The Mariners home record as a function of fan attendance

Over the past five seasons, the Mariners have played 408 games at Safeco Field (81 per season and then that weird three-game "away" series against Florida in 2011, when the Marlins were forced out of their home park by Bono, The Edge, and those two other guys with less memorable, normal names). Over that span, they have put up a 0.468 winning percentage at home. That's not very good... but when compared with their road winning percentage of 0.423, it doesn't look quite as bad. (That road record was even bumped up by the M's winning record away from Safeco in 2014; they won less than 39% of their road games between 2010 and 2013 - blech.)

Despite last season's superior road record, home field advantage is pretty clearly a benefit that exists for the Seattle Mariners. This makes sense - there are so many perks to playing at home. Players get to sleep in their own beds, they don't have to travel thousands of miles late into the night to get to work the next day, they're familiar with the dimensions/playing conditions of Safeco, they can enjoy some delicious home cookin', they have the support of their fans, etc.

I imagine that many of the people who read this blog are also Seahawks fans. As such, some of you are likely comfortable with the idea that a large number of enthusiastic fans in attendance at a sporting event can potentially impact the outcome of the game. Obviously, the average fan at a Mariners game is significantly less rabid/better behaved than the average fan at a 'hawks game, but I was curious as to whether or not an increase in fan attendance has had any impact on the results of Mariners games. Do larger crowds at Safeco "help" the Mariners win? I sincerely doubt it, but figured it was worth spending an afternoon figuring out. For this reason, I compiled the following table, which looks at attendance numbers vs. the M's winning percentage at home:

*Using 47,476 people as the capacity of Safeco Field.

"Wow! Look at that winning percentage when Safeco is at least 80% full! Everyone should round up 5,000 of their closest friends and head down to SoDo for every game - the M's would be way more likely to win!"

If the above is your first thought, I'm apt to question your critical thinking skills, but I do heartily support your fanaticism and fervor. Safeco Field is way more fun when it's chock-full o' people, and a greater number of folks should go out and see the M's more often.

However, as fun as it would be to stop this post here, the numbers in the table above tell only a very small, incomplete part of the story. It would be great if simply selling out Safeco resulted in a 20% boost in the M's chances of winning, but that's almost certainly not what's going on. First of all, 10 of the 30 games with 38,000+ people occurred this season, when the Mariners were a much better team than they have been in recent years. Additionally, their winning percentage actually decreases pretty significantly as attendance increases from between 20-40% full and 60-80% full; this certainly doesn't support the narrative that more fans equals a better chance of winning. I would guess that this trend is likely influenced by the strength of the opposition, as opposed to any attendance effects. To look into this, I assembled the following graph:

Here, the blue squares represent the M's winning percentages in games as a function of the attendance at Safeco Field (these numbers are the same as the ones listed in the table above). Alternatively, the turquoise diamonds represent the winning percentage of the average visiting team over the past five seasons, also as a function of attendance. (This is just a simple way to determine the strength of the teams that the Mariners are playing under different attendance conditions.) We can see that the average winning percentage of the teams faced in games where at least 38,000 people attend is 0.521, whereas when fewer than 19,000 attend a game the average opponents' winning percentage is only 0.499. This shows that, over the past five years, people are more likely to attend games featuring a better opponent. This fact seems fairly intuitive.

Additionally, it's not surprising that as the quality of the opposition increases, the Mariners record suffers. This trend holds true up to 38,000 fans, as the M's record dips from ~0.500 all the way down to ~0.400; however, their winning percentage subsequently shoots up to 0.567 when Safeco is more than 80% full. On the one hand, this makes very little sense because the opposition was the most difficult in games with more than 38,000 attendees. One would expect them to  have the worst record against this group of teams as opposed to the best. But on the other hand... Felix!

Below is a table detailing the attendance conditions when Felix Hernandez has been on the mound at Safeco:

Felix has made 80 starts in Seattle over the last five seasons. In more than 20 of those, Safeco has been less than 40% full. That's absurd! Shame on all of us. More to the point of this post, Felix has started 12 of the 30 games when Safeco was filled near bursting. The Mariners won eight of those games. This clearly helps to explain why the Mariners have such a good record when more than 38,000 folks are in attendance.

If attendance were evenly distributed by random chance, we would expect Felix to have started around 20% of the games in each attendance category (because he represents 1/5th of the Mariners starting rotation). Of course, attendance is not randomly distributed; people are much more likely to come out when Felix is pitching because he's amazing and fans like to watch their team win. (Over the last five seasons, the Mariners are seven games over 0.500 when Felix pitches and 95 games under 0.500 when he doesn't. Contrast!)

Jeff talked about The Felix Hernandez Attendance Bump two off-seasons ago, so I won't really go into this except to say that 1) this Bump is still alive and well and 2) over the past five years, Felix has boosted attendance on days that he's pitched by more than 14% (~3,300 people). Using The Fan Cost Index, which estimates that over the past five season an ~average fan spends a little less than $50 at a baseball game at Safeco, Felix has brought in an extra ~$2.5 million in ticket sales/concessions each season ($50 x 3,3000 people x 16 home starts per season). This is very much a back-of-the-napkin calculation, but the point stands that Felix's impact on the Mariners is beneficial in so many ways.

In closing... surprise! The Mariners probably don't actually perform any better simply because their stadium is full. However, the Mariners do perform better when Felix pitches because Felix is crazy good and people are more likely to pay to come see Felix pitch, which does boost attendance, which could make it look like having more people at a game improves the Mariners chances of winning... but that's just not how things work.

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This silly post has been brought to you by the lack of Mariners-related moves so far at this year's Winter Meetings. Hopefully that changes soon so y'all will have something a little bit meatier to read. Until then... Go M's!