If you want to know how unusual yesterday's comeback by Newcastle against Arsenal was, consider the expected point value of first and second half goals.
One way to compare the point value of goals it so calculate their values depending on when they were scored. To keep the analysis simple (after today's match), I was wondering simply whether first half goals are more valuable than second half goals?
Here's one possible answer. Below are the average point values of first and second half goals over a span of five seasons (2005/06 - 2009/10) in each of the four big leagues (it's the average number of points a team won in a match when the team scored varying numbers of first and second half goals).
But looks can be deceiving, if ever so slightly. Turns out there are some small, but noticeable differences, and they occur in each of the leagues. Curiously, these differences show up when we examine the point values of no goal or 1 goal scored in the first and second halves.
No. of goals and point values (by half)0 goals: .90 v. .73 points (1st v. 2nd half)
1 goal: 1.77 v. 1.67
2 goals: 2.44 v. 2.44
3 goals: 2.84 v. 2.80
4 goals: 2.96 v. 2.96
5 goals: 3
Strangely, scoring no goals in the first half seems slightly more valuable point-wise than not scoring in the second half (.9 v. .73), and scoring a single goal only in the first half will bring more points than scoring a single goal in the second half (1.77 v. 1.67). After that, the values are very similar, if not identical. And while the values vary slightly across the leagues, the general pattern of first half goals (or 0 goals) holds across the leagues.
How do you explain this? I'm not sure, except that many more draws end in 0-0 and 1-1 than in, say, 2-2 or 3-3 or 4-4, so not scoring the first half (or perhaps scoring just one goal) appears to be a harbinger of an eventual draw. But remember that one of the things we're interested in is what the added value of a goal is; using this metric, scoring a single goal in the second half adds slightly more value than scoring a single goal in the first half (1.77 minus .9 v. 1.67-.73 or .87 for the 1st half and .94 for the second half), and scoring 2 goals in the second half, relative to only one adds more points (.77) than scoring 2 goals in the first half relative to just one (.67).
It's easy to make too much of these numbers; to me, they suggest overwhelming similarities across leagues and seasons in terms of first and second half goals. At the end of the day, they seem very much the same, if you ask me.
This brings me back to Newcastle and Arsenal. The score alone was unusual: only .26% of all matches in the past five seasons ended in a 4-4 draw (that's one quarter of one percent of all matches played in these leagues). More importantly, as you can tell from the graph above, not a single team that managed to score 4 goals in the first half failed to take 3 points from the match. So Newcastle's feat to wrest 3 (almost) certain points away from Arsenal was a real accomplishment to be proud of, statistically speaking.
But turn it around, and the day doesn't look so amazing for Newcastle either if you consider this: only one EPL team in the last five years failed to win the match when they scored 4 goals in the second half. That team was Liverpool when they came back from 4 down in the second half against none other than Arsenal on 21 April 2009. What is it with Arsenal blowing 4 goal halftime leads?
