Lies, Damn Lies, and Statistics

[Sean Pickett]

Back in January 2016 forum poster Freddie started a thread tiled “2015-16 winning percentage by goals scored”. Their simple analysis showed that teams that score 3+ goals won more games than they lost. The next day BC fan Nick Papagiorgio posted his thesis, based on a very small and select sample size, that the first team to get to 3 goals almost always wins. This led me to compile data on winning records for teams scoring the first goal and the first to score their second and third goals for both men’s DI games and NHL games for the entire 2015-16 season. I also compiled the data for the 2013-14 and 2014-15 men’s DI teams. For those three seasons there were 2,684 games in which at least one team scored 3 goals and the team to score the third goal first had an overall record of 2358-181-145 for a 0.906 winning percentage. I moved onto other thing for a few years, but during the pandemic I decided to expand my research and also make it more granular, To date I have compiled the more detailed data for 2018-19 through last weekend. For those season seasons there were 6,010 games in which at least one team scored 3 goals and the first team to score three had an overall record of 5301-416-293 for a 0.906 winning percentage.

Attendance

Pre-pandemic there had been a lot of talk about the downward trend of attendance at sporting events, including men’s college hockey. To date the average and median attendance figures (excluding exhibitions) are close to the 2018-19 and 2019-20 regular season averages.

[TABLE="class: Table, width: 139"]
[TR]
[TD="colspan: 2"]2018-19[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,896[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,502[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2019-20[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,843[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,437[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2020-21[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]155[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]374[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2021-22[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,561[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,155[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2022-23[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,874[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,393[/TD]
[/TR]
[/TABLE]


The current average is between the 2018-19 and 2019-20 regular season averages. The median is lower, likely due in part to St. Thomas (4 games) and Long Island (2 games) playing home games in rinks with small seating capacities. Looking at attendance for 2018-19 and 2019-20 only through the end of October shows this season ahead of 20181-19, but behind 2019-20.
The current average is between the 2018-19 and 2019-20 regular season averages. The median is lower, likely due in part to St. Thomas (4 games) and Long Island (2 games) playing home games in rinks with small seating capacities. Looking at attendance for 2018-19 and 2019-20 only through the end of October shows this season ahead of 20181-19, but behind 2019-20.

[TABLE="class: Table, width: 139"]
[TR]
[TD="colspan: 2"]2018-19[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,688[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,291[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2019-20[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]3,003[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,509[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2022-23[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]2,874[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]3,393[/TD]
[/TR]
[/TABLE]


It remains to be seen of this season attendance decrease like the 2019-20 season or increase like the 2018-19 season.

First Goal

This season the median first goal of the game has been scored at 8:37 of the first period, while the average first goal has been scored at 11:21 of the first. That’s the earliest median and average for the first goal in the regular season since 2018-19, when the median was 8:00 and the average was 11:21.

[TABLE="class: Table, width: 139"]
[TR]
[TD="colspan: 2"]2018-19[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]8:00[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]11:21[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2019-20[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]8:44[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]12:18[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2020-21[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]8:50[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]11:46[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2021-22[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]8:45[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]12:04[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2022-23[/TD]
[/TR]
[TR]
[TD]Median[/TD]
[TD]8:37[/TD]
[/TR]
[TR]
[TD]Average[/TD]
[TD]11:21[/TD]
[/TR]
[/TABLE]


Scoring

Another stat that has been discussed a lot is overall scoring per game. This season the current average is 5.86 goals per game. The average goal differential per game this season is currently 2.46 goals per game, the widest margin over the past 5 seasons:

[TABLE="class: Table, width: 139"]
[TR]
[TD="colspan: 2"]2018-19[/TD]
[/TR]
[TR]
[TD]Avg Goal Diff[/TD]
[TD]2.17[/TD]
[/TR]
[TR]
[TD]Avg GPG[/TD]
[TD]5.59[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2019-20[/TD]
[/TR]
[TR]
[TD]Avg Goal Diff[/TD]
[TD]2.22[/TD]
[/TR]
[TR]
[TD]Avg GPG[/TD]
[TD]5.54[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2020-21[/TD]
[/TR]
[TR]
[TD]Avg Goal Diff[/TD]
[TD]2.36[/TD]
[/TR]
[TR]
[TD]Avg GPG[/TD]
[TD]5.73[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2021-22[/TD]
[/TR]
[TR]
[TD]Avg Goal Diff[/TD]
[TD]2.36[/TD]
[/TR]
[TR]
[TD]Avg GPG[/TD]
[TD]5.68[/TD]
[/TR]
[TR]
[TD="colspan: 2"]2022-23[/TD]
[/TR]
[TR]
[TD]Avg Goal Diff[/TD]
[TD]2.46[/TD]
[/TR]
[TR]
[TD]Avg GPG[/TD]
[TD]5.86[/TD]
[/TR]
[/TABLE]


So, while scoring has increased, it appears that all of that increase has been by the winning teams, while the losing teams have seen a slight decline in scoring.

Winning Predictors

As I mentioned in my opening paragraph, I am currently compiling a fair amount of data regarding games. Using the first team to 3 in over 90% over 7+ seasons, but so far this season it is currently at 94% (179-9-5). It appears to be due to several factors: 1) more teams are not losing the lead this season. After being around 82% the previous four seasons it is currently at 85.5%; 2) when the both teams score at least 3 goals the teams doing so first have a 33-9-5, 0.755 record, well above the 8 season record of 988-416-293, 0.669; and 3) Over the eight seasons both teams reached 3 goals in 22.8% of all games, but this season both teams have done so in just 20.7% of games played to date.


I’m also now compiling data on other benchmarks as well. Here are some records through last weekend:

[TABLE="width: 264"]
[TR]
[TD="class: xl63"]First goal[/TD]
[TD="class: xl66"]156-55-15[/TD]
[TD="class: xl63, align: right"]0.704[/TD]
[/TR]
[TR]
[TD="class: xl63"]First to 2[/TD]
[TD="class: xl66"]184-26-12[/TD]
[TD="class: xl63, align: right"]0.856[/TD]
[/TR]
[TR]
[TD="class: xl63"]First to 3[/TD]
[TD="class: xl66"]179-9-5[/TD]
[TD="class: xl63, align: right"]0.94[/TD]
[/TR]
[TR]
[TD="class: xl63"]First to 4[/TD]
[TD="class: xl66"]133-2-4[/TD]
[TD="class: xl63, align: right"]0.971[/TD]
[/TR]
[TR]
[TD="class: xl63"]First to 5[/TD]
[TD="class: xl66"]83-1-2[/TD]
[TD="class: xl63, align: right"]0.977[/TD]
[/TR]
[TR]
[TD="class: xl63"]2-0 lead[/TD]
[TD="class: xl66"]106-11-9[/TD]
[TD="class: xl63, align: right"]0.877[/TD]
[/TR]
[TR]
[TD="class: xl63"]3-0 lead[/TD]
[TD="class: xl66"]60-2-4[/TD]
[TD="class: xl63, align: right"]0.939[/TD]
[/TR]
[TR]
[TD="class: xl63"]4-0 lead[/TD]
[TD="class: xl66"]43-0-2[/TD]
[TD="class: xl63, align: right"]0.978[/TD]
[/TR]
[TR]
[TD="class: xl63"]5-0 lead[/TD]
[TD="class: xl66"]21-0-0[/TD]
[TD="class: xl64, align: right"]1.000[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]When scoring to take a[/TD]
[/TR]
[TR]
[TD="class: xl63"]2-1 lead[/TD]
[TD="class: xl66"]77-15-3[/TD]
[TD="class: xl63, align: right"]0.826[/TD]
[/TR]
[TR]
[TD="class: xl63"]3-2 lead[/TD]
[TD="class: xl66"]37-5-1[/TD]
[TD="class: xl63, align: right"]0.872[/TD]
[/TR]
[TR]
[TD="class: xl63"]4-3 lead[/TD]
[TD="class: xl66"]18-1-0[/TD]
[TD="class: xl63, align: right"]0.947[/TD]
[/TR]
[TR]
[TD="class: xl63"]5-4 lead[/TD]
[TD="class: xl66"]5-0-1[/TD]
[TD="class: xl63, align: right"]0.917[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]When a team’s largest lead is[/TD]
[/TR]
[TR]
[TD="class: xl63"]1 goal[/TD]
[TD="class: xl66"]38-51-9[/TD]
[TD="class: xl63, align: right"]0.434[/TD]
[/TR]
[TR]
[TD="class: xl63"]2 goals[/TD]
[TD="class: xl66"]54-9-5[/TD]
[TD="class: xl63, align: right"]0.831[/TD]
[/TR]
[TR]
[TD="class: xl63"]3 goals[/TD]
[TD="class: xl66"]52-2-2[/TD]
[TD="class: xl63, align: right"]0.946[/TD]
[/TR]
[TR]
[TD="class: xl63"]4 goals[/TD]
[TD="class: xl66"]38-1-2[/TD]
[TD="class: xl63, align: right"]0.951[/TD]
[/TR]
[TR]
[TD="class: xl63"]5+ goals[/TD]
[TD="class: xl66"]29-0-0[/TD]
[TD="class: xl64, align: right"]1.000[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]When leading[/TD]
[/TR]
[TR]
[TD="class: xl63"]After 1[SUP]st[/SUP][/TD]
[TD="class: xl66"]120-32-12[/TD]
[TD="class: xl63, align: right"]0.768[/TD]
[/TR]
[TR]
[TD="class: xl63"]After 2[SUP]nd[/SUP][/TD]
[TD="class: xl66"]167-14-9[/TD]
[TD="class: xl63, align: right"]0.903[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]When scoring first goal[/TD]
[/TR]
[TR]
[TD="class: xl63"]In 1[SUP]st[/SUP] 5 min[/TD]
[TD="class: xl66"]47-13-1[/TD]
[TD="class: xl63, align: right"]0.779[/TD]
[/TR]
[TR]
[TD="class: xl63"]After 5 min[/TD]
[TD="class: xl66"]109-42-14[/TD]
[TD="class: xl63, align: right"]0.703[/TD]
[/TR]
[TR]
[TD="class: xl63"]When scoring[/TD]
[TD="class: xl67"] [/TD]
[TD] [/TD]
[/TR]
[TR]
[TD="class: xl63"]A powerplay[/TD]
[TD="class: xl66"]143-96-9[/TD]
[TD="class: xl63, align: right"]0.595[/TD]
[/TR]
[TR]
[TD="class: xl63"]Shorthanded[/TD]
[TD="class: xl66"]30-7-3[/TD]
[TD="class: xl63, align: right"]0.788[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]Winning faceoffs by[/TD]
[/TR]
[TR]
[TD="class: xl63"]21+[/TD]
[TD="class: xl68"]7-4-1[/TD]
[TD="class: xl63, align: right"]0.625[/TD]
[/TR]
[TR]
[TD="class: xl65"]11-20[/TD]
[TD="class: xl66"]22-13-2[/TD]
[TD="class: xl63, align: right"]0.622[/TD]
[/TR]
[TR]
[TD="class: xl65"]1-10[/TD]
[TD="class: xl66"]79-73-12[/TD]
[TD="class: xl63, align: right"]0.518[/TD]
[/TR]
[TR]
[TD="class: xl69, colspan: 3"]And finally[/TD]
[/TR]
[TR]
[TD="class: xl63"]Home team[/TD]
[TD="class: xl66"]131-79-16[/TD]
[TD="class: xl63, align: right"]0.615[/TD]
[/TR]
[/TABLE]


Pulling the Goalie

I’ve also started compiling data on pulling the goalie at the end of the game. I’m not including when goalies are pulled on a delayed penalty, as the penalized team usually can’t get an empty net goal (although UML did against BU once due to sloppy puck control). My data may not be 100% accurate, but hopefully it is close. Over the past 5 seasons the goalie has been pulled 2,423 times. In those games an extra attacker goal has been scored 407 times (16.8%), while an empty net goal has been scored 1,055 times (43.5%). In 1,285 games the goalie was pulled when trailing by a goal and in just 158 of those (12.3%) was the game tied up. In 871 games the goalie was pulled when trailing by 2 goals and in just 15 of those (1.7%) was the game tied up. In 245 games the goalie was pulled when trailing by 3 goals and in just 3 of those (1.2%) was the game tied up. Finally, in 20 games the goalie was pulled when trailing by 4 and in none of those games was it tied up.

Sean

 

[giwan]

Great data, hate to ask BUT any chance of knowing what time those goalies got pulled? Somewhere I read that pulling the goalie earlier showed more benefits.

 

[Patman]

Stuff like this is skewed by differential talent, in other words, team strength varies wildly. if you're looking at something more inherent to the sport with a larger data set i'd look at NHL data. There's a bit of chicken and egg, good teams are more likely to score goals. They score goals they win. I mean, duh of course. However, when you have a larger spread between teams the better teams will score more often so what is inherent to the sport when looking at two equal teams vs what's inherent to the sport due to disparate talent? Well, that's not so separable. In fact, it is never separable.

But that's why, if I'm not going to idealize by model, I'd be happier to use pro-sports data.

That being said, even using model ideals, 3 goals is a hard one to overturn. Last time I looked average goal rates in the NHL were in the 2.4-2.6 range per team. College was dropping but it was in the 2.8-2.9 range.

----

edit: some further tinkering

Idealized model (Poisson random draw), 60 minute game whoever scores 3 goals first is estimated to be a winner 85.2% at a Goal per team rate of 2.5 (5.3% loss 9.5 tie). 2.9 goals per team its like 82.8% (6.8% loss, 10.3% draw). Again, equal teams, Poisson model, no overtime, etc.

So I'd say it exceeds model. I even looked at an unbalanced split (2.9 times 1.5 and 2.9 divided by 1.5). Bumps up to 88.9 for a win and 6.4 for a tie. Again, model, so on so forth.

I'd take this to mean that "first to three" probably exceeds what we'd expect to happen with a standard probability model. Then again, I always thought psychology plays a hand and teams will play differently with a 3 goal lead and a good team can just choke you away. Simple probability models don't deal with change in strategy. Drop the goal scoring rate for both teams via intentional strategy and comebacks become hard.

 

[Patman]

Great data, hate to ask BUT any chance of knowing what time those goalies got pulled? Somewhere I read that pulling the goalie earlier showed more benefits.

Probability models suggest pulling the goalie very early is a the right strategy but you have to deal with those assumptions. Even so, if you make the scoring rate something ridiculous... say start at 3 per side per game and then bump it up to say 4 for you and 16 for them... then you are still better off pulling with 5 or more minutes to go.

I never got around to running the full simulation and thought experiment and everything boils down to assumptions but there is model-based evidence. The problem is that Monte Carlo simulation is needed and estimating the time where the two strategies (goalie pull vs not) equalizes is more an art than anything else. Mostly because the strategy does switch back once you score or may further switch if you score in your favor at equal strength.

With hockey of course there's some obvious things you don't want to do like play with the goalie pulled on an in-zone face off. However, there is some indications that it might be worth it and scoring on an empty net is not as easy as it seems.

In the end its the coaches that will play chicken with that idea, but i think they've been playing more to the "out" earlier recently... 2, 2:30. where as earlier it'd be more like 1:30. Now what I'm proposing is something far more radical like 7-10 minutes left in play.

The simulation isn't too bad. The problem is creating charts and graphics for the propositional situations and so on. Expected wins and all that other bullcrap. It was never worth the effort to put it together when its all modelling assumption.

edit: I remember back in the day finding the empty net goal rate for the NHL and I think it was something like 16. Don't hold me to it. I dont remember where I got that data and it could be 15 years ago