Several
years ago, the NHL changed their system of awarding standings points. In 19981999 and before, teams got 2 points
for a win, 1 point for a tie, and 0 points for a loss. But starting in 19992000, teams who lost in
overtime nonetheless received one point.
This meant
that some games would be worth more total points than others. Games won in overtime would be worth 3
points (to the two teams combined), while all other games would only be worth 2
points.
In the
first few years of this system, not all overtime games resulted in a
winner. From 199900 to 200304, about
47% of overtime games ended in a victory.[1] And so, in those seasons, games tied after
three periods awarded about 2.5 points to the two teams – three points when the
game was won, and two points when the game ended in a tie.
Starting in
200506, the league instituted a shootout for games that were tied after
suddendeath overtime. That meant that,
now, 100% of overtime games ended in a victory for one team, and so three
points would be awarded for all overtime games.
A summary:
Seasons

Points awarded for nonOT games

Points awarded for OT games

199899 and earlier 
2 
2 
19992000 to 200304 
2 
2.5 
200506 and later 
2 
3 
With the
new system, it would be in every team's interest to play a lot of overtime
games. Currently, a team which loses as
many OT games as it wins would capture 1.5 points for each such game. To match that in nonovertime games, the
team would have to win 75% of its nonovertime games – and hardly any teams are
that good. Even back when OT games were
worth only 2.5 points, a nonOT team would have to have a .625 winning
percentage to match the points of an average OT team.
So almost
all teams, even the best ones, have a strong incentive to play as many overtime
games as possible. So, in every NHL
game, both teams should adjust their strategy to try to get the game to OT if
at all possible – unless, of course, they are so dominant that they feel they
have at least a 75% chance of winning in regulation.
That
doesn't necessarily require collusion between the coaches. If the game is tied in the third period,
both teams could independently settle on a strategy of slowing the game down –
taking longer to move the puck out of their own zone when unchallenged, for
instance. They will also be less
inclined to take risks. For instance,
suppose the game is tied with thirty seconds to go, and team A has the puck
deep in team B's zone. The puck comes
up the boards towards the blue line, and A's defenseman has to decide whether
or not to pinch. Suppose if he does
pinch, A has a 10% chance of scoring – but, at the same time, B has a 5% chance
of turning the play into a 2on1 goal.
Without the extra point for overtime, it's a chance worth taking: A's
expectation would go from 1 point to 1.05 points. But, with overtime, the expectation would go from 1.5 points to
1.475 points:
Result 
Probability 
Points 
Expectation 
A scores 
.10 
2 
0.2 
B scores 
.05 
0 
0 
Overtime 
.85 
1.5 
1.275 
Total 


1.475 
Basic
economics decrees that people respond to incentives. So we would expect to see teams independently pursue strategies
to increase their expected standings points – the effect of which would be to
increase the proportion of games that go into overtime.
Does the
record support the hypothesis?
Kind
of. Here is the historical percentage
of games that have gone into overtime:[2]
Season 
Games 
OT games 
Percentage 
199798 
1067 
211 
.198 
199899 
1107 
222 
.201 
19992000 
1148 
249 
.217 
200001 
1230 
262 
.213 
200102 
1230 
265 
.215 
200203 
1230 
310 
.252 
200304 
1228 
307 
.250 
200506 
1225 
281 
.229 
200607 
1127 
259 
.230 
The three
groups of seasons (no extra point for OT, no shootout, shootout) are set off
with bolding.
There
appears to be clear evidence of an increase in overtime games with the
beginning of the extra point in 19992000.
Indeed, the two earliest seasons, the ones without the extra point, have
the lowest proportion of OT games of all nine seasons. The chance of this happening randomly is 1
in 36.
If I run a
regression on the "percentage" column, against only a single
indicator variable for whether or not the extra point is awarded for an OT
loss, the results are significant at p=.04.
And, if I
divide the data into two groups – the first two lines in one group, and the
other seven in another – and run a ttest on the averages, the Zscore is 7.74,
which means the probability of this occuring by chance is pretty much zero.
So there is
clear evidence that the introduction of the extra point in OT resulted in more
overtime games, just as the economics would predict.
But what
about the introduction of the shootout?
That had as large an effect on total points as the introduction of the
extra point – the first rule change added half a point, and the shootout added
another half point. You'd expect the
teams' reaction to the shootout to be similar – even more conservative play,
and even more overtime games.
But the opposite
happened. In 200506, the first year of
the shootout, the proportion of overtime games actually dropped from the
previous season (which was actually two years earlier because of the
lockout). In fact, in the two seasons
before the shootout, about 25% of games were regulation ties – but in the two
seasons after, it was only 23%. What's
going on?
First,
notice that the 200203 and 200304 seasons had a very high proportion of OT
games compared to the seasons before.
Was there a rule change in 2002 that caused this to happen?
Kind of –
in those two seasons, and the one before, goals scored were at historic
lows:
Season 
Goals per game (OT/SO not included) 
Percentage of games going to OT 
199798 
5.31 
.198 
199899 
5.20 
.201 
19992000 
5.46 
.217 
200001 
5.53 
.213 
200102 
5.16 
.215 
200203 
5.20 
.252 
200304 
5.11 
.250 
200506 
6.01 
.229 
200607 
5.75 
.230 
You'd
expect that the fewer goals scored, the closer the games would be, and the more
tie games after three periods. Using
only the middle five rows, to keep the rules constant, I ran a regression of
overtime percentage on goals per game.
The
rsquared was .44, which was not statistically signficant (p=.23). However, the relationship was strong in a
hockey sense  every additional tenth of a goal scored reduced the percentage
of OT games by seven thousandths (.007).
Let's assume that's true regardless of which of the three OT rules is in
effect, and normalize every row to 5.5 goals per game:
Season 
Actual goals per game (OT/SO not included) 
Percentage of games going to OT if GPG were 5.5
using 7% adjustment factor 
199798 
5.31 
.185 
199899 
5.20 
.180 
19992000 
5.46 
.214 
200001 
5.53 
.215 
200102 
5.16 
.191 
200203 
5.20 
.231 
200304 
5.11 
.223 
200506 
6.01 
.265 
200607 
5.75 
.247 
Now, we
have an obvious effect for both rule changes.
The introduction of the extra point in 1999 raised the proportion of
overtime games from about 18% to about 21%.
Then, the introduction of the shootout bumped it up even further, to
about 26%.
I do have
to say, though, that I'm not 100% sure the adjustment is kosher. The "7%" figure has a standard
error of 4.5 percentage points, so it's not very precise (as evidenced by the
fact that it's not statistically significant from zero). And it does seem kind of high.
And other
research gives us reason to believe it's not very accurate at all.
In 2004,
Alan Ryder wrote a study called "Poisson
Toolbox," in which he examined what happens when you assume that teams
score goals according to the Poisson distribution. On page 9, Ryder gives the formula for computing the probability
of a tie game. For teams scoring a
combined 5 goals per game each, the probability is 18.4%. For teams scoring 6 goals per game, the
chance is 16.7%. By this logic,
increasing by one goal per game should create 1.7% more overtime games, not 7%
as we found.
However,
there are reasons we can't take the Poisson method at face value.
First,
18.4% and 16.7% seriously underestimate the actual proportion of regulation
ties actually observed, which suggests that goals may not be close enough to
Poisson for the 1.7% result to hold.
Second, the
result assumes two equal teams. In real
life, teams are often mismatched. That
should reduce the number of ties – but the observed percentage of overtime
games goes the other way – it's more, not less, than predicted.
What should
we do? Let's start with the 18.4% and
16.7% numbers. The real life numbers
appear to be in the low 20s. So let's
bump up both numbers by multiplying them by 1.25. That gives us 23% and 20.9%.
That's a
2.1 percentage point adjustment – still much less than the 7% from the little
regression.
Just for an
example, let's look at what happens if we assume a 2.5% adjustment factor. 2.5% is exactly one standard deviation away
from 7%; also, it's close to the 2.1% estimate from the Poisson method. (More importantly, I have the calculations
already done for 2.5% as I write this, and I'm too lazy to recalculate.)
Season 
Goals per game (OT/SO not included) 
Percentage of games going to OT if GPG were 5.5
using 2.5% adjustment factor 
199798 
5.31 
.193 
199899 
5.20 
.194 
19992000 
5.46 
.216 
200001 
5.53 
.214 
200102 
5.16 
.224 
200203 
5.20 
.245 
200304 
5.11 
.240 
200506 
6.01 
.242 
200607 
5.75 
.236 
If 2.5% is
the correct factor, then we have no evidence that the shootout increased the
number of regulation ties – the postshootout numbers look similar to the two
closest prelockout seasons. But there
is still strong evidence that the extra point did increase the incidence of
overtime games.
Regardless,
we need to do a bit more research to figure out the best adjustment factor –
perhaps by looking at more seasons, or subsets of seasons.
Even if we
did that, though, there would be other contributing factors to consider. For instance, at the same time the NHL
instituted the shootout in 200506, they announced more stringent enforcement
of clutching and grabbing. This
resulted in more penalties, which is presumably part of the reason goal scoring
rose.
However,
all else being equal, more penalties should reduce the number of regulation
ties. That's because, in the absence of
penalties, both teams have an incentive to keep the game slow to take it to
overtime. But if one team gets a man
advantage in a tie game late in the third period, they have a good chance to
secure their full two points without overtime – and at very little risk,
because the chance of the other team scoring shorthanded is slim.
So the
tendency of teams to play conservatively because of the shootout might be
counterbalanced by an increase in aggressive, riskfree manadvantage
play. I don't know how big an effect
this would be – I'd guess it's fairly small – but it's something you'd have to
consider.
Obviously,
any incentive to shoot for a regulation tie would occur only if the game is
already tied. If a team is ahead, it
wants to stay ahead; if behind, it wants to catch up. All of the change in behavior related to overtime should be
observed if, and only if, the game is tied.
It would
also seem that the effect should be higher in the third period. Overtime is much more likely in a tie game
with ten minutes to play than a game with fifty minutes to play. If the change in team play is proportional
to the probability of achieving the incentive, we should see a stronger effect
later in the game.
Here's a
chart of how often games went into overtime, counting only games that were tied
after forty minutes:
Season 
Percentage of games tied after two periods 
Percentage of those games going to OT 
199798 
.207 
.389 
199899 
.220 
.348 
19992000 
.231 
.408 
200001 
.234 
.389 
200102 
.241 
.392 
200203 
.228 
.434 
200304 
.237 
.457 
200506 
.237 
.372 
200607 
.222 
.408 
The results
are mixed, and interesting. For the
first two years of the study, the effect seems to exist for the entire
game. There are fewer thirdperiod ties
going to OT, but there are also fewer thirdperiod ties in general. So teams seem to have adjusted their play
all through the game, not just in the third.
But, now,
check 200203 and 200304. In those
seasons, there was a very high proportion of thirdperiod ties going to
overtime. But the number of third
period ties was pretty average. Was
there some rule change in those two years that affected only the third
period? One possibility is that
referees those years were exceptionally reluctant to call thirdperiod
penalties in close games, and that kept scoring down.
But the data
don't support that:
Season 
Percentage of twoperiod tie games going to OT 
Goals scored in third period of games tied after two
periods 
199798 
.389 
1.570 
199899 
.348 
1.463 
19992000 
.408 
1.570 
200001 
.389 
1.635 
200102 
.392 
1.470 
200203 
.434 
1.544 
200304 
.457 
1.567 
200506 
.372 
1.855 
200607 
.408 
1.880 
The number
of third period goals in 200203 and 200304 are average – but the percentage
of regulation ties is very high.
So I'm not
sure what to think. There is clear
evidence that teams skated to more regulation ties starting in 19992000, when
they received the extra point for an overtime loss. But, then, there was another sudden increase in overtime games in
200203, which also carried over to the next season – even though there was no
obvious change in the conditions of the game.
Finally,
the addition of the shootout in 200506 made overtime even more desirable. But there was no increase in regulation ties
at that point. In fact, there was a
slight drop, proabably attributable to the increased scoring. Adjusting for the increase, the frequency of
overtime was roughly the same as in the two previous years.
There is a
possible explanation for the absence of this second increase. The rule change of 19992000 increased the
point expectation of a tie from 1.00 to 1.25.
It's possible that teams took maximum advantage of that incentive at the
time. So, after the introduction of the
shootout, there was little else teams could do to take advantage of it.
For
instance, suppose you drop a dollar bill on the street, and you find that 99.8%
of people are willing to stop and pick it up.
Then, you drop a twodollar bill on the street. The number of willing people increases from
99.8 to 99.9%  but it's barely measurable.
Even though the changes in incentives are equal (in each case, an extra
dollar), the change in response happens only for the first incentive.
The same
could be true for overtime. When the
extra point was added in 1999, it's possible that almost every team started
slowing the play down when the score was tied,
and that they did so to the maximum possible (without being called for
delay of game). Although the subsequent
shootout rule made ties even more desirable, there was little else teams could
do, except to take slighly fewer risks.
And so, the second change in behavior was barely noticeable in the
statistics.
I'm not
sure whether or not this is the right answer, but I find it at least
plausible. I do suspect that the change
in behavior for the second incentive would have to be smaller than for the
first incentive. But not zero  I
suspect that the increase in penalties has, to some extent, counteracted the
tendency towards more ties, and if we adjust for that, we'll see a small
increase.
But that's
just a hunch.
 Phil
Birnbaum (revised 3/30/07)
[1] Before 199900, teams played 5on5 in overtime instead of 4on4, and only 2530% of overtime games ended in a goal.
[2] Data
for 200607 is to lateMarch. Total
games for prior seasons may be slightly inaccurate due to anomalies from the
data source and/or my programming. Data
from www.hockeynut.com .