Thursday, December 10, 2009

Four Games under .500: Bad Bowling or Bad Luck?

Last season, we finished the first half with a record of 29-35, or six games under .500. This season, we are on a similar pace, currently four games under at 24-28. We have had our fair share of bad bowling days, but we have also had days when we have bowled really well. Winning and losing in league bowling is funny thing. There are games you feel like you should have won but did not because some guy on the other team put up a perfect game (this has happened to us). There are other games you should have lost but won.

There are those things you can control, most notably how your team bowls. There are things you cannot control, such as your opponents' bowling. Accordingly success or failure in league bowling can be boiled down to two factors, performance and luck.

For example, this season, we have lost four games in which we recorded 900 handicapped pins or better. In our league, anything over 900 is a good game. Two of these losses occurred on the same night. Ouch that hurt. That is just plain bad luck. But on September 21, against Lazer Wash, we won a game in which we bowled 828. With that score, we had approximately a 30% chance of victory, but we won. That's good luck.

What has been eating away at my soul, though, are two seemingly incompatible facts. First, we are bowling better than we have ever bowled before. Second, we have a losing record. It just doesn't add up.

To seek solace in statistics (one of my favorite bad habits), I decided to look into this situation a bit more carefully using something called a Monte Carlo simulation. It's pretty simple, really. Based on our past record of wins and losses, I know with a certain degree of confidence the chance of winning a game given the team handicapped pin score. In the Memorial League of Bernaski, it is approximated by the formula:

win probability = [handicapped pin score] x .004 - 2.965

If you play around with this equation, you will find that a score of 867 represents a 50% chance of winning a game. Anything above that, you are more likely to win than lose. A game of exactly 900 has a 63.5% chance of victory. This formula is not a perfect representation of reality for reasons I won't get into, but it's pretty close.

So, here's what I did. I took our handicapped pin scores for the season. That's 52 games of bowling (technically 39, with 13 representing average HDCP pin score for the night). For each of these, I calculated a probability of victory. Then, I simulated these games 10,000 times to find what is the most likely number and total expected range of wins given our bowling performance over this season. When you do this, you get the following result:

In essence what this graph says is that the most likely outcome given our actual bowling performance is 27 wins, or a record of 27-25. So, the answer is bad luck. It could be worse, though. If we were really unlucky, we could have 20 or fewer wins, although this should happen only once in every 100 or so half seasons. On the other hand, if we were really lucky, we could have more than 35 wins.

While this does provide some solace, I must admit that I also find it somewhat troubling. In this simulation, I found that anywhere from 15 to 40 wins is possible given how we have bowled. That's a big range, and ALL of that range can be attributed to luck because I have held skill or performance constant. In that sense, it makes you wonder to what extent league standings are determined not by how well you bowl, but instead by the hands you are dealt.

Think of it this way. Let's say you show up night after night to bowling league, and your team does not bowl well. But for some reason, the team whom you face always bowls very poorly. You go on to win the league. Did you earn it?

8 comments:

  1. How come when I look at that chart, the word kurtosis pops into my little, peanut-sized brain?

    How would you have handicapped this (our series last Tuesday-- we were outbowled by 1,000 pins scratch)? (And we're in a 5-man league.)

    Scratch (Opp.): 659-703-688:2050 (956-1010-1084:3050)
    Handicap (Opp.): 413 (181)

    Just curious. When I saw the 232 difference in handicap, I felt certain that if we could produce an avg. of 150 pins per game per bowler (5 x 150 = 750 x 3 = 2,250 scratch + 1,239 handicap = 3,489). I would have bet on us, though I'm not sure of the odds.

    There is no reason (okay, besides me)...wait, it's not unreasonable to expect a 150 avg. from the majority of our bowlers-- someone usually has a good night to offset the bad bowling. Even a 145 avg. is doable (I think it's about where we are, anyway).

    The x-factor is how well the other team will bowl. On Tuesday, those guys put on a show (even the blind guy helped).

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  2. What's your league format? How many bowlers bowl each game? Do you know how your handicaps are calculated? Is it 100%, 90%, 80%?

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  3. 5 bowlers bowl, handicap is avg. subtracted from 230, then multiplied by .90

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  4. Well, if I am doing my calculations correctly, and I think I am, you guys had an above average night. Unfortunately, your opponent had a ridiculously good night. Your games 2 and 3 normally would be wins, but you were very unlucky. In fact, the probability of losing all three games is pretty low, only 9.3%. What that means is that if you bowled this way for 10 weeks in a row, you would only be expected to get swept one time. Sorry. Lady Luck hates you.

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  5. I knew it!!

    (that Lady Luck hates me)

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  6. Interesting stats. My gut feeling in the past has been that we will probably lose a game if we score lower than 1100 handicap, will probably win a game with a handicap score of 1150 or better, and have a 50/50 chance with a score in between. By the way, our expected score Tuesday (average + handicap) was 1094 vs games of 1072, 1116, and 1101.

    Bottom line, the other guys bowled well.

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  7. Doc,

    I like that you like my favorite posts, those that are stats heavy. 1100 makes sense. We bowl with four bowlers. You bowl with five. If you add one bowler, 1100 should be near the magic number, rather than 900, the key number for our league. If you really want to know the secret number, track handicap pin scores and wins and losses.

    Here's how I do it. I divide handicap pin scores into 20 pin intervals. I have something like 100 games for which I know win or loss and HDCP pin total. I then calculate the percentage of wins and losses for each 20 pin interval. From this, you can estimate that equation.

    -Todd

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  8. I agree with Mick; however, if we bowl average, we lose. That 1094 means a 681 series...not good enough (well, last Tuesday, nothing we could have done would have been good enough). No matter who we bowl, from the best to the worst, we have the capability to pull off a near-750 series each week.

    And we came close to the team doctor's predicted 1094. We averaged a 1096 handicap series on Tuesday (that's a 137 pgpba, about 10 or so pins below our realistic potential-- rather than theoretical potential-- on a given night).

    Of course the team is only as good as its weakest link, which just happens to be me of late. :(

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