Split Personality Disorder

Lately, I have been plagued by splits, and so have two of my compadres (JD and JL). This week our team put up 18 of those pesky buggers. We have had more than 10 for seven of the last eight weeks and have maxed out at 20. Splits are huge nuisance, especially pocket splits. They are keeping our pickup percentage down. For instance, this week, I picked up 9 of 17 spares or 52.9%. Of the eight that I did not collect, 6 were splits. So, of the "normal" leaves, I had, I actually got nearly 82%. If I could largely eliminate splits, then, I could probably add at least 10 pins to my average. This goes for most bowlers.

Well, in this post, I would like to make the argument that splits are a sign of improvement in bowling; I'd actually like to turn this rise in splits into a good thing. It's rare in sports that a gain in skill comes with an unfortunate side effect, but I'm pretty sure that's exactly what's going on here.

I'd like to start with a simple conceptualization of skill in shooting a basketball. The same idea could be applied to darts or any activity where something is propelled toward a target. In basketball, the target is the center of the rim. If a shooter shoots 1,000 free throws, they will make some and they will miss some, but if we were to look at the average location at which the ball would have passed through the plane of the rim, it will usually be the center of the rim. Parenthetically, did you know that the diameter of the rim is twice the diameter of the ball?

For a really poor shooter, Shaq for instance, that scatter of dots representing each shot will be wide. Some will be air balls. Some will be swishes. Some will clank off the rim to the right or left. Some will brick off the back of the rim or backboard. For a really good shooter, like Steve Nash, that scatter of points will be much tighter. Most will be near the center of the rim, and the misses will be near misses. The scatter of points made by both shooters should be centered on the center of the rim. For a good shooter, though, the dispersion, or the width of that scatter, will be much tighter.

Now let's apply the same concept to bowling. On the first ball, we all aim for the pocket, the 1-3 if you are a righty. Some of us are better at consistently finding it than others. For a really low skill bowler, if we could average all of the locations of contact of the pins (say the board of entry), it would be the pocket. In fact, this would be the most likely shot, but a large number of shots would miss, and many would miss badly, with some even finding the gutters. Below is a graphical representation of the system as I envision it. (Click on it to make it larger).
The beige curves above the pins represent the frequency distribution of 1st shot locations for low, intermediate, and high skill players. If I had actual data for this, I would expect the distribution to be normal, bell-shaped, or Gaussian, named after Karl Friedrich Gauss (the old guy in the pic up there). Incidentally, if you are interested in tracking board (or location) statistics, check out Bowl SK, a bowling stats package maintained by our friends at the 10th Board. In brief, the height of the curve represents how commonly a shot reaches the pins at a particular location. The most common location is the pocket for bowlers of any skill, but as we improve, those shots on the edges of the pins become increasingly rare until they largely disappear. Professional bowlers are almost always very close to the pocket.

Here is the interesting part. As your skill increases from low to intermediate, you should find the pocket and its surroundings more frequently. Because most splits derive from striking the 1 pin straight on (very close to the pocket) , splits should actually increase in frequency as you improve. If you can get beyond this stage to the high skill level, they should drop off again.

I don't have board statistics for our team to demonstrate this phenomenon. As quantitatively anal as I am, I just can't bring myself to record this information while bowling, but I do have one way of looking at the problem: 1st ball average. If you have a high 1st ball average, it means that you are regularly near the pocket on your 1st toss. If it is low, you are all over the place. It should be a good proxy for skill. So, we can ask whether the number of splits increases as first ball average increases?

Above is a graph of 1st ball average vs. the number of splits for 93 individual series of bowling for bowlers of low to intermediate skill.Notice that above a 1st ball average of 7.5, the average number of splits per series increases by one for every 0.5 pins gained in 1st ball average.

What does this mean? It means that if you are getting more splits and you are improving from low to intermediate skill, this is exactly what should be happening, as annoying as it may be. It is a sign of improvement. So, try not to think of it as a bad thing, as I have been. It is my contention, although I do not have the data to back it up, that as you improve even further, the number of splits you get will decline again. Here's one little bit of evidence to support that idea. Two weeks ago, JD put up a first ball average of 9.03. It was the first time any of us had broken the 9.0 mark. How many splits did he have that night? Only one.

A Hard Fought Battle

It was a battle of the Laramie's bowling elite on Monday night at the Lanes of Laramie. Or perhaps more accurately, it was Laramie's bowling elite vs. Laramie's bowling losers, the Movements. We gave it our all, but the Lazers took three of four. We had a solid night, putting up nearly 1,900 pins. We had two 900 games but only managed to win one of them. With every game, one could hear the swords of gorgons clashing on the battlefield, whatever that means.

I'll just hit the highlights. Game 2 was a spectacle to behold. Despite a team handicapped 902, we lost. The real battle was among the Lazers. It was the Briefcase vs. the Kid Wonder in a death match to 300. The Kid started with seven straight, but The Briefcase later countered with his own seven-bagger. They both ended with matching 268's, so nobody had to die this night. Even though The Bruin was having a hard time finding the pocket and that they had an absent bowler (Baker, Jr, who still bowls like 228 when he isn't even there), we could not compete with the raw talent of the Lazers.

In Game 3, we were already down two games and about a Roman C of pins, but we fought to the end to win the game. I will demonstrate the fortitude of the BM's with a new tool on the BM Report, the Victory Probability Tracker®. The VPT was inspired by similar graphics used to describe a team's chances of winning a baseball game as the game progresses. Here's an example. Unlike the much more sophisticated baseball model, our model does not take into account what the other team is doing because we lack those data. It is instead based on team frame by frame scores and past outcomes. Here's the VPT for Game 3 last night:


We started off strongly early on. Johnebob went X, X, 6/, X for his first four. I struck the first followed by a split. The Rook went strike-spare. JD went 9, man spare in the first two. After the scoring for Frame 1 was complete, we already had a 63% chance of victory, but over the next five frames, we slipped back to 50-50. The game was looking lost, but for the last four, we bowled toe to toe with the Lazers. Daniele, who had struggled to get X's all night landed a four-bagger. Johnebob put a double on top of that. I got an X and a couple of slashes, and the Rook added one of each. By the end of the game, we had pushed our chance of victory to near 70%, which was good enough to get one on the night.

Since I love the numbers, I'd like to point out one more interesting happening. Johnebob absolutely dominated the first frame. In Game 1, he started with a turkish delight. In Games 2 and 3, he started with two-baggers. In all, he averaged a hefty 28.0 pins in the first frame. One should keep in mind that the maximum that can be attained for any frame is 30, so an average of 28 is very beefy. In fact, nobody has ever come close. The graph below shows the frequency distribution of average frame scores for the Movements for all series on record.


This is a lot of data. In fact, it includes 1,152 average frame scores. That's 10 frames per bowler for four bowlers for 38 nights of bowling. In short Johnebob's 28 pin average for the 1st frame was sick. It is a major outlier. Nobody has gotten even close. The next closest was a 25.3 pin average for the 2nd frame from February 2, 2009. Who did that? Johnebob of course, the master of choosing a frame to dominate for the night. Lest he get a big head, I will note that for Frame 10 last night, he averaged 8.3. That's bowling for you.

The truth is hard to admit

It's so hard to admit what we know to be true that only two of us can admit it (left: Urban Magic Johnson, right: Movement2). The Battle for Bad Bowling Supremacy has been played, and HCLC, The A Team, has triumphed.

Congrats, guys and gals!

Seeing the Forest

Bowling is a noisy system. From week to week, our scores fluctuate wildly and for no apparent reason. This frustrates some people to no end (I'm talking to you, E.B.). We all want to get better, and we do with time, but it generally takes a long time to notice that improvement. We seem to be going nowhere fast. Week to week performance distracts us from that long term trend. If I think back to four years ago, when we joined the Bernaski League, our improvement is obvious. We have all added around 30 pins to our averages. If I think of the last few weeks, it seems like nothing is changing. Weekly bowling scores are simply trees that distract us from seeing the forest. But the forest still there, and it can be teased out of all of those stupid trees.

Our team time series down there on the right is an excellent example of this. It seems to go up and down wildly with no apparent trend. There are many factors to account for this. For example, our team membership has not been constant. Last year, we had the Canadian in the three spot. Now, we have Ging. There are weeks when we have subs, like K-Terk and Becker. These changing factors will affect our week to week pin totals. There are underlying constants, myself, John, and Joe. We have been there from the beginning, and its not difficult to tease out our improvement over this time frame.

Here's how I did it. I looked at averages from week to week for the three of us. There were weeks when one of us was missing, but I ignored this small factor. But to smooth out the wiggles caused by those weekly trees, I used a 10 week running average. I simply looked at our average game score for the last ten weeks of bowling, and when I did, the pattern became very obvious. Here it is:
The dots in gray are our weekly averages. The red dots are the running average, our average over the last ten weeks. Last season, John, Joe, and I peaked early, around the middle of February, and we limped into the end of the season. This season has been a different story. Our average has increased steadily with a couple of bumps. The good news is that ten weeks into this season, we are bowling better than we have ever bowled. We have averaged just under 156 pins per game. It may seem odd. We went through a horrific slump when we could not win a game. We have all had good days and bad days. But when you look at three bowlers over a ten week period, you are averaging a total of 90 games of bowling, and all of those distracting trees give way to a forest that is easy to see. In this case, I like the look of the forest. I'd sure like to see it look like 160 trees, and eventually it will. I'm not sure when exactly, but we'll get there.

The Battle for Bad Bowling Supremacy

In less than 30 minutes, the battle for bad bowling supremacy will begin. This competition of bowling not-so-greats will be played not on the hardwood but on the gridiron. Game time: High Noon. Location: Laramie, Wyoming. The wager has been proffered and accepted. Frogs vs. Cowboys. Movements vs. HCLC. The world will have their eyes fixed on this game, the most important game ever played in the history of bowling.

Will a new bowling ball improve your game?

Last Monday, I wrote about bowling balls, specifically that the USBC is changing one of its regulations on ball specifications to take a little bit of action out highly engineered balls. Apparently, the USBC feels that advances in ball technology are inflating scores. I equated this problem to the use of steroids in baseball , which made one commenter, who apparently sells bowling balls, a bit irked. All of this got me thinking about the age old question of how much equipment really matters. A friend of mine once said, "Golf is men's excuse to go shopping." Dudes like new toys, and sports marketers have done a good job training us to believe that we could definitely do better at any sporting endeavor with some new gear. Is this true?

At the end of last season, three of us retooled our bowling bags. We all made the change from what were basically house balls to bowling spheres with a lot more break. It was my hope that we would start getting a lot more strikes. Well, the time has arrived to see if in fact that has happened. Since we reequipped, each of us have more than 24 games and 240 frames to our name.

I decided to look at strikes and spares individually, the two major currencies of success in the art of rolling. Let's begin with strikes. The graph below shows the strike percentage for each bowler before and after the upgrade. There are three questions here: Was there a change? Which way did it go? And is it meaningful? The last question is the most subtle. Statistically speaking, we would expect slight variation in strike percentage due to chance even if there was no change. Going back to my favorite analogy, flip a coin 100 times and count the number of heads you get. Now repeat the experiment. You are likely going to get a slightly different result even though nothing changed. Likewise, if you roll 100 frames twice, you will very likely get a slightly different number of strikes each time. Statistically, it's not difficult to evaluate whether any of the observed differences are meaningful, which would indicate that something other than chance can explain the change, such as the use of a new bowling ball.

So what happened? In short, not much. The only meaningful difference is for JD. He has gone from a strike percentage of 23% with his Qubica House Ball to nearly 32% with his new Hammer Raw Acid. This means he gets about one more strike per game. JPL has gone in the opposite direction. His strike percentage has dropped about 5%, although the difference is not significant. My strike percentage is up over a little more than 1%, something that can easily be explained by chance. For all of us combined, strike percentage has improved from 27.8 to 29.8%, a difference that is not meaningful.

In short, the new balls seem to have no effect for two of us, but Daniele seems to have made a big jump. I'm not sure why he is the only one reaping the benefits of a new ball, but it might be explained by custom fitting. Prior to the switch, he used a hand me down ball that was not drilled for his hand. Johnny and I both had custom fits prior. Or perhaps, as Hammer would like us to believe, his ball has actually helped him. I actually lean toward the latter.

What about spares? It's hard to imagine how our upgrade would affect our pickup rate. Having a ball with a lot of break isn't really an advantage when cleaning up leaves. You could even see it as somewhat detrimental. (e.g., It's harder to tuck into the 10 pin if you're a righty.) Interestingly, all of us have improved our spare game. The greatest difference is for myself, with an 8% improvement. None of the differences for individuals are statistically meaningful, but for all of us combined, there appears to be a real difference. We are getting 4% more spares than before the switch. Is this due to the equipment change, or is it just because we are becoming better bowlers? I favor the 2nd explanation- it is about skill.

In brief, after the Great Ball Transplant, we have benefited slightly, especially Daniele, who has been getting a lot more strikes. We all have made slight gains in our spare game, something I think is difficult to attribute to our new balls. So, will dropping $150 on a new hi-fi ball add 10 pins to your average? I don't know. For the three of us, only JD seems to have spent his money wisely. Those people who make and sell balls will tell you that it will for sure. Maybe we bought the wrong balls. All I can tell you is that I hoped for more strikes with my Brunswick Smash Zone, and it just isn't happening. I can also tell you that the next time I tell my wife that I need a new ball, she is going to point to this and say, "Uh huh, sure you do." I will respond, "I need a Hammer Raw Acid. Look what it did for Joe." By the way, Hammer, did I mention that were are looking for a sponsor?

Two Perfect Games

We arrived a tad later to the lanes on Monday. The prior league was just wrapping up as we migrated to our usual preleague booth in the lounge to enjoy some cold golden bowling juice. I didn't have the time to pour myself a mug by the time we had to migrate to Lane 14. Upon arrival, Cody Caldwell, the Kid Wonder, walked up. He said, "You should check out that screen. In the 1st game, Brett [Baker] and I both rolled 300's." He was pretty excited about this, as you might imagine. I slipped out of my shoes, into my bowlers, and checked out the screen. It was true. Two 300's in the same game by two guys on the same team. Wow. That's cool. But we had our own business to attend to.

Our foe for the night was Prairie Rose, the team anchored by the Eickbush's, father and son. Leading off is Shef, a man with an intimidating demeanor on the surface, but he is a very nice guy. They were missing their 3 man, Talley, so once again we would bowl with a slight advantage, 10 pins per game. No advantage, however, can overcome bad bowling, and in Game 1, we managed to continue our streak of sucking. We lost. It seemed like a long night was upon us yet once again.

But something happened between Games 1 and 2, what it was I have no idea because Game 2 was a beautiful thing. Even though P. Rose put up a game well into the 900's, we broke 1,000 for the 2nd time this season. Daniele led us with a 200, his 2nd of the season, and once again, he hit 200 on the money. Gingy put up his best game of the season with a 187. Scratch, it was a 731, handicapped, a 1009. This was easily a new BM record for Game 2.

We took Game 3 with a 925 game, again led by Daniele. In fact, in Games 2 and 3, P. Rose also hit the 900's and lost both. I felt badly for them because it seems like that happens to us all too frequently. They bowled very well, but Games 2 and 3 for our team felt like perfect games, at least as close as our team can get to perfect games.

We set a number of records as a team. In addition to a new high for Game 2, we set records for strikes (47), strike% (35.9%), and accuracy (48.7%). The Rook earned a 180 patch, which he desperately wanted, and our team series was our 2nd best ever (1,931). This was, however, JD's night, who took the high score for all three games and had his best night of the BIA. He finally joined the 700 club, a 200 game with a 500 series by going 539 for the night, and he set a new record for first ball average, with a 9.03. This is the first time any of us have gone over 9, and it fulfills one of my goals for the season. He was all over the pocket all night. To give you an idea of why it's so difficult to do this, check out the frequency distribution of his 30 1st ball scores below.


It was a great night for the team. Heck, it was the first time I had seen us win a game in a month and a half. At the night's end, we had one more pitcher of bowling juice to celebrate, and Kid Wonder came over to our lane. I asked him what it feels like when you a bowl a perfect game. Specifically, I asked what does it feel like to step up to bowl after you have hit eleven in a row. He said, "You know, my mind went blank, completely blank." That's probably why Cody now has three 300's to his name, and I will never have one. (Brett has more than 10!) He does not over think it. He just rolls. Well, there's also the factor that Cody is a really good bowler, and I really suck. Next week, we're up against Cody, Brett, and the Lazers. It should be a good time, except they owe us a beatdown. We are 6-2 against them this season.