Silver Nuggets: Playoff Probabilities

So how about last night's game, eh? The Senators kept taking the lead, and eventually hung onto it against the Bruins. It was very exciting hockey, and all worth it because the Sens won in the end. We all know how big of a deal the game was:

Tonight's game for the Senators is the most important for any team so far this year. pic.twitter.com/2tORTBUDes

— Micah Blake McCurdy (@IneffectiveMath) March 19, 2015

Sports Club Stats says that last night's results (including the Capitals' win) jumped the Sens up to 50.4% while the Bruins dropped to 54.7%. Those are amazing odds considering how bleak the Sens' season looked even a couple weeks ago.

All this got me thinking about how the odds are actually calculated. Full disclaimer: I love the process of stats. Not specific to hockey, just in general. Statistical analysis is fascinating to me, how people have developed systems to plow through large amounts of data. If you don't love stats, this next section might not be too interesting to you. But if you love clicking on buttons and watching numbers change, you might still find it interesting.

Sports Club Stats has this great section where they explain how they calculate their odds. You can read the whole explanation if you want, but in short, they use what are called Monte Carlo methods. These work exactly how you'd expect big simulations to work: an algorithm runs a whole bunch of randomized simulations following a certain set of rules, and then the outcomes are averaged. In the case of playoff predictions, they simulate the outcome of every game for the rest of the season, and see where each team ends up. There is an interactive section at the Sports Club Stats explanation link above where you can click to see the 2006-07 playoff race results after 1, 2, 3, 4, 5, and then powers of ten up to 10,000,000 simulations. It really illustrates how the technique works.

You may notice I said the simulations follow a certain set of rules. For Sports Club Stats, they just use a team's earlier home and road records, and apply this to the number of home and road games upcoming. Obviously, there are flaws in this. For one, some teams are better than their records (such as the Kings) and some are definitely worse (perhaps the Flames). As they point out themselves, it ignores factors such as mid-season serious injuries to players who have now returned to the lineup. It also assumes that home-road win-loss rates are repeatable, which is a contentious claim.

Micah Blake McCurdy (@IneffectiveMath) with the username tolstoi around these parts wrote an article a little while ago explaining his simulation technique, Pip. He also uses Monte Carlo methods, but instead of using a team's win-loss record, he uses Fenwick (USAT) as a predictor. Basically, he looks at each team in each game's typical Fenwick for and against. He's developed weights for the four inputs using years of past data, and combines them to predict the likely outcome of a game. The simulation takes these into account when randomizing each game outcome. This does away with some of the issues of the Sports Club Stats simulations, since Fenwick is a better predictor of future performance than straight wins and losses, but still doesn't account for things like injuries and recovery.

Thanks for indulging my little stats spiel. No model is perfect, but the models are getting better. And in my opinion, talking about the importance of games is more fun when you can quantify it. I'm just thankful there are people smart enough and patient enough to put together this information for the rest of us to use.

Tonight's games that matter:

Really, there aren't any. There are only three games, and only Detroit at Tampa Bay could have implications for the Sens. If you want Montreal to win the division, cheer for Detroit, who are less likely to catch the Habs. But if Detroit still leaves you with a sour taste in your mouth (like they do for me) then follow your heart. It probably won't matter much.

Sens Links:

• In case you missed it, the Sens beat the Bruins last night, 6-4. Here are the recaps. [Silver Seven, Rank The Performances, Ottawa Citizen, SenShot, SensChirp]
• If you can remember all the way back to Tuesday, the Sens won then too, 2-1 in a thrilling game against the Hurricanes [Silver Seven, Rank The Performances, Ottawa Citizen, SenShot, SensChirp]
• Amelia has this week's Five Thoughts, including a look at 3-on-3 OT [Silver Seven]
• Zack Smith (remember him?) has been sent down to Binghamton on a conditioning stint [Silver Seven]
• Amelia takes a look at the youth impact for the Sens, and asks who you think will have the biggest impact next season [Silver Seven]
• Some well-deserved praise of one of those youth players, Mark Stone [SenShot]
• Erik Condra isn't thinking about how he needs a new contract... yet [Ottawa Citizen]
• Andrew Hammond had a below-average game last night, but he still took it in stride [Ottawa Citizen]
• A look at Bobby Ryan's work in promoting the Special Olympics floor hockey championships [Ottawa Citizen]
• Bryan Murray is adding the spread of awareness about cancer to his NHL legacy [Globe and Mail]
• Ever wondered how to make Hammond look like the Hamburglar in Photoshop? Capital Gains helps you out! [Radek Bonk's Mullet]
• Trevor Shackles argues why Robin Lehner should still be regarded as the goalie of the future [SenShot]
• Nichols looks at the legend of Andrew Hammond (before last night's game) [6th Sens]
• Watch Curtis Lazar eat a burger that was thrown onto the ice after last night's victory:

Non-Sens Links:

• Matthew Wuest, the founder of CapGeek, passed away yesterday morning from colon cancer. He put immeasurable time into CapGeek, made it available for free online, and never went looking for the attention he could've for having such a crucial site in the hockey universe. He will be truly missed. [Metro]
• Last night Jaromir Jagr scored his 718th career NHL goal, passing Phil Esposito to take sole control of the fifth-highest total in NHL history. Just think how high he could be without those years in the KHL. [NHL]
• Team Canada has made the 1-2 Page Playoff at the Women's World Curling Championships, on the back of a 9-2 record in the round robin. Jennifer Jones' group has looked shakier than usual this tournament. The Canadians take on the Swiss tonight and if it's anything like when the teams met earlier this week, it'll be a doozy of a game. [TSN]