Attention fellow NDLS bowlers! If you were confused about your team’s ranking, you’re not alone. There is absolutely no statistical significance to the current order of teams. The way the bowling alley handled the first-week scoring was incredibly asinine, with the result that statistical rounding error determined the current “standings.”

It all revolves around handicaps, scoring averages, and odd numbers vs. even numbers. Let me try to explain.

Each player was assigned a handicap based on his or her performance last week. The handicaps are designed to give everyone an artificial first-week score of 200. So, 200 minus the player’s actual score equals their handicap. Thus, if you add a player’s handicap to his/her score in the round from which it was calculated, you get… 200. Duh!

For this reason, it makes no sense to apply handicaps retroactively to the round from which they were calculated. That’s like declaring that “10 minus 5 plus 5 equals 10,” and thinking it’s some sort of revelation. You’re adding the very same number that you just subtracted, so of course you get the number you started with!

Yet, because no one at the bowling alley seems to understand this basic math, they did exactly that — calculated the handicaps, then applied them retroactively — so hypothetically, everyone in the league should be tied. We should all have the exact same score: 200!*

But that’s where rounding error comes in.

The handicaps are based on each player’s average score. But players whose total, two-game score was an odd number have an average score that ends in .5. For example, a total score of 295 becomes an average of 147.5.

Before calculating the handicaps based on these averages, the league rounded averages ending in .5 down to the next lowest whole number. So 147.5 becomes 147, which translates to a 53 handcap (200 - 147 = 53).

That’s .5 higher than the player’s “earned” handicap of 52.5 (200 - 147.5 = 52.5).

Multiply the handicap by two (because we played two games, and the handicap was applied to each game), and a player whose total score was an odd number gets a one-point advantage over a player whose total score was an even number.

This statistical rounding error accounts for the entire difference between “good” teams and “bad” teams in the current standings. The teams that did “well” owe the totality of their success to the number of players on their team with odd-numbered scores; the teams that did “poorly” did so because they had too many even-numbered scores. It would literally have been better to have six players get scores of 1 than to have six players get scores of 200. Amazing! Idiotic!

With two rounds and six players per team, each team should hypothetically have a total score of 2400 (200 x 2 x 6). In reality, the team scores ranged from 2402 to 2405. Why? The teams with 2402 had two of their six players finish with odd-numbered scores; the teams with 2405 had five of their six players finish with odd-numbered scores.

The head-to-head matchups were in turn recalculated based on these adjusted scores. So if your team had three players with odd-numbered scores, and your opponent had four players with odd-numbered scores, you “lost,” 2404 to 2403.

And that’s what the standings are based on. A completely random statistical anomaly.

The handicaps will be fair from now on, but using them the first week made absolutely no sense. What needs to happen is, the league needs to either wipe out the first-week standings entirely, or else base the first-week results on “scratch” (no handicap) scores. I’ll be talking to the SBA and the bowling alley, and trying to make that happen. In the mean time, since the “official” standings are completely worthless, I’ll post the real standings here on this blog, once I’ve had time to do the math. :)

Note: If anyone in the league had averaged better than 200 — i.e., if someone a zero handicap — they would have done better than everyone else for reasons unrelated to rounding error. But no one did. Chris, on our team, came the closest with a 197.