I follow a great NFL stats blog called Advanced NFL Stats, that uses live win-probability modeling to determine which of the two teams is most likely to win. This football off-season the author of that blog has started looking at other sports, hockey being one of them. The post on March 9th was his first about modeling hockey games. In the post, he describes the Poisson equation and how to determine the probability of a team scoring or allowing a certain amount of goals, and through that, the possibility of them winning games.  Go ahead and read his post. I’ll wait….. OK! So I thought it might be neat to see what the Sharks numbers were…

To recap,the Poisson equation looks like this,

Pr = ((x^k) * e^(-x)) / k!

where x is the average goals over the time period of 60 minutes, k is the particular goal amount in question, and Pr is the percent chance of it happening.

He uses the Boston Bruins as the example team.  Their average goals scored in 60 minutes is 3.3, while they allow 2.2 goals.  After going through the whole process, he comes to the conclusion that they win 60% of their games and tie 15.8% at the end of regulation.  Assuming the team wins in overtime about 50% of the time, then the Bruins chance to win any particular game is 60% plus 7.9%, or 67.9%.  Before today’s games, they were at 67 games played and 43 wins, or 64.2%.  Like the Pythagorean Theorem in baseball, the Poisson number shows that the Bruins might be a better team than their record shows.

So what about the Sharks?  I took the Poisson equation using the Sharks goals for (3.26) and goals against (2.45) as of this morning.  Here’s the graph.

Sharks Poisson Numbers thru March 12 2009

If you’re a fan of the team, you like the high red line on the left hand side, and the teal line’s peak to be closer to the right.

I charted the 81 different possibilities of zero to eight goals by either team and used the values from the above data to figure out the possibility of that outcome happening.

At the end I’ve added up the percentages for a win, loss and tie at the end of regulation.

Like with the Bruins, we can assume that the Sharks win half of their overtime games, or 8.1%.  Add that to the win percentage, and you get 62.4%.  As of this morning, the Sharks were at 43 wins in 65 games, or 66.2%.   Based on these numbers, their projection being lower than the actual shows the Sharks may not be quite as good as their record shows.

That’s it.  The Sharks are performing better than they are expected to based on the amount of goals scored and goals allowed.  Over long enough period of time, I would expect the Sharks to drop closer to their projected numbers, as I would expect the Bruins to rise to theirs.  This doesn’t bode well for the Team in Teal, but it’s a good thing they still play the games!

Something interesting to do next would be to figure out the numbers compare for each month, or even from the beginning of the season until the slump started.  Did the slump drag down their numbers?  There may not be enough results in the pool to get reliable numbers, but it would still be fun to see nonetheless.

I’m not new to MySQL databases or SQL queries, but the existence of a free baseball database was news to me, so I downloaded and imported the beast.  It’s quite an interesting blob of data and you can use it to analyize and discover tidbits about your favorite teams and players. 

I wanted to find out how payroll and team wins are related, specifically from this past year.  I was messing around with the database, and came up with a query for data that is probably easy to find out and already analyzed on lots of other websites. But where is the fun in that?  So I created a query that would take the sum of all players’ salaries on each team, and then divide it by the number of wins that team had.  A simple calculation, but a little more wordy when written out as a query:

SELECT t.teamID, t.W, t.L, (t.W/t.G) as wpct,
 sum(s.salary) as payroll,
 sum(s.salary)/t.W as dpw
FROM Teams t, Salaries s
WHERE t.teamID = s.teamID
 AND t.yearID = s.yearID
 AND s.yearID = 2008
GROUP BY s.teamID
ORDER BY dpw DESC 

I won’t go into detail on what each line of the query does, because you can find that out elsewhere if you are interested.  It query outputs the wins, losses, win percent, payroll and dollars per win that the team spent for 2008.  Here are the results, with dollars in millions:

teamID
W
L
wpct
payroll
dpw


NYA
89
73
0.5494
207.9
2.336


SEA
61
101
0.3765
117.7
1.929


DET
74
88
0.4568
137.7
1.861


NYN
89
73
0.5494
137.8
1.548


ATL
72
90
0.4444
102.4
1.422


LAN
84
78
0.5185
118.6
1.412


BOS
95
67
0.5864
133.4
1.404


CHA
89
74
0.5460
121.2
1.362


CHN
97
64
0.6025
118.3
1.220


LAA
100
62
0.6173
119.2
1.192


SDN
63
99
0.3889
73.7
1.169


SLN
86
76
0.5309
99.6
1.158


TOR
86
76
0.5309
97.8
1.137


SFN
72
90
0.4444
76.6
1.064


PHI
92
70
0.5679
97.9
1.064


HOU
86
75
0.5342
88.9
1.034


CIN
74
88
0.4568
74.1
1.002


BAL
68
93
0.4224
67.2
0.988


CLE
81
81
0.5000
79.0
0.975


WAS
59
102
0.3665
55.0
0.932


COL
74
88
0.4568
68.7
0.928


MIL
90
72
0.5556
80.9
0.899


TEX
79
83
0.4877
67.7
0.857


ARI
82
80
0.5062
66.2
0.807


KCA
75
87
0.4630
58.2
0.777


PIT
67
95
0.4136
48.7
0.727


MIN
88
75
0.5399
56.9
0.647


OAK
75
86
0.4658
48.0
0.640


TBA
97
65
0.5988
43.8
0.452


FLO
84
77
0.5217
21.8
0.260

What does this tell us?  I’ve highlighted the teams that made it into the postseason. Most of them were in the top half and around 1.2-1.4 million per win. 

There are two reasons you could have a high dpw:

1) High Payroll.  The more you pay, the more each win will cost you.
2) Low Wins. The less you win, the more those you do win will have cost you.

Let’s look at a few teams.

The Yankees with the highest per-win value (2.336m) had a tough year but came out six wins short of tying Boston for the wild card (assuming those wins didn’t come from Boston).  That number of wins would have lowered their dpw to about 2.2m.  Either way, their strategy, for the most part, is to pay for veterans who have proved themselves to be among the best in the game.  This year, it didn’t work out for them.

The Tampa Bay Rays, on the other hand, made the most out of a low payroll by taking their 452k per win to a World Series berth.  I imagine that their dollars-per-win will go up over the next few years as their young stars start to get into the mature part of their contracts, though I haven’t researched that.  Also, perhaps the higher revenue from an excited fanbase translates into more money for free agents.

Seattle has the second highest dpw value with their 118m payrool and only 61 wins.   Even though the Yankees have the highest dpw, I think the Mariners are the most offensive (as in offending, not in run production) team this year.  They are in a smaller market and have less revenue coming in than the Yankees do and the losing record and current roster makes me think that they are a lot of big changes away from being competetive.

The Oakland Athletics are pretty low on the dollars-per-win chart with a sub-.500 year that threatenend for awhile to be a winning year.  They are adding payroll this year and should pick up more wins, though I still expect them to be near the lower quarter of this graph next year. 

So what does dollars-per-win tell us?  Is payroll releated to team wins?  Yes, but not always.  A team like the Yankees can be successful year after year by throwing money at the best players, but that will not guarantee them a 100 win season each time.  They can do that though because they are in a large market and can count on the revenue coming in to make up for the higher cost.  Smaller market teams need to be smarter and more efficient with their payroll in order to compete for a playoff spot on a yearly basis since they don’t have the same kind of revenues.

I don’t think there is anything wrong with having a high dollars-per-win ratio. I think it depends on how you’re getting it.  If the team isn’t making it to the postseason (or getting close to it) then the players they are paying for are probably not worth what they are earning.  I think dollars-per-win could be considered an effiency thing, i.e, what is the team doing with the money they are paying out.  In the end (competetivly), nothing matters more than a World Series but you’ll never get there without the wins, so wins become important.   And in the end (business-wise) you just want to make money, and wins will keep people coming to the park.

Where to go from here?  First, I should take a look at previous years and see what the patterns are.  Do most teams come from the top, or is there always a team or two that comes from the depths?

It would be interesting to look at the similar calculation of net revenue-per-win, but I don’t know where to get those numbers.  The results would take into account their market and attendance and put it up against wins.  Teams that have a higher attendance dispite a poor team would probably rate well.  Maybe net revenue-per-win would mean more for the bean counters than the stat heads.

Am I assuming too much with dollars-per-win?  Have I made any mistakes?  Any other thoughts?