THE BOOK--Playing The Percentages In Baseball

I am glad Tango brought this topic up for discussion. I never understood why the NHL shortened the OT period to 5 minutes, when they added the shootout to decide tie games. 10 minutes of overtime and then a shootout, seems like the perfect compromise. Too many games are being decided by shootouts.

They didn’t shorten the OT, it always was 5 minutes.

Right, it was always 5 minutes.

The correct number of minutes would be based on the percentage of tied games that should go to shootout, compared to the cost of making your players play more minutes.

OT wasn’t 10 minutes before the lockout?

It was ten minutes way back when; 60 years ago I think.

Oops, didn’t mean to post already.

I wonder at which point, if any, fatigue sets in.  For example, the rate of scoring may be 7.14 per 3600 seconds in a 5-minute period, but there’s also a chance that in a longer period, that rate goes down because of fatigue, right?

It sure seems that in the playoffs, the longer a game goes, the chances of it going even longer seem to increase as players begin to look like they are skating through quicksand.  Would love to see some research on thsi.

If you thought the statement about the OT being 10 minutes was stupid, how about believing that Josh Beckett won the Cy Young Award last year.  Patriot corrected me on this about a month ago. For an entire year, it never even occurred to me that Sabathia had won the Cy-Young in 2007. You think I would of somehow stumbled upon this fact by accident.

I think a tie is a legitimate sporting outcome. Why not just call it a day after 60 minutes? The game has demonstrated that both teams are relatively equal (which we know is actually true). I know there’s an argument that both teams tend to play for the tie near the end of the game, but ... I think that’s mainly an issue when there’s no incentive to win (ie both teams well out of the playoffs).

Either that, or ... award the extra point to the team with more shots on goal. That’d liven things up.

Maybe the NHL could be the first major pro league to base its standings on goal(point) differential, rather than wins and losses.

I seem to remember soccer (NASL maybe?), at some point, using goals in their standings, in addition to wins.

Correct.  For its entire history (1967 to 1984), NASL calculated its standings based on 6 points for a win, 3 points for a tie, and 1 “bonus” point for each goal scored in a game (with a maximum of 3).

The league eliminated tie games in 1975, but kept the 6 points per win and up to 3 bonus points per game, and added a bonus point for a shootout loss.

Tom,

One minor quibble - as I noted in the comments on Mirtle’s piece, the distribution of OT goals is approximately uniform, but the scoring rate is actually going up substantially as you progress through overtime (since games that have ended are no longer contributing to the total elapsed time.)

I’m just not sure how to project the goal-scoring rate from minute 5 to minute 10.  I assumed the scoring rate would continue to increase at the same rate, but we just don’t know.

Gabe,

I’m not sure I follow you.  The number of goals scored, for each slice of time, is uniform.  That’s what we care about.  It doesn’t matter that we have say 60 seconds times 100 games in the 1-minute to 2-minute slice and that we have 60 seconds times 70 games in the 3-minute to 4-minute slice.

If you can provide a concrete example, I’m sure we can work it out to both our satisfaction.

Let’s try this one:

1st minute: 10 goals in 100 games (rate=10/100 mins)
2nd minute: 10 goals in 90 games (10/90)
3rd minute: 10/80
4th minute: 10/70
5th minute: 10/60

If we extend the uniform number of goals, then no games go to a shootout.

If we fit an exponential to the data above, we end up with 12 games going to a shootout.  If we project 1-this data, we get 15.  (I actually fit an exponential to the real data, which gave a slightly different answer.)

Or do we contend that an exponential does not actually capture the change in goal-scoring rate and that we get some other distribution over time?  Your estimate of 22% would imply that.

I see your problem.  It’s not that 10 goals are scored per time slice, such that even as the number of games decreases that the number of goals is uniform.  (Is that what your data is showing?  I’d be shocked.)

Rather, it’s that the RATE (0.1 goals per game in your illustration) is constant, so that in your example, it should be:
10/100
9/90
8.1/81
etc, etc

Clearly, if you are down to 10 games, you are not going to have 10 goals scored.

The rate is per unit of time, not some gross number.