadium.co.jp) and supplies baseball data to internet portals, such as Yahoo Japan, who present it in text/html format.

I've come up with a system for pitch locations. They are coded 1-9 as follows (from batter's point of view):

7 8 9
4 5 6
1 2 3

For example, 7 - high inside corner for right-handed hitter.

Balls are notified with additional symbols: ^ - high (7^ above the high inside corner), ~ - low (3~ - lower then low outside corner), < - left (4<, missed inside), > - outside (6> - missed outside), = - symbol for 7=, 9=, 1=, 3= pitches that miss the strike zone by both height and width.

What's most interesting is that unlike the Russian hitters you are talking about, in the majors an evolution has taken place over the last 30 years to the point where almost all hitters ... are low-ball hitters.

It sure has something to do with the low zone thay had in the majors until a few years ago, and I very much liked the move to get back to the rule book strike zone (the Japanese leagues followed the MLB iniative as well).

Look, I very rarely see mlb baseball on video, as I follow baseball exclusively via the web (video feeds currently not an option). The 2003 World Series being televised by Russian TV was a great thing. And from what I've seen, this is not the same type of baseball it was 10-15 years ago.

Does the strike zone that is called in the Russian league extend above the belt? ... I'm wondering if a different strike zone causes this change in style.

RL strike zone? Not only above the belt, the upper edge recently went somethere to the armpit level. Add the fact that we use wooden bats since the 2000 season and you see the picture - our hitters face not a so easy task.
The huge strikezone might compensate for the mediocre pitching we have - only two regular pitchers throw consistenly in high 80s, but I think in general it does a disservice for the hitters, who seem to hit shoulder high pitches better than those just below the belt.

It seems that in Russia pitching the ball a the knees is going to be the royal road to success.
It sure does, but for no apparent reason, our hurlers are still up in the zone most of time. Platonov was a great example (full.gif) - pichers started him off great (66% fastballs with less than 2 strikes, he took almost everything low), but mostly threw him high breaking balls with two strikes. The Platonov's graphics actully refer to 2002 instead of 2003.

To further illustrate, I've put up a more recent graph, that shows our perennial batting title contender Alexandr Nizov (RH hitter) against RHP last season (COMN). The bigger box on the left shows distribution of fastballs Nizov saw from righty pitchers.

Looking at Platonov's chart, he didn't even do anything with the down-and-in stuff that good hitters here eat for lunch, but it looks like he did very well up-and-in, where hitters over here are taught to be very careful of.The inside stuff he hit well in 2002 was mainly breaking balls. Last year he tried to change his approach and look for a fastball up and inside from time to time. He even hit a homer in a crucial game against archrival CSK VVS (Platonov plays for Tornado) off a 7^ fastball. But despite the quick success, the shift in approach disrupted his pitch recognition in the following games.

http://redrival.com/rlb/nizov.html
It turned out that Geocities forbid hot-linking to images, so I'll add a new link to Alexandr Nizov's graphs from 2003 season (COMN).

Sergei, let me just tell you that your Russian/NPB baseball site is awesome - one of the ten or so I frequent most often.