This one goes to eleven: why stats are hard

In Evan Schemenauer’s Random Thoughts article from January 8, 2018, he talks about Calgary’s offensive struggles so far this year, and how scoring fewer than ten goals will not win you many games. Then he drops this:

Graeme Perrow can probably tell us the stat, but your odds of winning a game scoring less than 10 goals must be less than 10%.

Challenge accepted.

I began writing this for my Stats Central column on IL Indoor but all I really have here are the numbers. There’s not much in the way of analysis. But I wanted to answer the call nonetheless so here we go.

From 1987 to 2017 inclusive, there were 2008 games played in the NLL. Five of those were 10-minute mini-games, so we’ll exclude those. Of the remaining 2003, only 103 of them (or 5.14%) were won by a team that scored fewer than ten goals. So that’s the answer to Evan’s question: if you can’t manage to reach double digits, you will lose almost 95% of the time.

The next logical question: how high do you have to go to win more than half of your games? Thirteen goals should do it, right? That would have been my guess, but not quite. 13 goals was enough to win 45.7% of NLL games but to get over the 50% mark (57.7%) you needed 14 goals.

So that’s it. Going by NLL history, in order to win more than 50% of your games, you need to score 14 goals.

Or do you?

No, you don’t. I’ve calculated the wrong thing. What I found above was that 50+% of games were won by a team that scored 14 goals. Did they need to score 14 goals? Not always; if the final score was 14-8, they only needed to score 9.

ElevenWe need to look at this question the other way around – how many goals did the losing team score in these games? (Warning: “expert” analysis ahead) In order to win, you need to score one more than that.

We’ll start small. In 7.2% of games, the losing team scored 6 or fewer goals. That number exactly doubles to 14.4% for 7 goals, and jumps to 25.4% for 8. The 50% mark is at 10 goals: in 53.3% of all games, the losing team scored no more than ten goals. So there’s the real answer: in order to win those 53.3%, all you needed to score was eleven.

The two “next logical question” paragraphs above (after the 95% answer and ending with “Or do you?”) I wrote while honestly thinking I’d answered the right question. But I hadn’t, I answered an entirely different question. I even thought “Wow, 14 seems high, I wouldn’t have expected that” and checked my numbers again. But the numbers weren’t the problem, the interpretation of them was. Rather than rewriting the whole article, I left all of my “reasoning” there as an illustration that reading the stats is easy but interpreting them is the real challenge.

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