Goalie Aging Curve

I think we all know aging curves are important in sports. It's a vital component in projecting how players will perform in the future. This type of research has been done for every sport (here's one by Eric Tulsky concerning Corsi ). And actually, a study was once done on goalies by @garik16 here. My study will closely mirror his with a couple of differences. To those people not acquainted with the work done on aging curves I suggest reading the following pieces listed below (along with Garik's piece).

http://www.hardballtimes.com/how-do-baseball-players-age-part-2/ (Also Read Part 1)
http://www.hardballtimes.com/fielding-aging-curves/
http://www.sbnation.com/nhl/2013/11/5/5024738/nhl-free-agency-age-contracts

Due to the dearth of data I'll be using All-Situation SV% available at http://www.hockey-reference.com/. I'm fine generalizing this to even strength Sv% (how to apply it to the different danger zones is a different story). I'll also go back to 1990, so 26 years. Because of that I'll have to adjust for changes in Sv% (The average All Situation Sv% in 1990 was 88.6%, this past year it was 91.49%).

Also, I'll be using the Delta Method here, with each couple weighed by the harmonic mean of their shots. I take each player who played in back to back years (no matter how many shots they faced). I calculate the difference in Sv% and weigh that by their harmonic mean.

Of course there is one concern (and this is where my work differs from Garik). Basically those who survive to play in year 2 aren't only, on average, better players but also luckier players (this is noted here by Tango).  So they likely did better than their actual talent in year 1. This would magnify the difference because in year 2 not only will they decline due to age but they will regress downwards. So the difference between pairs will look bigger than it actually is. We need to try to isolate just the aging component. So I'll have to regress year performance.

The amount I'll regress year 1 performance is based on the following: I took every player who played at 30 games in back to back years. A ran a regression and got an r of .296. The average player in the sample faced about 1450 shots. Doing (1-r)/r* Avg. Shots......we get about 3400 shots. For even strength Sv% the number is about 2950. So this is a little higher. Makes sense to me.

Okay now we can finally get to the numbers. Due to sample size issues I'll only go from the 20-21 couplet to the 37-38 (we'll extrapolate for other ages). Now I'll do something similar to what garik16 did. I plotted the differences for each pair and to smooth it out I fitted a line onto it. Here it is:

As you can see there's a pretty clear downward slope. As we would expect. The older you get the more you are expected to drop off from the previous year. Fitting a line is important because, as you can see, the numbers jump around a bit due to sample size. Goalies don't improve as they turn 33 as the graph shows. It's a blip due to small sample sizes. Note: This isn't me saying that aging is linear. I'm merely using a linear relationship to model the differences between pairs (or how much you age between ages). Those are two different things. If it was linear you would expect a player to decline the same amount each year. Instead here how much a player declines each years increases at a linear pace (The reason I chose to do it this way is because, like Garik, I found the numbers to be more believable. Either way, there isn't that much of a difference). Nevertheless, here are the exact numbers:

Age	Change
18	0.0009
19	0.0007
20	0.0005
21	0.0003
22	0.0001
23	-0.0001
24	-0.0003
25	-0.0005
26	-0.0007
27	-0.0009
28	-0.0011
29	-0.0013
30	-0.0015
31	-0.0017
32	-0.0019
33	-0.0021
34	-0.0023
35	-0.0025
36	-0.0027
37	-0.0029
38	-0.0031
39	-0.0033
40	-0.0035

This corroborates previous work showing that goalies start declining early (Note: I believe this underestimated the amount a goalie should improve between 18-22.....but this is the best I got). One may also notice that this is less aggressive than what Garik found (look at the bottom of his post) For example: At age 30 he has -.002 and I have -.0015 and at age 36 he has -.004 and I have -.0027. This is a consequence of me regressing year 1 performance. As I said before, it narrows the gap because the goalies, on average, likely overachieved in year 1 which then conflates the difference.

I guess the last question here is how to translate all this to Low/Mid/High Sv%. Well........I don't know. One has to take an educated guess here. I played around with the numbers a little and I settled on dividing the weights by 4 for Low_Sv%, using the same numbers as above for Mid_Sv%, and Multiplying by 2 for High_Sv% (Slightly higher might be better). These are obviously arbitrary but they fit the overall aging pattern well and I think it makes sense. High_Sv% should be the highest as it contains the most "skill". Low_Sv% has a ton of noise so the adjustments should be small (honestly one could do without adjusting for age here). And Mid_Sv% should be somewhere in the middle (one could possibly argue a little lower than what I suggested).

To conclude, this post doesn't do much. I merely suggest (to the few of you who care) a slight amendment to Garik's aging curve. I am also fine applying this to Even-Strength Sv%. The Danger Zones are a little trickier. My suggestions are noted above.

***All Data Courtesy of Hockey-Reference