9 February 2009

Shoot first...

...ask questions later?

My previous investigations into the numbers behind the history of the NHL shootout looked at the business end of the universally-popular tie-breaker - “clutch” attempts to either win it or keep it going.

This time around, my thoughts strayed to one of the strategic decisions made before stick touches puck: Shoot first or second?

By way of explanation, the home team has the option of shooting first or second - this has been the case every year of the NHL shootout except the first, 2005/06, when the road team always had to shoot first. I have seen arguments in favour of both strategies, for example:
  • Shooting (and scoring) first puts all the pressure on the second shooter
  • Shooting second means you are more likely to have the final shot to win
  • Shooters are more likely to miss than score, so you should always shoot second, since missing the first shot puts you “behind”
Naturally, I wanted to see if the numbers supported any of these arguments.

Does scoring the first shot matter that much?
The none-too-surprising answer here is “yes”. On average, if the very first shooter scores, his team wins 72% of the time, compared to only 40% of the time if he misses. The chart (of course there's a chart) below shows the record of each team when scoring or missing the very first shot of the shootout (through 8 February):

  • As you'd expect, records across the board are much better when scoring the first shot, with only a few exceptions. Most notably, Florida, Tampa Bay and Toronto have better records when missing the first shot – suggesting it would be better for them to miss the first shot on purpose...
  • Florida, in particular, have done remarkably well to lose all three of the shootouts where they have scored the very first shot
  • LA and Boston, on the other hand, have yet to lose when scoring the first shot
So, we should always go first then?
Not so fast...time for a quick lesson in conditional probability (e.g. if I start start talking about probability theory, then there is a 99.9% chance that nobody will read past this point).

The probability of the team shooting first winning can be seen as the sum of the following:
  • Probability of scoring x Probability of winning having scored
  • Probability of missing x Probability of winning having missed
The league average for scoring the very first shot is 32% (for all shots, it is slightly higher at 33%). The really intelligent among you will be able to work out that the league average for missing the very first shot is, therefore, 68%. So, we have the four numbers we need to plug into the sum above:

Probability of team shooting first winning = (0.32 x 0.72) + (0.68 x 0.4) = 0.50

So, this suggests (at a league-wide) level at least, that there is an equal chance of winning or losing if you shoot first. Meaning either everybody is wrong, everybody is right or it doesn't matter. The following chart shows the overall record of each team when shooting first and second (through 8 February):

  • Rather freakishly, the overall league record is exactly even at 282-282 when shooting first as at today's date
  • Naturally, there is quite a bit of variation around the 50% mark when looking at individual teams' records
  • Teams that seem to do significantly better shooting first (with a decent sample size) include Atlanta, Calgary, Colorado and Ottawa (although they stink either way)
  • The reverse is true for Anaheim, Chicago, Philadelphia and San Jose
  • Phoenix are unbeaten (unbeatable?) when shooting first, but have only ever done so twice
Looking at the premise that scoring or missing puts more or less pressure on the second shooter (the first opposing shooter), the numbers similarly don't support such an argument. The second shooter scores 38% of the time when the first shooter scores and 37% of the time when the first shooter misses. (I can't think of an obvious reason why the scoring percentage is higher for the second shooter than the first – or any other shooter in the first six – though.)

Do teams have any tendencies?
Yes – whether due to any historical success, superstition or something else. The chart below shows teams' records when choosing to shoot either first or second (i.e. records of the home team since 2006/07 – through 8 February):

  • Firstly, having the choice in itself does not seem to support either strategy – winning percentages are still very similar (and home teams' records are slightly below .500 since 2006/07)
  • Most teams have a fairly clear policy to shoot first – indeed, seven teams have never opted to shoot second
  • Conversely, only a handful of teams select to shoot second more often – New Jersey and Phoenix the only teams to do so every time (nothing in their overall records really supports this choice though)
Player records
Obviously, having a particularly good first shooter or good shootout goalie may justifiably lead to a tendency that the league-wide averages don't support. I'll leave any detailed player/team analysis for another decade, but FYI, the final two charts below list the best individual records when taking or facing the very first shot (minimum five attempts - through 8 February):