Fives Afield
By Joe Harder - Guest Writer & Owner of the Charlottesville Meadows
12/08/2006
The Charlottesville Meadows have Jason Giambi, Barry Bonds, Frank Catalanotto, and David Ortiz on our 25 man roster, all of whom received 5 fielding ratings in the 2005 MLB card set.
Bonds and Catalanotto primarily serve as pinch hitters (Barry only had 51 plate appearances that year), but to get both Giambi and Ortiz in the batting order requires one of them to play first base.
Giambi, at 1b-5e18, is the choice over Ortiz’s 5e30. Herewith is what has happened so far this season through 39 of our 54 games with x-chart chances for these “iron glovers.”
How stratomatic uses x-chart chances
On any stratomatic pitcher’s card, you will find the following distribution of defensive x-chart results out of 108 total card chances:
| X chart distribution | ||
| # out of 108 | % of card | |
| p | 2 | 1.85% |
| c | 3 | 2.78% |
| 1b | 2 | 1.85% |
| 2b | 6 | 5.56% |
| 3b | 3 | 2.78% |
| ss | 7 | 6.48% |
| lf | 2 | 1.85% |
| cf | 3 | 2.78% |
| rf | 2 | 1.85% |
| 30 | 27.78% | |
Thirty of the 108 rolls on each pitcher’s card (more than one-fourth) are a test of his team’s defense. Shortstop and second base each have at least twice as many x-chart chances as the other positions, with seven and six respectively, doubling catcher, third base, and centerfield’s three.
The corner outfielders, first baseman, and pitcher have two chances each. The distribution of x-chart chances reinforces the importance of strength up the middle, since catcher, second base, shortstop, and center field collectively comprise almost two-thirds (63%) of the x-chart rolls, and the double play combo of second and short alone make up 43% (an even distribution of x-chart chances would result in 4/9 or 44% in the first case and only 22% in the second).
The 1% risk factor with a “5” at 1b, pitcher, left field, or right field
Let’s take a look at Jason Giambi and his 1b-5e18. A 1b(x) roll should occur about 1% of the time overall. Well, .925% of the time, precisely, since 1.85% of the rolls off the pitcher’s card are 1b(x), and half of all rolls should be off the pitcher’s card, as opposed to the batter’s.
The first question is whether or not he commits an error, independent of his abysmal range factor (but my other option, Big Papi, is even worse at 5e30).
According to the Super Advanced Fielding Chart, a first baseman with an error rating of 18 commits a one-base error if the total on three six-sided dice is 11, 12, or 14, and a two-base error with a total of 17.
By looking at the distribution of the 216 possible combinations of three dice and summing the probabilities we see that, statistically speaking, Giambi would make an error thirty two percent of the time that he is involved in an x-chart play (just under 2% of rolls off the pitcher’s card, or about 1% of all rolls.
The Super Advanced Fielding Chart also shows that forty percent of the gb-1b(x) rolls will be singles (more if a runner is being held), and sixty percent will actually be ground outs, independent of the error result (though by far most of those are groundout 3’s, with all runners advancing one base).
If I understand correctly how this works, that would mean that for the 1% or so of the time that there is a 1b-x when Giambi is in the field, the results would be as follows:
· a single plus error 12.96% of the time (32.41% times 40%)
· an error by itself 19.44% of the time (32.41% times 60%)
· a single by itself 27.04% of the time (67.59%*40%)
· an out 40.56% of the time (67.59%*60%)
Not very pretty odds, overall, so how badly has Giambi done thus far?
Giambi and Ortiz are primarily designated hitters for a reason
In thirty nine games, he has had nine ground ball x chances. Of these nine chances, four were singles (one of which had a two-base error as well), two were one-base errors, and three were groundouts. That’s just a thirty three percent out ratio compared to the 40.56% outs expected from the analysis above, so he’s performed slightly less well than expected.
Of the non-outs, a hit plus error result occurred 11.1% of the time (close to what would be expected), a single by itself 33.0% of the time (6% more than expected), and an error by itself 22.2% of the time (3% more than expected).
Amusingly, one of Giambi’s 1b(x) plays was a “rare play,” due to a 5 being the total of the three dice during the consultation of the error chart, which, coupled with a 20 split, meant that even though the Outlaws’ Travis Hafner had tripled to lead off the inning, with one out and the infield back, pinch hitter Jason Michaels lined a shot up the middle that hit the pitcher and caromed to Giambi, who held the runner at third, and tossed to the second baseman covering first for the out!
Overall, the Meadows have had one gb-1b(x) every four and a third games…is that the 1% or so of total rolls we would expect?
Digging into the data
Through thirty nine games, Meadows pitchers have faced 1522 batters. We would expect half of those rolls to come off the pitcher’s card, or 761, and 1.85% of those, or roughly 14 should be 1b-x plays. In fact, to this point the Meadows have been lucky, with only nine grounders to Giambi/Ortiz, when we would expect more than fifty percent more!
Total x-chart chances make up about 28% of the rolls off a pitcher’s card, so should run at 14% of overall rolls. Dividing the 1522 batters faced by 39 games gives (amazingly?) 39 batters faced per game on average. Therefore, in the twenty four games played on my computer (rather than on an opponent’s with me inputting results manually), we can assume there have been 937 batters faced (24 games * 39 batters). If half of those results come off the pitcher’s card (468.5), we would expect 130 x-chart chances (27.78% total x-chart rolls on the pitcher’s card * 468.5). Actually, they have occurred 141 times, almost 10 percent more than expected (more of a test of my bad defense!), and the Meadows have converted only 63 percent into outs.
Of these 141 x-chart chances, here are the expected and actual distributions:
| of 141 chances | ||
| expected | actual | |
| p | 9 | 9 |
| c | 14 | 18 |
| 1b | 9 | 5 |
| 2b | 28 | 26 |
| 3b | 14 | 11 |
| ss | 33 | 34 |
| lf | 9 | 16 |
| cf | 14 | 16 |
| rf | 9 | 6 |
| 141 | 141 | |
Shortstop, second base, pitcher, and center field are all pretty close to expected. Catcher and left field have been relatively more tested than we would expect, and first base, right field, and third base have been let off the hook, relatively speaking.
No need to play the percentages with a relief pitcher as far as x-chart results are concerned
One interesting thing I discovered in this exploration is that apparently x-chart rolls are identical from one side of a pitcher’s card to the other. That is, if a roll of 4-4 is a CATCHER-X vs. left handed batters, the same is true on that pitcher’s card against righties.
This means that, at least with regard to x-chart rolls, there is no advantage or disadvantage to specific lefty/righty substitutions. A given roll off the pitcher’s card will either be an x-chart result or not, regardless of whether he is facing a left or right handed hitter. One of the implications of this is that if your opponent brings in a lefty to hit for a righty, or vice versa, not only do the chances of getting an x-chart roll stay the same, but the exact dice rolls stay the same. If nothing else, this is one fewer thing to think about when selecting pinch hitters and relief pitchers.
All I want for Christmas is a “pair of fours”
Looking ahead, I’m hoping and praying that Giambi and/or Bonds can somehow pull a four defensively for the 2006 cards, and I’ve learned the necessity of strong defense, especially up the middle, by taking an in depth look at the numbers. A four is not great, to be sure, but if Giambi were a 1b-4e18 rather than a 5e18, we would expect an out on 47.31% of the 1b(x) rolls, instead of the current 40.56%. With defense, every little bit helps!
Again, just looking at games played on my computer, here is how my opponents have done so far on their x-chart chances. The Outlaws converted 25 of their 29 chances in six games, an .862 clip. The Casinos are close behind, with 12 of 14 in three games, an .857 pace. The Mohawks, at .720, The Team, at .700, and the Goths’ .647 puts the Meadows and our .631 second to last here, bettering only the Busy Bodies, who were at .533 (and still took five of six games from the Meadows).
I hope this analysis and reflection is helpful to you as you think about building a championship caliber team in your own league.