## Bocce Statistics?

I’ve been reading Curl with Math, which seems to have a very similar goal to this weblog. In curling, however, there are apparently a lot of compiled statistics available which make mathematical analysis a feasible activity. As far as I know, there are no such significant compilations of statistics for bocce.

So I’ve been thinking about this; if I were to start keeping statistics, what would I even want to record? Obviously, we’d want to start with number of balls played, how many points were made, how many opponent’s points were beat, how many shots connected. But this would only give an incredibly superficial picture of performance. Over the next few weeks I’m going to just record some info on all my shots and then see if we can come up with a bocce equivalent of RBIs or slugging percentage or QB rating.

Anyway, this week was actually quite uneventful (from an interesting-situation viewpoint). We dropped our first game 12-0, then won the next two 12-8 and 12-8. I didn’t really run into any particularly tough decisions during the match, but since we finished up early I got to watch a match between two pretty tough teams on the next alley. this situation came up:

*Red to play.*

It’s hard to tell in the photo, but green is sitting on one point, but just a nudge to either his inside ball (Green B) or the red holding ball (A) will give him two points. The red team debated between lagging in along vector 1, trying to either beat the green A ball or to get lucky and maybe bounce off of the red A ball and sneak in behind for one point, or shooting hard along vector 2, hoping to pick the A ball off.

At first it appeared that lagging was the no-brainer. It seems much safer, but it’s a very difficult shot. Not only does the speed have to be just right to be successful, but the position of the pallino makes accuracy extremely important. There is a very narrow needle-eye that you have to thread in order to curve the ball in to the right spot. The chance to sell out and give green two points is there, but it’s very slim. The vast majority of times a lag is going to have zero effect either way.

Shooting, on the other hand, seemed suicidal at first glance. But a couple of things changed my mind. First of all, the two green balls are close enough that they make one effectively large target. It’s pretty easy to split them down the middle. If you make that shot, there’s a good chance both green balls will kick down the court and the played red D ball will basically die where it is. In general, a shot ball that hits a single target will carry quite a way, but one that hits two targets will usually transfer all of its momentum between the two. Further, the red A ball has the nail, so even if red knocks everything off the court, red still stands to make one or even two points.

The sell-out opportunities for shooting are really low probability. Basically your worst-case scenario is giving up three points, but doing so would require an incredibly bad shot. More realistically, red could pick off just the green B, having no effect, or kick green A into red A, which would probably give a net zero effect. The most important thing to consider here is that it’s relatively early in the game, so red shouldn’t mind a higher-variance shot here if it leads to a greater expected point outcome in the long run. Lagging, you’re looking at something like 1 point for green 90% of the time, and 1 for red 10% of the time. Shooting, let’s say you’re looking at 2 red 30% of the time, 1 red 20% of the time, 1 green 20%, and two green 30%. If that’s the case, your expectation for lagging is 0.8 green points, and your expectation for shooting is basically zero. You’ve got to take the shot.

Speaking of shooting, I took this clip of my uncle shooting with my cell phone. Next time I’ve got to remember not to stand in the ditch while recording.

*(temporarily removed)*