Archive for the ‘strategy’ Category

Playing to Your Weakness

Saturday, March 15th, 2008

As you progress as a bocce player, you invariably develop faster in some aspects than in others. You might notice that you like playing a short game, with the pallino up close, in order to maximize your shooting effectiveness. Or you might tend to place the palino near the sideboards and angle your lags in. It doesn’t really matter what your particular quirk is, the important thing is to realize that you’re developing a comfort zone. A routine.

Everything’s great. You feel like you’re really starting to get on top of your performance. You’re executing more consistently. You’re confident in your abilities.

Then the bottom falls out. You get clobbered, even though you’re playing to your strengths. What happened?

It’s simple. You forgot that in bocce playing well doesn’t matter.  What matters is playing better than your opponent.  You just ran into an opponent who is better at “your” game than you are, and you didn’t even notice, much less adjust.

So the next time this happens, you notice. Now what? How do you adjust?

You do the only thing you can do: play to your weakness. The trick, of course, is finding a weakness of yours that is an even bigger weakness for your opponent. If you can’t do that, pick a strategy that you think you’re somewhat decent at and that has a lot of variance and hope you get lucky. In general, that means getting away from a finesse game and into a hard-hitting shootout.

Adjusting to Court Conditions

Friday, February 8th, 2008

I’ve been on hiatus for a while; between business travel and getting the flu I haven’t had much time to play since the holidays. My first week back after a long stretch and I get to play on alley 4, which is known as the “worst” court in the club; what that really means is that it’s the most inconsistent surface (breaks can vary wildly over even very short distances, so even if you know how your ball will break you have to be more accurate than on other courts in order to get the desired result) and it’s also the most sensitive to changing weather conditions (and over time, this is almost certainly what has caused the inconsistencies in the surface). Our alleys are indoors, but there is no foundation under the courts. There’s just the earth, a layer of gravel, and the Har-Tru clay surface. When it rains, water seeps under the building and into the alleys, and #4 gets more of it than the other three put together.

The good thing is that you can easily see the difference between wet and dry areas in the clay, and the effect of the wetness is fairly consistent. By far the biggest effect is on ball speed – wet courts play much, much slower than dry courts. The other effects are relatively minor and are basically negligible. Things get interesting when you have a court with some wet spots and some dry spots – and they get really interesting when you’re playing in the winter the day after a big rain. When the heaters come on, they can dramatically increase the drying time of the alley, so a surface that starts out pretty sloppy can get considerably dryer over the course of an evening, and can even change significantly within a single game. If you can adjust to this change better than your opponents, you can build a huge advantage.

The biggest mistake I see in this sort of situation (and one I myself made three or four times last week) is a “double adjustment.”

2008-02-07 Figure 1

Lagging shot selection. Click for larger image.

A player will start off lagging along path A, through a wet spot. His ball will get bogged down in the mud and stop short of the target. He decides to adjust by moving over, lagging along path B to avoid the mud. However, your brain will also want to adjust (increase) your lagging speed; this double adjustment results in a big overcompensation and the lagger goes from a ball that is ten feet short to one that is ten feet past the pallino. Making a single adjustment is, of course, much easier, and since your brain is subconsciously recalculating the speed you need to get to the ball, staying along the same path is a better choice. It’s much easier to keep your position constant than to keep your speed constant. Your brain will be at least partially on auto-pilot for the speed recalculation, and fighting that is going to be counterproductive.

* * *

Changing gears, I saw one fairly rare but interesting situation this week.

2008-02-07 Figure 2

Green to play. Click for larger image.

It’s early in the game, and normally green would be ecstatic to have three balls to play with all the red balls spent. However, lagging in for multiple points here is going to be extremely difficult. Shooting red balls out of the way is another option, but there are lots of things that can go wrong here. It’s a high variance situation. Should green really consider dropping three balls and just locking up the one point in the hand?

The most important factor in making this decision is the relative skill levels of the green and red teams. If the green team is more skillful, they should drop the balls and take the one point. If green feels outclassed, they should gamble and go for the big score. It’s quite simple, if you’re behind in skill you want to make luck as big of a factor as possible in order to level the playing field out. As variance increases, the chances for an upset increase, too. Shaking things up and going for big scores is a prime way to add variance here.

As the gap in skill widens, the need for the underdog to take big chances increases, too.

Aggression vs. Dropping

Saturday, December 15th, 2007

The most frequent big mistake I see is a team playing “conservatively” (i.e. “scared”) when they are in scoring position and their opponent is out of balls. Teams will regularly drop their last ball instead of going for more points because they fear “selling out” (making a bad play that flips the position such that the opponents end up scoring). While the sellout is a huge turn of events, if the fear of it dominates your thinking you’re going to leave points on the table that will come back to bite you in the ass later.

Any time you have a chance to score multiples, you must look for every opportunity to capitalize. The difference just between scoring one and two points is enormous over the long term, and yet teams will pass up easy chances to go for an additional two or even three points even if their downside is giving up just a point or two a small fraction of the time.

2007-12-15 Figure 1

Green to play.

In this example, if green can move the pallino back just a bit (lagging along path A), the court would be wide open for scoring three or maybe four points. However, the position of the red balls makes the green player lag from the opposite side of the court, and in our league most players avoid these cross-court lags because the centers of the alleys are rough and bumpy, which totally wrecks accuracy. Shooting along A is no good since red has two decent balls down court on the nail. Shooting along path B is another possibility, though the outcome of such a shot is extremely hard to predict, even if it is perfectly executed. The pallino could end up down court, or the green A ball might get carried away leaving red with one point. Despite the risk, this choice shouldn’t be ruled out immediately since green has three balls left, leaving a good possibility to clean up any sellout if the shot does go wrong.

In the end, I decided to play along path A. The mistake I made was in lagging just hard enough to get to the pallino and maybe move it a foot or two. In this case there is plenty of room behind the green ball so even if the pallino goes too far for the A ball to remain in scoring position it should be possible to get three points. If I had come in a little harder, the increased momentum of the ball may have negated a bit of the variance from the bumps in the middle. As it turns out, my ball went off-course and didn’t have any significant effect.

The important part of this example, though, is that I’ve seen many players in this situation simply give up and “drop” their remaining balls and simply “take one point” because “it’s too tight in there.” Taking one point is “safe” since it avoids the sellout. But early in the game, a one point lead isn’t that big of a deal, while a three or four point lead is (my gut feeling here going on nothing but experience is that a 4-3 lead would hold up about 55% of the time, while a 7-3 lead would hold up closer to 70% of the time). On top of this, if your first ball does “sell out” you’ve still got two chances to recover! Grow a pair, get greedy, and load up!

Now, here’s another situation where dropping might make sense:


Green to play.

In this case, green can’t lag in along the normal routes off of the side boards since Red A and B are blocking. A lag along path A would probably be safe on a semi-regular court, but with the bumps and variances of our clay courts, it’s pretty risky. Red A could get bumped up into scoring position, or Green A could get bumped out of position. Shooting along path B (basically the same path) with the intent to pick the pallino out is worth considering, especially if the setup is a relatively short (shooting the pallino gets really hard as the distance increases). If the shot is successful, green can easily drop ball D in behind to pick up two points.

In this case, though, if green misses the shot, the downside is huge. A particularly bad outcome would have the shot pick the green A ball cleanly out, leaving red with four points and green with one ball to try to salvage something. Of course, green could try shooting the pallino again, with one less ball laying around to get in the way. Shooting your last ball when the opponent is sitting on four points is never a pleasant situation, though.

Dropping the last two balls is probably the way to go here. Green already has one ball in position, the best possible upside is to come out with two points, and the downside is catastrophic. Further, this is closer to the midway point of the game, where small edges are worth more than in the early stages.

Aggression is in general the best policy, but (just as with any other strategy) the difference between a journeyman and a master is knowing when the exceptions come up and it’s time to back off and play it safe.

Bocce Statistics?

Friday, November 16th, 2007

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:

14-Nov-2007 Image 1

14-Nov-2007 Figure 1

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)

Week 1: Shooters vs. Laggers

Thursday, November 8th, 2007

One week into the season and I’ve already come across two excellent cases for examination.

Our league is organized into three-man teams. Last night, both of our teams were missing a man, leaving us with an interesting situation. The bad guys were two players who are basically pure laggers, while we had one shooter and one pure lagger.

The first things that should have popped into my head:

  • Shooting accuracy decreases much more dramatically with distance than lagging accuracy.
  • More balls in play favors shooters over laggers (assuming roughly equal players otherwise).

The reason more balls favors shooters is that your effective shooting percentage will probably be significantly lower than your effective lagging percentage; more balls means more chances to hit, and also means you’re gambling with a smaller percentage of your total balls for that round with each shot. On the other hand, if the players are significantly mismatched, more balls favors the better player since more balls equals lower variance per round. It’s easier to get lucky when you’re only throwning one ball than when you’re throwing three or four.

So, the first adjustment we should have made, but didn’t, would be to place the pallino closer when we’re leading off. I generally lead off for our team, and I like lagging deep precisely to defend against better shooters, but in this case I should have been playing a significantly shorter game. I think over the long term, this strategy could be worth as much as two or three points per game, especially if your opponents are super-reluctant to shoot at all. That’s pretty huge.

The next adjustment we could have made is really due to a loophole in our club rules. When a three-man team plays a two-man team, either all players play both ends, with the three-man team getting two balls per man and the two-man team getting three per man, or one player from the three-man team plays both ends while the other two play a single end each. The rules don’t address the situation where both teams are missing a man; sometimes both teams play three balls per man and sometimes they play two per man. We should have pushed for three per man (although I suspect we didn’t really lose much here since I doubt our opponents would have gone for it).

Now, for an actual in-game situation. This play came up at the end of game two. Green to play with one ball left. Red is out of balls. Green needs two points to win the game and is currently sitting on one point.

7-Nov-2007 Figure 1

Figure 1. Click for larger image.

Green is looking at two possibilities:

  1. Lag off the board and slide in for one more point.
  2. Shoot the pallino and take two points off the nail.

There are pros and cons to both of those. Most obvious is that if you shoot you have a chance of missing completely, or even worse picking off the green A ball, giving red two or three points. On the other hand, if you lag and come in just a bit too hot you can just as easily pop the pallino back into the red balls. The image doesn’t do a good job of showing this (I’ll hopefully be improving my diagramming as this blog progresses), but at the time the red D ball was in a position that made a lag here trickier than it looks in the diagram. It was not an obvious call either way. In the end, my assessment was that shooting would more frequently result in two points and a victory, but would also more frequently result in giving points away, while lagging was much safer, but much less likely to gain additional points. Given these choices, the only time you’d go for the shot and the immediate victory is if you feel that you’re seriously outclassed by your opponent. Taking an 11-8 lead is huge, even if you’re a slight underdog.