Baseball Musings: Defensive Positioning

January 05, 2007

Defensive Positioning

I'd like to explore positioning as part of the Probabilistic Model of Range. One thing that I believe would be easy to record is the direction and distance the fielder moved to get to a ball. The direction could be coded using the digits 1-9 as follows:

1	2	3
4	5	6
7	8	9

Where 5 would be straight at the fielder, 8 would be in front, 4 to the fielder's right, etc. What I'd like to get opinions on is if the X and Y axis should be fixed for all fielders or float depending on the position. For centerfielder and pitchers, the X axis would be a line that went through home plate and second base, while the Y axis would go through third and first. But for a shortstop, the X axis could go through second and third base, with the Y axis perpendicular to that. In the case of a fixed axes through 2nd-home and 3rd-first, a ball in the hole that's fielded by the short stop would be coded a 7. In the second case, where we adjust the axes to the fielder, it would be a 4, since the fielder moved to his right. My feeling is the second way is superior. However, with so many shifts being employed now, which often put the shortstop on the second base side of the bag, the fixed axes approach might be more accurate. I'd like to hear your opinions on the matter.

Posted by David Pinto at 01:25 PM | Defense | TrackBack (0)

Comments

I like the second way. But...

I'd suggest making "8" always mean going towards home plate. So, for a SS, that would mean that the X axis doesn't go through third and second base, but rather at an angle. On the plus side, you'd end up knowing that an "8" means the ball was hit slowly (since the fielder is charging for it) and a "2" means it was hit hard. It's not as pretty as your second way, but you do get that extra information of ball velocity. Plus, with your X axis crossing third and second base (for a SS), I don't think any of those numbers could accurately describe someon e fielding a bunt.

Posted by: Mike at January 5, 2007 03:01 PM

I agree with Mike, and I can't quite make sense of an x axis that goes through second and third. It sorta feels like, in that scenario, the SS is standing facing right field.

Since most fielders orient themselves toward homeplate, shouldn't home plate be true north. Not saying the axes should be fixed for all players but I would think they should all more or less be oriented toward home plate.

Maybe I'm missing something though.

Posted by: Steve at January 5, 2007 03:05 PM

Don't be so hung up on right angles - they're not so great! How about a circle - lets say a clock - and the defenseive player is at the center. Orientation should be home=true north, as Steve suggested, so a line from home would run thru 6 o'clock, the player and then 12 o'clock. A SS charging a bunt would be 6 while going into the hole would be 9 or 10 o'clock. The circle would always be fixed to where the player was when the pitch was thrown. You don't want the distance of any shift to be included in the distance to make the play. How did you plan on indicating distance??

Posted by: Phil at January 5, 2007 03:14 PM

I thought distance would be on a scale of 0 to 5 where 0 was straight at the fielder, and 5 was he moved a long way.

Posted by: David Pinto at January 5, 2007 03:19 PM

Are you just looking to measure how well a player positions himself? If that's the case then, why worry about direction at all? Just worry about distance as that would be the best measure of how close the player was to being "on target".

As for coordinate systems if you really want directional info, polar coordinates (r, theta) with the origin on home plate and 0deg line along RF line would seem to make the best system. You can cover the entire field with one coordinate system for everyone. Move to the left means lower theta, move to right means higher theta for every player independent of starting position. If you were doing the data collection by hand you'd need special graph paper, but that can be done.

Posted by: Miguel at January 5, 2007 03:35 PM

mixed the theta directions in above post

Posted by: Miguel at January 5, 2007 03:36 PM

If you want to use a grid, then I'd suggest that 8 always point home. You're looking for how the fielder moved relative to his original position and orientation, which is always facing home when the ball hit.
I happen to be the lead AI programmer for a major MLB video game and my main focus is programming the defensive AI. The model we use is the circle divided into pie-shaped regions, because it is easier to imagine and implement. This data could be augmented to include ball speed by using concentric circles, each representing a distance traveled.

Posted by: Jeff Mc at January 5, 2007 03:47 PM

Thanks, Jeff that's a good idea.

Posted by: David Pinto at January 5, 2007 04:24 PM

The responses seem right on to me. Here's another issue: the effect on range when there is a man on first and he is being held, with the second baseman cheating a bit toward second for a DP. How many more balls are likely to go through the right side? It would be nice to evaluate the strategy of not holding a runner on first, factoring in both added hits (because of reduced range) and runners advancing to third on all hits (if not being held).

Posted by: Joel at January 6, 2007 12:16 PM

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