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Chad Johnson saves the day – or at least helps a little November 11, 2015

Posted by tomflesher in Hockey, Sports.
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The Sabres (7-8-0) picked off the Lightning (7-8-2) last night in Tampa Bay, scoring four goals including one empty-netter by Rasmus Ristolainen with an assist from goalie Chad Johnson. The lanky Albertan started his ninth game of the year and pulled his 2.47 goals against average down with a one-goal complete game. Ristolainen has 3 points and a -2 plus/minus over his last five games, so the empty-net goal was a nice lift for him.

The Lightning outshot the Sabres 31-26, so Johnson’s performance was quite important. In the 2014 season, shots had about a .50 correlation with points and a slightly smaller (.49993) correlation with wins. A quick regression analysis shows that shots on goal have a statistically significant effect on both wins and points: one shot corresponds to about .023 wins and about .045 points, both significant at p < .01. Since the Lightning outshot the Sabres last night, there’s a reason that Johnson’s ‘miraculous’ saves were so key.

The Kate Smith Effect July 18, 2010

Posted by tomflesher in Baseball.
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From the Mountains…
To the Prairies…
To the Oceans…
White with foam….

It’s “well-known” that when Kate Smith sings “God Bless America” – whether live starting in 1969 or on videotape now – the Philadelphia Flyers play better, or at least they’re more likely to win. As Wikipedia indicates, she’s considered a good luck charm for the Flyers. How much does she help?

Since 1969, the Flyers have played in 3268 games and won 1631 of them for an observed win percentage of .4991. That’s very close to the long-term win percentage of .50 that we’d expect for any team. Of those games, Kate Smith sang or was played at 114 of them with a total record of 87-23-4, and the record when Kate Smith did not sing was 1544 wins in 3154 games for a “non-Kate” win proportion of .4895. I’ll make the null hypothesis that the Flyers play exactly the same way in games where “God Bless America” is sung – “Kate games” – as they do when it isn’t. That means that

H_{0}: p(Win \mid Kate) = p(Win \mid Non-Kate) = .4895

The simplest way to attack this is to note that the Flyers’ win percentage in Kate games is .7632. Qualitatively, that’s quite a jump – surely, it must be significant. Of course, we can’t leave it at that.

First, note that with an observed proportion of .4895, the binomial probability of winning 87 games in 114 trials is approximately .00000000145 – that’s about 145 in one hundred billion. That’s highly unlikely. However, other methods can help us quantify the Kate Smith Effect.

The standard error for proportions is

\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{.7632(.2368)}{114}} = \sqrt{.0012} = .0346

With 113 degrees of freedom and a 95% confidence interval, I used Texas A&M’s t Calculator to find that the appropriate critical value is 1.98. That means that we can be 95% confident that the win percentage in Kate games after controlling for other factors is somewhere in the range

.7632 \pm 1.98 \times .0346 or approximately .6947 \le p(Win \mid Kate) \le .8317

Since the true proportion in non-Kate games is .4895, that means the Kate Smith Effect is somewhere in the range

.2051 \le \hat{\delta} \le .3421

Though I can’t explain why, it’s apparent that there’s a Kate Smith Effect of at least 20% in terms of winning percentage. This isn’t to say that playing Kate Smith’s “God Bless America” causes good luck. Since the Kate video is considered a good luck charm, it’s probably more likely that the players play harder in games that are deemed important enough to play it.