# Some simple ice hockey math

Everybody and their dog sitters aunt is commenting on the “lousy refereeing” in last nights FIN-CZE game at the hockey world championships.

The outcome of a hockey game (or any game, really!) is a sum of many factors. Probably dozens, really. But some general grouping of them can be used to arrive to the following function:

Outcome = Home team performance + visiting team performance + refereeing + luck

Last night Czech Republic (officially the visiting team) gave a solid performance. Luck was pretty neutral as far as I saw: no weird bounces or inopportune broken sticks to speak of.

Refereeing was bad, some pretty obvious calls were missing while other shady ones were made. And maybe more significantly, it seemed to be bad with a bias.

But that doesn’t remove the first variable, home team performance! And last night, the “home” team, Finland, played bad hockey. Simple as that!

Could Finland have won, given the way they played, if the refereeing was up to par? Maybe. With some luck? Probably. But they were not “robbed the victory”. If anything, it was just made little bit more difficult for them, a difference significant enough to make a difference and to prevent them from winning with weak performance. They also could have played better, and thus made the bad refereeing insignificant enough.

Outcome of a game is a sum of many things. Refereeing, no matter how obviously and painfully bad, is just one of them.

# Finland can’t score

Every Spring few things happen here in Finland. Well, few things relating to the ice hockey world championships, that is. First it’s a general outcry over how we’re not getting anyone worthwhile on the team (we do). Then it’s the debate over goaltenders (like that matters when they’re all amazing). Then it’s complaining over how Team Finland can’t score. And then how Sweden always always always gets lucky. (I’m not even going to acknowledge the obvious puns in there.)

I’m not going to touch the Swedes (yeah, I went there, shame on me) but I did look into the whole “Finland can’t score” issue. Is it true? Or are we just biased, based on our preference of seeing Finland score more goals?

Looking at the past five tournaments (2010-2014) the average number of goals scored by a team per game is 2,73 goals. The range is from 2,46 (2010 tournament) to 2.94 (2012). The team specific averages, of course, vary quite a bit. Canada of 2012 holds the record with 4,75 goals per game in the tournament. (Disclaimer: for all the following the official score was used. So if a team won 2-1 on shootouts, it’s as if they scored 2 goals and the opponent one.)

Looking at how Finland performs, then, I compared their performance to the whole tournament (all 16 teams) and also to “TOP 7”. The “TOP 7” does not mean the top 7 teams of the tournament, but the “Big 7” if you wish, the teams that are expected to come out on top (Canada, USA, Russia, Finland, Sweden, Czech Republic and Slovakia).

And it doesn’t look too good. Finland has scored 2,74 goals per game during the five tournaments. The range, however, is from 1,86 goals per game (2010) to 3,56 goals (2011). The overall average of the TOP 7 teams is 3.29 goals per game. In fact, the average was over 3 goals in all five years.

Of course, goals scored doesn’t mean anything, unless you consider how much everyone else is scoring. Obviously the number of goals Finland allows matters, when it comes to winning games. Over the five years, that’s 2,14 goals allowed per game. So at least we’re scoring more than allowing!

Because everything is relative, I also compared Finland’s scoring to that of other teams, and calculated Finland’s ranking compared to the rest of the tournament (other 15 teams) and to the other TOP 7 teams. In three tournaments Finland ranked on the lower half of the list when looking at the goals scored per game average (13th, 9th and 9th in 2010, 2012 and 2014 respectively). In 2011, the year we won, mind you!, Finland ranked 3rd. And in 2013 our 2,90 goals per game average got us on 5th place.

But surely there are some flukes, right? Norway scoring with every second shot against Italy or something? Well, yes, Norway did have a scoring percentage of 15,84 in the 2012 tournament. But mostly Finland’s getting beaten by the TOP 7 teams. 4 out of 5 times we’re on the bottom half of TOP 7 in terms of goals scored per game average. The only year we were not was 2011 again, when we were 3rd, both overall and in TOP 7 ranking. In 2010 we ranked last (7th), as well as in 2012. 2013 was a good year, only 4th, whereas a year ago we were 6th again.

So yes, it would seem that Finland cannot score. At least relative to other teams, and more specifically to the other “big” teams.

Of course one can look at the issue of scoring from the point of view of efficiency. Is it that Finland cannot score, or that they don’t try that much? That is, are they shooting as much as everybody else?

So I looked at the shooting percentage, and also the number of shots taken. For simplicity (read: I was getting hungry) I only looked at the TOP 7 teams. Mind you, there seems to be no relationship between how much you shoot and how well you shoot. Teams with high number of shots have both high and low shooting percentages, as do teams with low numbers in shots taken.

It it truly heartening to read. Compared to the TOP 7 teams, Finland’s shooting percentage is below average on every single year except 2011 (I think we can all agree that was an exceptional year) and even then we merely managed 2nd! In both 2010 and 2012 we were worst of the TOP 7, and in 2014 we were 5th. 2013 and a scoring efficiency of 9,54 ranked Finland 4th. Compared to the whole tournament, Finland ranked in the lower half 3 times out of 5, and the highest was 4th (you guessed it! In 2011!)

But Finland isn’t helping its cause. On average, over the last five tournaments, Finland has shot at goal 32,14 times per game. And every year except 2010 Finland has shot below TOP 7 average of shots per game. The ranking, should you be interested, are 2nd for 2010, and then 3rd, 5th, 5th and 7th chronologically from 2011 to 2014. (The average for 2011 was 35,99 shots, boosted by Canada’s impressive 44,86 shots per game, and Finland managed 35,78 so that was at least very close to the average.)

So I guess the public outcry is right. Finland can’t score. Good thing we have amazing goalies!

p.s. In case you were wondering about the 2015 tournament, Finland has so far scored 3,17 goals per game (19 goals in 6 games). That gives us the rank of 5th both overall and within the TOP 7 teams. The overall average is 2,17 goals per game and the TOP 7 average 4,05 goals per game. That does not include today’s games.

Edited: May 14th, added the years for the second to last paragraph that were missing after the word “chronologically”. Sorry about that bit of confusion.

# Does the NHL even know what it’s doing?

Earlier this month London School of Economics blog ran a post by Asit Biswas and Julian Kircherr about the disconnect in information between academia and general public, including policy makers. The problem is two-fold: On one hand, the way a scholar’s merits are measured purely by the amount of publishing in peer-reviewed journals, and on the other, how people outside of academia aren’t accessing the information.

Many scholars aspire to contribute to their discipline’s knowledge and to influence practitioner’s decision-making. However, it is widely acknowledged practitioners rarely read articles published in peer-reviewed journals. We know of no senior policy-maker, or senior business leader who ever reads any peer-reviewed papers, even in recognized journals like Nature, Science or The Lancet.

And they continue:

First of all, most journals are prohibitively expensive to access for anyone outside of academia. Even if the current open-access-movement becomes more successful, the incomprehensible jargon and the sheer volume and lengths of papers (mostly unnecessary!) would still prevent practitioners (including journalists) from reading them.

But, hope endures. Those in academia are, albeit slowly, taking to writing op-eds and blogs to provide the rest of the world easier access to the discussion. Is the rest of the world meeting them half-way?

Now, I don’t know if anyone in the National Hockey League is reading academic journals. I don’t know if publications such as Journal of Sports Economics has ever crossed the desk of anyone in the league. Maybe so. But from what I can tell, they certainly didn’t read the article “The “Second” Season: The Effects of Playoff Tournaments on Competitive Balance Outcomes in the NHL and NBA” by Neil Longley and Nelson J. Lacey (JSE, Volume 13, Number 5, October 2012).

Or if they did, they did not understand it.

Longley and Lacey studied the extent playoffs rearrange the regular season standings and find the “the natural reconfiguring effect of playoffs can be further enhanced by the choice of playoff structure employed by a league” (p.473). Tournaments, such as the playoffs in a league, can be thought to have objectives such as “delayed confrontation” and “sincerity rewarded”. Delayed confrontation simply means that the tops seeds meet as late in the tournament as possible, and sincerity rewarded is the way top seeds are given more favorable first-round match-ups.

In the article Longley and Lacey compare the fulfillment of these objectives under different tournament structures. The 16 teams making the playoffs are all given a quality measure Q usually measured by total points, such that the best team is of quality Q1, the second best Q2, and so on to Q16. Depending on the tournament structure, the teams are seeded, so that the team in first place is seed 1 (S1), the second-place team S2, and so on to S16.

League Pooling, or the “stationary” playoffs

The simplest case is that of league-wide pooling, the system used for example in Finnish hockey. The teams are all ranked together as one group, and Q1 is seeded as S1, Q2 as S2 and so on. The playoff match-ups are then assigned so that S1 plays S16, S2 plays S15 and so on.

Under league pooling, then, the best team in the league always faces the 16th best team, the second-best the second-poorest etc. This system “provides the maximum reward for the best teams” (sincerity rewarded) and has the “greatest likelihood of preserving the regular season ordering”. The likelihood of upsets is the lowest under league pooling.

Conference pooling

In conference pooling the teams are divided to two conferences (A and B), and 8 teams from both conferences make it to the playoffs. Teams are seeded within conference, so that the highest seeded team in conference A (S1a) plays S8a, S1b plays S8b, S2a plays S7a, and so on.

Now teams opponent depends on the quality of the team (Q, determining how high the team is seeded) but also on the quality of the other teams in the conference. Assuming random assignment to conferences, 12,870 different combinations of teams in two conferences exist.

Notably, random assignment does not mean teams teams are drawn out of a hat with “Okay, and Minnesota will be playing in the Eastern Conference this year”. It simply means that the allocation of teams to conferences does not depend on their quality. So in effect the team qualities are assigned at random.

For example, let’s say the playoff teams in conference A are Q1, Q2, Q3, Q6, Q9, Q10, Q12, and Q13. So conference B has Q4, Q5, Q7, Q8, Q11, Q14, Q15, and Q16. The conferences look, at a glance, relatively even, as both conferences have good and poorer teams in the mix. Yet, as the playoffs are played within conference, each team in A has a less favorable matchup than they would have under league pooling! Q1 plays Q13 instead of Q14, Q2 plays Q12 instead of Q13, and so on.

Longley and Lacey took the 12,870 different conference allocations and calculated the probabilities of each potential matchup under conference pooling. For example, whereas Q1 faced Q16 for sure (100% probability) under league pooling, now the probability for that is only 46.7%. There is even a very small but positive probability Q1 faces Q8 in the first round (if all Top 8 teams are in the same conference).

When the expected matchups are calculated, “Q1 to Q8 all fare worse under a conference-pooling system” and all 8 lowest quality teams  gain. Conference pooling, then, “should increase the likelihood of first round “upsets””, thus “having a good regular-season is less rewarded under a conference-pooling system”. (p. 484)

Divisional pooling

What if conferences are broken down even further? The NHL did this for 82-93 period. Four divisions, with Top4 in each advancing to intradivisional first round, with S1 playing S4, S2 playing S3 in each division.

Assuming random allocation of teams/quality, as above, there are 1,820 different combinations of teams for each division. Again, Longley and Lacey calculated the probabilities of each matchup occurring. Now the odds of Q1 facing Q16 is 0.200. (Remember, it was 100% under league pooling, and 0.467 under conference pooling.) And while highly unlikely, it is possible (0.2%) Q1 could be facing Q4!

The expected matchup for Q1 goes from Q16 under league pooling to Q15 under conference pooling to Q13 under divisional pooling. Overall, the divisional pooling compresses even further the first-round matchups, benefiting the lowest quality teams.

Modified conference pooling

This is the system used in the NHL (94-98) and NBA (84-04). Two conferences, both with two divisions. Top 8 in each conference are seeded just like under conference pooling, except that the first-place teams in the two divisions are automatically seeded S1 and S2 in the conference.

This means, that in extreme cases, as Longley and Lacey point out, Q15 could end up S2 in its conference. (If Top 6 in conference are all in same division, so Q15 wins its division.) This would mean that Q15 would face Q14 in the first round.

The expected playoff matchups are slightly more complicated to calculate, so I won’t go through it. But suffice it to say that while the modification has no effect on Q1 or Q16, it does impact other teams, in general favoring the poorer teams. This is because it provided them with a possibility to “jump up” in the seeding, like Q15 in above example.

So how did it go, really?

Longley and Lacey looked at the different systems as they have been used in NHL and NBA, and found the results conform very closely to the predicted outcomes. Under divisional pooling the correlation was +0.86 with the NHL data. Modified conference pooling had correlations of +0.95 for NHL and +0.99 for NBA.

Few points from the actual data that are interesting:

• under divisional pooling, Q1’s average opponent was 12.75. The predicted expected opponent was Q13. Both are well above the Q16 of league pooling.
• also under divisional pooling, Q16’s opponent was, on average, 5.75. (Under league pooling Q1). Q10, on the other hand had the 4th favorable matchup in the league (10.17), which is better than those of Q4, Q5, Q6, Q7, Q8 or Q9! And Q14 faced a more favorable opponent than Q6, Q7 and Q8 above it.
• under divisional pooling, both matchups Q2 vs Q3, and Q14 vs Q15 occured.
• under modified conference pooling, Q12 vs Q13 happened in both leagues.
• in the NBA, under modified conference pooling, and over 21 years, the average first round matchup for Q9 was more favorable than for Q6, Q7 and Q8.

But it evens out in the end, right?

Yes, it does, a little. And that’s only if you make it through the first round. Longley and Lacey calculated the cumulative probabilities of Q1 advancing through different rounds in the playoffs under different pooling systems.

Probability of Q1 winning 2 rounds under divisional pooling is 0.4046, whereas under league pooling it is 0.4775. That is, the highest quality team is 15.27% less likely to win two rounds in the playoffs under divisional pooling than under league pooling!

Three rounds of wins have probabilities of 0.2346 under divisional pooling and 0.2760 under league pooling. And the probabilities of Q1 winning the championship are 0.1284 under divisional pooling and 0.1460 under league pooling. That means that under divisional pooling the Q1 is 12.05% less likely to win the championship than under league pooling!

The difference does even out somewhat, because as the team advances it is now facing the poorer teams that made it through to further rounds. But it doesn’t completely disappear. In conclusion, then, Longley and Lacey state, that “different playoff tournament structures will provide different levels of advantage to the best teams”. And the further we brake the pooling, the more it favors the poorer teams.

So should we have league pooling?

Not necessarily. There are plenty of valid arguments in favor of smaller pooling, such as

• profit maximization: it makes sense, purely in terms of logistics, to have more geographically focused matchups. Travel costs, both monetary and otherwise, are an issue. There are also potentially more fan interest in regional matchups (local rivalry in a factor in fan interest) so ticket sales cold factor in here. Also in terms of visiting team fans, as far-away fans are less likely to show up.
• fan interest in upsets: people seem to like “Cinderella stories” and cheering for the underdog. Which, some could argue, is the whole point of playoffs.
• income compensation: in so far as regular season wins/standings are influenced by payroll the playoffs offer an opportunity to poorer (literally) teams to make up for weaker regular season performance. Thus it would positively influence competitive balance. Of course, under salary caps, this isn’t such a concern anymore.

But, as Longley and Lacey conclude, “less-than-stationary playoff systems can be quite ingenious in that they appear quite legitimate and fair … but at the same time these systems are actually providing a disproportionate benefit to the lower quality teams” (p. 490) Doing so, they diminish the meaningfulness of the regular season, creating incentive issues which are potentially reflected in fan interest.

Really, NHL? The divisional bracket system?

The NHL completely redid their playoff tournament structure for this season, coming up with essentially modified within-division bracket system. Which I guess I almost get, as the bracket is so very pretty, and easy to promote and sell to the fans. The whole “predict the bracket”-thing? Great! My Twitter feed was full of predictions. (And no, I’m not being sarcastic for once, I promise.)

But, if we look at the matchups, and compare them with the stationary (league pooling) version, things get interesting.

Two of the matchups actually correspond to the stationary matchups. Anaheim (Q3) plays Winnipeg (Q14) and Tampa Bay (Q5) faces Detroit (Q12).

In the Vancouver vs Calcary we’re letting them off easy. Both teams are facing a poorer opponent they would be under league pooling. Vancouver (Q8) faces Calgary (Q16). Under league pooling the matchups would be Q8 vs Q9 and Q16 vs Q1.

In the Washington vs New York Islanders series it’s the same only less so, as Washington “should” be facing Q8 and Islanders Q7. However, the series really is Q9 (WSH) vs Q10 (NYI). So both teams are facing a poorer teams than under league pooling.

In the rest of the series teams are facing higher quality teams than they would under league pooling. We have New York Rangers (Q1) vs Pittsburgh (Q15), whereas under league pooling the pairings would be Q1 vs Q16 and Q15 vs Q2.

It gets more severe as we go on. Montreal vs Ottava is now Q2 vs Q13, instead of Q2 vs Q15 and Q13 vs Q4. In the St Louis vs Minnesota series we have Q4 playing Q11, whereas under league pooling we’d have Q4 vs Q13 and Q11 vs Q6.

Finally, poor Nashville and Chicago. They’re facing each other, despite being Q6 and Q7, respectively. Under league pooling Nashville would face Q11 and Chicago Q10.

In conclusion, out of 16 teams, 4 faced who they would under league pooling, and another 4 faced a weaker opponent than their quality would suggest. That means half of the teams had a more difficult matchup than they would under league pooling.

I’d love to hear the reasoning for this change. Other than the pretty bracket with pictures and arrows and nice little boxes you can fill out.

# Quick odds for the NHL playoffs

I’ve already spent so much time lamenting the drawbacks of different ways points are given out in hockey, I’m not going to do that anymore. Nor am I going to talk about the new setup NHL has for the playoffs this season, because that’s another post, for later this week. But, the NHL playoffs are kicking off, so I decided to calculate the odds of each series.

Like with the Finnish league, I focused on the winning percentages for the teams, and, by calculating home and visiting win percentage separately, took into consideration also the home advantage. I did not include any measures to control for the strength of schedule, partially since these are, in effect, within division series.

Western Conference

* St. Louis Blues vs Minnesota Wild

The Blues have an impressive win percentage of 62.20%. Broken down to home and visiting, they have won 65.85% and 58.54% of their games, respectively. For the Wild, those same figures are 53.66% and 58.54%, which gives them an overall win percentage of 56.10%.

Based on those, and the series starting in St. Louis, the Blues should take the series with a probability of 55.70%.

* Nashville Predators vs Chicago Blackhawks

Nashville reached a win percentage of 57.32% in the regular season, winning 68.29% of their home games and 46.34% of away games. Chicago made me triple-check my figures, as they won 58.54% of their games. Over-all, home and away. 24 games won home, 24 games won as a visiting team.

The series starts in Nashville, but Chicago should take it with a probability of 50.64%.

* Anaheim Ducks vs Winnipeg Jets

Anaheim reached the same win percentage as Blues: 62.20%. Their home game win percentage was slightly above that at 63.41%, and away games slightly below at 60.98%. Winnipeg manages to win 52.44% of their games overall, with home and visiting win percentages of 56.10% and 48.78%, respectively.

No surprise then, that home-opening Anaheim wins the series with probability of 60.03%.

* Vancouver Canucks vs Calgary Flames

Vancouver, like Chicago, played equally good regardless of location, winning  58.54% of their games, be it home, away, or in total. Calgary had some fluctuation: win percentage when visiting (53.66%) wasn’t too impressive, but the home win percentage of 56.10% brought the overall win percentage to 54.88%.

That’s not enough for Calgary, though, and Vancouver should claim this Canadian series with a probability of 53.71%.

Eastern Conference

* Montreal Canadiens vs Ottava Senators

Montreal is another team that reached an overall win percentage over 60 by winning 60.98% of their games; 63.41% at home and 58.54% when on the road. Ottava, on the other hand, barely managed to break 50. Overall win percentage of 52.44% was boosted by the home win percentage of 56.10%, but brought down when the team only won 48.78% of the games when visiting.

As expected, then, Montreal should take the series, with probability of 59.10%

* Tampa Bay Lightning vs Detroit Red Wings

Tampa, another Club-60 team. Regular season win percentage of 60.98%, and home game win percentage of whopping 78.05%! Too bad they only won 43.90% of their away games. Detroit was consistent, if nothing else. Home win percentage of 53.66% and 51.22% away, combine to overall figure of 52.44%.

Tampa’s strong home game really is an advantage, and with probability of 58.34% they’ll win the series.

* New York Rangers vs Pittsburgh Penguins

Rangers won an amazing 64.63% of their games! 60.98% of home games and 68.29% of away games. Penguins, on the other hand, played weaker on the road, winning only 48.78% of the games, as opposed to 56.10% at home. Overall they won 52.44% of their games.

Despite Rangers being relatively stronger on the road than at home, and them starting the series at home, the odds are still in their favor: 61.41% probability Rangers win the series.

* Washington Capitals vs New York Islanders

Washington won 54.88% of their games this regular season: 56.10% of home games and 53.66% of away games. Islanders, on the other hand, won 57.32% of their games. Their home win percentage was 60.98% (same as Rangers, mind you!) and as a visiting team they won 53.66% of the games.

Washington may have the home advantage, but that’s not going to help them. Islanders will take the series with a probability of 51.60%

The Usual Disclaimer

As always, these are not even an analysis, there are simple exercises in probability mathematics. There are several factors that play into the outcome of a game and of a playoff series, practically none of which are used here. Not to mention, that the win percentages quoted above don’t even control for the strength of schedule. But I guess you could use these as a starting point to a more sophisticated analysis on team strengths and outcome probabilities.

# … And the Points Don’t Matter

(also known as: How Someone Needs to Stop Watching Old Whose Line Is It Anyways Episodes on Youtube)

I wrote about the shootout earlier, and asked why we need one at all. I am not a fan, I don’t think they fit the spirit of the game, and that they end the game on a sour note, regardless of the outcome. But obviously playing 6-period games like in this spring’s playoffs is also not an option during the regular season. So I ask again: why not agree to a tie?

And then I started thinking some more, about how I have both here and in the real world, complained about the unfair (in my mind at least) point schemes favoring the overtime. Why should we reward a losing team with a point for “good effort” if they keep the game close enough to make it to overtime, yet we do no such thing regarding the closeness of the game on regular time. Is a game that ends 0-1 on overtime really that much closer than a game that ends 0-1 on regular time? What about games that end 0-1 and 0-7, both on regular time? Isn’t the first game much closer than the latter? Yet the losing team gets no extra point there! So on one hand we’re saying a win is a win, no matter the goal difference. But then on the other hand we’re rewarding teams for “keeping it tight” and for putting up a good fight. Doesn’t seem logical.

All these different point schemes and spreads and schedules were running circles in my mind, so I decided to join them and play around a little. See what happens. I came up with 4 different possible point schemes:

– the one used in the Finnish league now. That is, win on regular time is worth 3 points. If the game goes to overtime, both teams get a point, and the team that wins gets additional point. Total points per game: 3

– modified 3 point game. As above, unless the game goes to Shootout. At that point it’s called a tie, and both teams get 1.5 points.

– 2 point plan. Win on regular time is worth 2 points, regardless of whether the game ends on regular time, overtime or in shootouts.

– modified 2 point plan. Win is worth 2 points on regular time and overtime. If the game goes to Shootout, it’s called a tie and both teams get a point.

I took the game-by-game regular season results for the Finnish league this year, the 2014-15 season, and reassigned the points for each game according to the different alternatives. Tallied them up, ranked the teams and compared the results. I also calculated the win percentages of the team, to provide a proxy for team quality independent of the point scheme used.

As the figure above shows, the different point schemes don’t really significantly rearrange the teams. (I did not assign secondary criteria for the rankings, so there are some teams with equal rank.) The 2014-15 line is obviously the status quo plan, with the “3p/g w ties” short for “3 point games with ties”. Similarly, “2p/g” and “2p/g w ties” represent the 2 point schemes without and with ties allowed, respectively.

The Top-8 teams would have been the same under all considerations, except for 2 point games with ties -scheme lifting Ässät to 8th place and dropping KalPa to 9th. If we consider the “pity-playoffs”, that is the Top-10 teams, the same teams show up under all considerations. Obviously there are some team-specific differences, like Blues climbing up to 2nd place under the 2 points/game scheme, or Lukko alternating between 3rd and 8th place. Mostly though, the differences are not significant.

What’s the best alternative?

Well, there isn’t one, really. The points don’t matter, apart from few special cases like mentioned above. I summarized some key things for you all. There are the usual suspects: total points available in the season, the average points, and the standard deviation of points, which can be thought to proxy the competitive balance.

I also compared the percentage of points that ended up with the team finishing in the 1st place, 8th place (the last playoff spot if we didn’t have the pity playoffs), 10th place which is the last playoff place, and the team finishing last.

Lastly, I calculated the points-per-game average difference between 8th place finish and being dead last. That is, how many points per game, on average, would the last team have needed more to have a same point score as the 8th ranking team.

Obviously, the standard deviations between 3 point games and 2 point games cannot be compared. But we can compare the schemes with equal number of total points available per game. And contrary to intuition, the schemes that don’t allow for ties, that is when games have shootouts if needed, would produce a more balanced season. But the difference is very small!

If only 2 points were given in a game, Kärpät who won the regular season, managed to obtain a larger share of the points than with 3 point games. And if we consider the differences whether we have or don’t have ties, the seasons with shootouts gave the teams towards the bottom of the standings (10th and 14th place) a bigger share of the points. So it would seem allowing for ties polarized the point spread. But the differences are, again, very small. If 3 points are given in a game, the 0.08 percentage point difference for last place team, for example, translates to exactly one point!

All in all, it doesn’t really matter which points scheme we use. Which is not to say I don’t have a favorite one. Which one, you may ask? And on what grounds? Didn’t I just say it doesn’t matter?

My suggestion

Personally, I’d like to see a 2 point per game plan put in place. Like I explained above, I’m not a fan of the “nice try, good effort” point given out to the teams when they make the overtime, regardless of who wins. A win is a win. Equally unsurprisingly to anyone who’s paid any attention to anything I’ve ever said, I’d get rid of the shootout and bring back ties. If the teams can’t hash it out within the agreed upon time frame, they are by definition equally good! And thus deserve to split the proverbial pie, with one point each.

But, here’s the twist! I’d double the overtime.

So instead of 5 extra minutes, there’d be 10. (You can keep the four-on-four if you wish. I’m not a fan, but I have been told, repeatedly, that I can’t always get what I want. So here I am, compromising.) 10 minutes of overtime with sudden death goal, and after that it’s a tie.

It’s not really that big of a deal, after all, in terms of game time. In 2014-15 season in the Finnish league 59 games out of 420 went to shootout. Which really are the games we’re considering here. If those games had been played with additional 5 minutes of overtime, and assuming no goals were scored so that the full 5 minutes was indeed played, that would have added a total of 295 minutes of game time to the season.

A team plays a total of 3600 minutes per season, without any overtime. So even if the same team had played all those 59 extra overtime games (that now went to shootout)? With the normal overtime + shootout, their season total would have been 3895 minutes of game time, plus shootout. Added to that the extra 5 minutes would have been a mere 8% increase to their game time.

So there, that’s my suggestion: Two points per game, double (10 minutes) overtime, and if the game is still tied, both teams get a point. If two teams are tied in points at the end of the season, regular time wins are preferred.

Any thoughts?

p.s. I realized the font I was using gave anyone reading it a headache. I deeply apologize. I’m revamping the blog over the rest of the week. I’m sorry for any inconvenience.

Edited April 11th: Fixed a confusingly written sentence about the game time increase with 10 min overtime.

# May the odds be in your favor

Or the story about the Finnish hockey league play-off odds. (And how one of these days I’ll actually have to read and/or watch The Hunger Games, considering how much I quote them.)

The play-offs are in full swing in Finland, at least if by “full swing” one means the extra “pity play-off” round went as it was supposed to go given the regular season standings, and the next round starts today.

I’ve posted earlier about the play-off probabilities in general, but this time I decided to focus on something slightly different. I though I’d calculate the odds of each match-up, simplifying heavily by considering the regular season win percentages as a proxy for team quality, but by considering home and away win percentages separately. There are two reasons for this:

1) Home advantage is an actual thing. It has been shown to exist in studies, and can be tracked down to small, yet significant, rules favoring the home team. Plus the “intangibles”, such as fan encouragement, and/or the pressure to play well because your mom is watching.

2) The teams in the Finnish league have very different win percentages when broken down to home and away games.

Taking a closer look at this, the win percentage is simply games won over games played. Contrary to the Finnish league’s (and all other leagues’ for that matter, and this is a whole other issue in and of itself) I treated each win as equal, regardless of whether it took place in regular game time or in overtime or shoot-out. A win is a win.

This revealed some rather disturbing issues. For example for Blues, a team that finished fifth in regular season and now faces JYP in the play-offs. Blues won 36 games in regular season. JYP, the team that will have home advantage in the play-off series, won 33 games. In fact, the only team that won more games than Blues, was Kärpät, the team that won the regular season! So now we have a team with win percentage of 60% playing a team with 55% win percentage, and the weaker team starts at home.

Once the win percentages are calculated separately for home and away games, the figures prompt some interesting questions. Like stated above, the home advantage is a real thing, largely because of the several points in the rules advantageous to the home team, for example the right to put players on the ice last, and thus making it easier to play specific players against other teams top players. And true to form, the teams making the play-offs had higher win percentages at home than away, except for SaiPa (8th in regular season) who played the same regardless of the arena.

Since the rules are the same for all home teams, one could argue that the differences in home win versus away wins changes according to the non-rules related variables, such as home crowd input (the players often mention an active home crowd is “the extra player on ice” giving them an advantage, and even yours truly isn’t quite cynical enough to think that is simply lip-service to sell tickets) or unintentional bias by the referees in favor of the home team, often credited to a pressure from active crowd.

While the above would feel intuitively pleasing, and is supported by the large differences in the win percentages of famously active and attentive home audience at Kärpät and HIFK games (for Kärpät, the home w% is 76,67 and away w% 56,67, whereas for HIFK they are 66,67% and 43,33% respectively), the theory fails for Blues. Displaying some of the weakest attendance figures in the league, Blues is really rocking it on home ice: their win percentage at home is 76,67%, better than all other teams’ except for Kärpät with whom they tie. When away, however, they tie for the second-to-last place with JYP and HIFK with 43,33%.

Another team that needs to up their away game is KalPa. Second-highest home win percentage (behind only of Kärpät and Blues) of 70% is brought down to a mere 55% overall, when you only win 40% of your away games. That’s the weakest of the Top 8 -teams.

What this means in terms of the play-off match-ups, then?

First I used only the over-all win percentage as a measure of team strength, that is, ignored the home team advantage, and calculated the odds of each team winning their respective best-out-of-seven series. Kärpät-SaiPa series would go to Kärpät with a probability of 51,42%. Tappara would defend their higher-ranking regular season finish, winning the series against HIFK with 50,71% probability. Lukko-KalPa would end up with a surprise victory by KalPa, at least with the likelihood of 51%. And with a probability of 51,46% visiting team Blues would continue to win more games than JYP.

But, since the home ice did seem to influence rather largely to the teams’ win percentage (unless you’re SaiPa), what are the odds of the home-starting teams taking the series? Unlike in the NHL where the team finishing higher in regular season hosts the first two games and then visits for two after which they alternate if needed, in Finland the home team changes after every game. Still, in a full 7-game series that gives 4 home games to the team with higher rank, as opposed to three.

In the first two pairings, regular season winner Kärpät playing SaiPa and second-placer Tappara playing HIFK, the home team (the team starting home) simply increases their odds of winning. Kärpät takes the series with a probability of 62,51% and Tappara with 56,57%. The difference in team strengths is considerable enough, that even if we turn things around and pretend the weaker team gets to start at home (SaiPa and HIFK, respectively), Kärpät would still win with probability of 60,24% and Tappara with 51,86%.

With the Lukko-KalPa match-up the odds are in Lukko’s favor as long as they get to start at home (which they do). The home advantage means they have a 51,44% chance of making it to the next round, whereas if the teams started on the KalPa home ice, KalPa would take the series with the probability of 54,5%. Remember that with the aggregate win percentages the series would also go to KalPa (51%). That’s because KalPa has a higher win percentage than Lukko, 55% to Lukko’s 51,67%, due to actually winning more games in the regular season.

With home advantage, JYP with over-all win percentage of 55% clinches the series with probability of 50,28%. If they started at Espoo, Blues’ solid performance at home would bring them the series with a probability of 57,64%. As stated above, with aggregate win percentages Blues (with 60% win percentage) would win the series with a probability of 51,46%. So really, the odds are in Lukko and JYP’s favor simply because of the home advantage they got due to the way wins in regular time versus overtime are valued in the league.

What’s going to happen, then?

Well I can say for certain that the following will happen: either the team starting at home or the team starting away will win. It’s the play-offs. Best out of seven games. Anything can happen. The odds above are not a prediction, they are simply what it says on the tin: probabilities of winning the best-out-of-seven series, given regular season win percentages. It doesn’t take into account team-versus-team performance, or game plans, or who’s injured, or who’s having a bad day, or which team’s got their groove on. All of which will play a role in a play-off series.

But the above does tell us something: if we assume the point in hockey is to win games, and thus the team that wins more games is better than the team that wins less games, we are not rewarding the best teams of the regular season with home advantage in the play-offs.

We’re actually leveling the playing field.

# Fan demand in hockey: what, where and why? Part 1

Every fall the media in Finland starts drumming up concern over how hockey fans aren’t finding their way to the stands. This time it started already during last season when Jokerit announced they’ll be joining the KHL for the 2014-15 season, and the hockey media in unison declared that to be catastrophic in terms of fan interest in the Finnish league.

I’ve been thinking about that whole thing for a while now, and decided to do some digging. Realizing that my posts in this blog are getting out of hand in terms of length as it is, I also decided to write about this whole thing, fan demand in hockey, in a series of posts. So welcome to the first installment of the Hockey Demand -series!

Is the Finnish media right? Is the fan interest dramatically diminished, compared to last season? Are fans gone from hockey? I thought I’d start the series by looking at the actual data for Finnish league and get to the “real” economic theory and analysis in later posts.

The basic idea in fan demand is simple. If we note ticket demand for a single game with D, we can assume the demand follows

D(ij) = H(i) + V(j) + M(ij).

, where D(ij) is the demand for tickets (i.e. the attendance) for a game between home team i and visiting team j. H(i) is the interest in home team i, defined by several variables such as market size, brand, fan base, local competition in terms of other sports and teams, arena capacity and so on. V(j) is the interest for visiting team j, again a combination of several variables, for example distance from j’s home area, brand, superstar players and so on. Lastly M(ij) is the match-specific interest, such as whether it’s a local rivalry, two teams competing for a playoff place, last season’s finalists, big promotional activities, TV visibility, day of week the match takes place… any and all such variables specific for a particular match.

Because of the different variables relating to home and away teams, it is important to notice that a game between two teams would draw a different attendance depending on which one is the home team. To consider that, I took the attendance in the Finnish league and broke it down by home team and by visiting team. Because the arenas differ considerably when it comes to size, simply comparing attendance figures would be deceptive. 4000 people would be practically full house to JYP (lowest audience capacity at 4365), yet it’s barely one third of seats for TPS (biggest arena with maximum attendance at 11 820). So instead I used relative attendance, or the fulfillment rate of the arena, that is, the attendance as a percentage of capacity.

Attendance during 2014-15 Fall season

During fall 2014 all but 3 match-ups took place, for a total of 228 games. 45 match-ups were placed twice, and 2 three times. For these a simple average was used. Because the data is mainly of single games for majority of home/away team combinations, far reaching conclusions are not advisable. The random match-specific variables, such as season opening, special promotions or simply the day of the week the game was played have too much effect on the attendance. However, certain trends do appear.

It is possible, for example, to identify teams with strong home-team demand. HIFK and Kärpät, for example, draw in good crowds regardless of who they’re playing against on their home ice. Since it could be argued that these two teams also have the strongest hockey brands in Finnish hockey, that comes as little surprise. It also follows that these two teams are interesting as visiting teams as well, an intuitive assumption supported by the attendance figures. For Kärpät, for example, the average attendance rate for home games is 83%, and not one game was played in front of a crowd less than 75% of capacity. As an away team, they attracted an average attendance rate of 73%. The lowest, and only rates below 60%, were against Blues and HPK (55 and 52 respectively), teams with overall very low home game attendance rates.

A similar story can be told about HIFK. With a home game attendance rate average of 79, even their lowest rate is still above 70%. Both teams have 7 match-ups above 80% (HIFK missing a home game against SaiPa). As a visiting team HIFK is also a clear favorite regardless where they go, with attendance rates staying below 60% only against TPS (49) and Ässät (59), and a visit to play against Pelicans still to take place. Four match-ups with HIFK as the away team rate above 90%.

On the other end of the spectrum, there are teams that cannot draw in the fans home or away. Blues is averaging at 56%, with 9 different match-ups below 60%. As an away team, they only break 80% against HIFK (85, a team with very strong home team demand and a local rival), JYP (84, another team with strong home demand) and SaiPa (86, solid demand at home with 6 match-ups above 80%). Another weak performer is KalPa, although the other way round. Where Blues couldn’t get the demand up at home, KalPa only dropped below 60% in 6 match-ups out of all 13, and even broke 80% in one. But that was against Kärpät. The average attendance rate for KalPa at home was 65%. As an away team, they managed to keep the average practically the same, at 64%, but that was helped by the strong home crowds when visiting HIFK (83), JYP (84) and Kärpät (89). In 7 match-ups the attendance rate remained below 60%.

I do want to bring up TPS, although it seems the club has taken enough of a beating both on and off the ice this season. They do start at a disadvantage when talking simply in terms of attendance rate, by playing in the biggest arena this season. The abysmal performance on the ice isn’t exactly helping. The fall season average attendance rate for TPS at home is 50%, and even that is helped by the sole out-of-pattern attendance for the season opener against Kärpät. That game was attended by 10 362 people. To put it in perspective, the average attendance without that game against Kärpät is 5570 people. In 11 out of the 13 possible match-ups TPS has remained under 60%, with the lowest being 34% against KalPa (disclaimer: only one game).

But here’s the truly interesting thing about TPS: they attract people when playing outside of their home town. Having visited all the other teams in the league during the fall, not one of those match-ups drop under the 60% attendance rate. In fact, they have an average of 73%, which is second highest in the league, tied with Kärpät and Sport, and only behind HIFK. Out of these three teams, HIFK and Kärpät have strong pull both home and away as discussed above, and Sport is the new team added to the league for this season and thus expected to stir up interest.

What about last year then: was it so much better?

As mentioned above, many of these figures are from single games, so too far-reaching analysis is strongly discouraged. However, if compared to similarly calculated attendance rates from last season, something interesting again occurs. HIFK and Kärpät displayed similar figures in 2013, no doubt boosted by their strong brands. Another solid performer was Jokerit, attracting an average of 80% attendance rate as a visiting team and 65% at home (notably their home arena capacity was 13 349).

As for aforementioned TPS, already in 2013 they drew in the crowd as a visiting team. But they performed poorly in terms of home game attendance with an average of 44%, with 61% the highest. It is intuitively pleasing to claim this is due to their large home arena, as that is bound to bring down the relative attendance. And there is no doubt some truth to that, as their average attendance is 5150. That’s more than full capacity for 4 teams in the league at the moment, three last season. So maybe TPS is simply playing in an arena far too big for them?

Both last season and this, the average attendance rates varied more when considering home team averages than with visiting team averages. This would suggest that home team demand variables have larger impact on the attendance than visiting team, which is not surprising. How much that is the case will be returned to later.

Overall it would seem the media outcry has been correct: the attendance has fallen in terms of attendance rate. Fall 2013 saw a league average attendance of 72% whereas this season the fall attendance stayed at 68%. This despite the fact that the team with the largest home arena, Jokerit, left to play in the KHL, and was replaced by Sport, a team with a capacity one third of that. But on the other hand, a team with an average home attendance of 9252 was replaced by a team with home attendance average of 3370. League-wide, the attendance average dropped from 4974 to 4295. Which leads to only one more conclusion: someone is picking up the slack.

Feb. 10: Edited to clear up some bad wording.