# Is Kate Smith a lucky charm or a statistical anomaly?

Perhaps the most storied “lucky charm” in sports is Kate Smith singing “God Bless America” at Philadelphia Flyers home games. Many details of her story, along with some of the statistics I will be using in this post, are available here. The story goes that on December 11, 1969, Flyers management decided to use a recording of Smith singing God Bless America instead of the Star-Spangled Banner for one game, which the Flyers won. They lost the next game, but when they brought back Smith’s recording for the following game, the Flyers won again. A tradition had begun. While it was used sparingly during those years, there seemed to be a significant positive impact on the Flyers when God Bless America was sung before home games. While I had heard of this tradition in passing, I became quite familiar with it in May 2010 when the Flyers played my Montreal Canadiens in the Eastern Conference Finals. Here is the anthem from the last game of that series (God Bless America starts at 2:12):

During the first three years of this tradition (1969 to 1972), the Flyers had a spectacular record of 19 wins, 1 loss and 1 tie in games where Kate Smith’s recording was used (note that her first appearance in person was only in October 1973). Smith’s recording was only used during regular season games at that time; the Flyers’ overall home record in those three years was a mediocre 50-38-28, and they only qualified for the playoffs once in those years.

Was there a statistically significant difference in the Flyers’ performance when Smith’s anthem was used before the game? In those three years, the Flyers amassed 128 out of a possible 232 points in all home games, for a winning percentage of .552. In the “Smith games”, the Flyers amassed 39 out of a possible 42 points, for a winning percentage of .929.

If we selected, at random, a sample of 21 Flyers home games in that three-year span, what is the probability that those 21 games would result in 39 or more points for the Flyers? The expected number of points in the 21-game sample, with 95% confidence interval, is 23.2 +/- 9.0. The 39 points from the Smith games is well outside of this interval; in fact, the probability of getting 39 or more points from 21 random games is only 0.12%. Said another way, if we repeated the sampling exercise 832 times, we would expect to get one sample where the Flyers amassed 39 or more points.

If we look at the first six years of this tradition, from 1969 to 1975, the Flyers were a brilliant 43-3-1 when Smith’s anthem was used, a winning percentage of .926 (87 out of a possible 94 points). Of course, the mid 70s were the glory days for the Flyers, winning two Stanley Cups. In that 1969-75 span, their overall home record (regular season and playoffs) was 156-63-40, for a winning percentage of .680. If we selected, at random, a sample of 47 Flyers home games in that six-year span, what is the probability that those 47 games would amount to 87 or more points? The expected number of points in the 47-game sample, with 95% confidence interval, is 64 +/- 13. The probability of getting 87 or more points from 47 random games is only 0.037%, or a 1 in 2686 chance.

Smith’s positive effect seems to have carried on through the decades, even to today. As of the end of the 2011 playoffs, the overall record when Smith’s rendition of God Bless America is used is 91 wins, 25 losses, 1 shootout loss and 4 ties, for 187 points in 121 games, and a winning percentage of .773. (I could not find the information on which games that her anthem was used in the 2011-12 season, although in recent years, it appears to be only used in the playoffs.) In the Flyers’ regular season and playoff history through 2011, they have amassed a home record of 1131 wins, 555 losses, 44 overtime/shootout losses, and 193 ties for a winning percentage of .638. (Please note that I am counting overtime and shootout losses as zero-point losses in these calculations, to maintain consistency through the years.) If we selected a random sample of 121 Flyers home games between 1967 and 2011, what is the probability that those games would amount to 187 or more points?

The expected number of points in the 121-game sample, with 95% confidence interval, is 154 +/- 21. The probability of getting 187 or more points from 121 random home games is 0.105%, which is a similar likelihood to the narrower spans studied above. Selecting from every Flyers home game, regular season or playoffs, we would repeat the sampling exercise 954 times to expect one sample where the Flyers amassed 187 or more points. (For perspective, the likelihood of rolling the same number on five fair six-sided dice in a single roll is 0.077%, or one in 1296.)

As a side note, it is interesting to note that Smith’s anthem was not used at all in the 1979-80 season, when the Flyers went on a 35-game unbeaten streak, a record unbeaten run in North American professional sports. 19 of those games were at home; their first home defeat of that season came in their 27th home game.

So is there really a “Kate Smith Effect”, where Flyers players get that extra little psychological boost when the game starts with her singing the anthem, or is this just a very freakish coincidence that may even out over the next few decades? The statistics would imply that it is very unlikely that the Flyers’ improvement when Kate Smith sings God Bless America is simply a random occurrence – the odds of it being random, over a span of 45 years and 1923 games, is in the order of 1 in a thousand, or around 0.1%. The Flyers seem to believe that she is a good luck charm, as they put a statue of her in front of the old Spectrum in 1987.

But perhaps there is another explanation, an explanation which is drawn from these calculated odds. We know very well that Kate Smith has never had a direct impact on a hockey game in Philadelphia. If we consider all the actions (or “traditions”) that are independent from the game, but have occurred at exactly 121 different Flyers home games – the 121 games where a fan wore a certain coloured tie, the 121 games where the popcorn machine was broken, the 121 games where the anthem singer wore a certain outfit, the 121 games where the couple behind the penalty box kissed at the opening faceoff – and looked at the Flyers winning percentage in each of those circumstances, we would expect that most would be around .638, but some would be higher and some would be lower. One out of every 954 “traditions” will lead to a winning percentage of .773 or better, just like one out of every 954 “traditions” will have a winning percentage of .503 or below. In fact, one out of every 20 “traditions” will either be doing better than .724 or worse than .552 – this comes from the calculated confidence interval, and it is simply the effect of the underlying random distribution.

The “Kate Smith Effect” is not happening because Kate Smith somehow influences the outcome of hockey games. (The Toronto Blue Jays have a 3-0 record in games I have attended in person, but I know that I am of no help on the field.) The “Kate Smith Effect” is that one-in-a-thousand coincidence that happens to have been noticed through the years. For all we know, there may be another person, perhaps a woman with a great singing voice, who has attended a fraction of Flyers home games and can vouch for an even better record when she is present. It’s not likely, but even the improbable can sometimes happen.

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Paul:Monday, April 30th 2012 at 12:49 |

It is likely to be even more complicated than that. I suspect that the decision at which home games to play the Kate Smith recording was not randomly arrived at. What exactly were the selection criteria? What were the records of the opponents of those games compared to the games where the recording was not used? There are dozens of factors that could add up to the alleged effect being both non-random, and non-significant.

Marc Leger:Monday, April 30th 2012 at 13:05 |

You’re right, and I did simplify things here. In recent years it appears they are using her recording only in the playoffs, which means the opponents should be tougher than usual, but that makes the streak seem even more amazing. In the early years, there didn’t seem to be as much rhyme and reason behind the selections, except that it was used more in the playoffs.

A better statistical analysis would be to determine the actual odds of winning every game that used her recording, perhaps based on that season’s home record, and then determine an “expected record” from that. But that wouldn’t be as much fun…