Wednesday, March 29, 2006
Review: The Book - simply awesome
The Book: Playing the Percentages in Baseball, is arguably the most important sabermetric publication since the Hidden Game of Baseball over two decades ago. Hyperbole, you might say. Maybe, but consider that the authors – Tom Tango (Tangotiger), Mitchel Lichtman and Andy Dolphin – are probably three of the finest sabermetricians on the planet, and you can begin to understand why I am so excited! Moreover, this book has been two agonizing years in the making.
Baseball is a simple game: win games by outscoring your opponents. And you don’t need to watch too much baseball to know that managers will do pretty much anything to eek out that vital victory. That’s because the manager’s job is to make decisions and trade-offs that maximize the win (or run) potential at every possible juncture.
But are they actually making the right decisions? This is where The Book comes in. Using a variety of statistical techniques, and a truck load of data, the authors set out to debate some of the many myths which managers swear black and blue by. These debates are played out are across a variety of chapters:
Buy the book at http://www.insidethebook.com
Baseball is a simple game: win games by outscoring your opponents. And you don’t need to watch too much baseball to know that managers will do pretty much anything to eek out that vital victory. That’s because the manager’s job is to make decisions and trade-offs that maximize the win (or run) potential at every possible juncture.
But are they actually making the right decisions? This is where The Book comes in. Using a variety of statistical techniques, and a truck load of data, the authors set out to debate some of the many myths which managers swear black and blue by. These debates are played out are across a variety of chapters:
- Batting and pitching streaks
- Batter / pitcher match-ups
- Clutch hitting
- Batting order
- Platooning
- Starting pitchers
- Relief pitchers
- Sacrifice batting
- Intentional walking
- Base running
- Game theory (responding to your opponent’s actions)
Ok, I know what you are thinking. Many of these topics have been discussed before, so what is different about Tango, Lichtman and Dolphin’s approach? Well, amazingly our pen-toting trio manage to break new ground on pretty much every subject. Part of the joy of reading The Book is the feeling of discovering and learning alongside the authors, so I don’t want to give too much away, but here are a few tasty morsels:
- Sacrifice bunting can make sense in certain situations
- Disruptive running has an enormous negative influence on batting
- Pinch hitting for non-pitchers rarely pays off
And the learning continues across all the debates. The conclusions are summarized in a box entitled “The Book says”, which contain the pithy takeaways that you’d do well to remember and reflect on when you are watching your next game.
Some reviews I have read commented that The Book is quite technical in nature. I disagree. Sure, you have to have an aptitude for learning, but the writing is so lucid and exact that a layman with a bit of time on his hands is perfectly capable of picking up the main points.
Another huge plus is the inclusion of a “Toolshed” chapter, as well as a detailed appendix on some of the statistical techniques used. In fact, reading through these sections was such an edifying experience that I have found that I consistently returned to many of the ideas to reaffirm my own thinking on the methods used. Topics such as regression to the mean and markov chains are explained succinctly yet with clarity that a book like this so often lacks.
The only slightly negative comment I can make is that some of the studies with small sample sizes seem slightly out of place with the overall ethos of the book, and here the authors struggle to establish firm conclusions while still persisting to dive deep into the data. Still, even these analyses are a joy to pore over and reinforce the central concept about drawing accurate conclusions from data.
In summary, if you are reading this review then buy The Book. To hear the opinions of three of the most respected sabermetricians in baseball is a joy and a privilege. It sets a standard of work for others to aspire to, and I can only hope that volume 2 isn’t another two years in the making.
Buy the book at http://www.insidethebook.com
Sunday, March 26, 2006
Comments on line drives
I thought I'd post some comments on my line drive article last month which appeared on BTF. Based on this feedback I'm going to take another look at line drive using a regression from the mean technique, which is similar to that outlined in Tango et al's book.
http://www.baseballthinkfactory.org/files/numbers/discussion/36553/
I'd like to thank the guys at BTF for linking to my article. I'm in the process of adding links to this site and I'll definitely be adding theirs - it is an invaluable resource for all sabermetricians
http://www.baseballthinkfactory.org/files/numbers/discussion/36553/
I'd like to thank the guys at BTF for linking to my article. I'm in the process of adding links to this site and I'll definitely be adding theirs - it is an invaluable resource for all sabermetricians
Atlanta Braves: worth $400m?
Come on, admit it. We have all fantasized about being in charge of our favorite baseball team. Every year when we pick a fantasy team we ponder what life might be like as the General Manager of a ball club, resolving dilemmas like: deciding between A-Rod and Pujols, trading-off pitching and hitting, desperately trying to fill that last roster slot with the best sub-par hitter, wheeling and dealing the middle order, and picking up a rookie on waivers who (hopefully!) goes on to spank 30 homers, but probably doesn't. Even better, what about being an owner? Well, my team, the Atlanta Braves, is up for sale and I'd love to buy them. So how much will it cost?
Ultimately a baseball club is a business, just like any other company, and therefore we can value it using similar techniques. The method I'm going to introduce is called Discount Cash Flow (DCF) analysis. Don't be put off by the name, although investment bankers are paid hundreds of thousands of dollars to perfect DCF we will use it in its simplest form.
DCF values a business or investment by calculating the present value of all future cash flows. What does this mean? Suppose that I sell you a product, eg, a financial option, which can be sold this time next year for $100. How much would you pay for it today? $100? Well, no - our trusty friend from the 1970s called inflation means that $100 today is worth less this time next year. If inflation is 5%, $100 next year is worth $95 today. Therefore the maximum that you'd pay in this instance is $95 - less if you wanted to make a profit.
A business is similar except rather than generating a single payment it spits out cash year after year. If we know how much money our business generates in all future years, and also what the inflation rate is for each year, we can work out the maximum that we would pay for it. Ok, so much for the theory, lets see how it works in practice. We need to work out what the present value of all those future cash flows are. A good starting point is to work out what the current year cash flow is. To do this we need to know revenues and costs. Revenue minus cost equals profit and, for this purpose, cash. Technical note: this excludes capital expenditure (adjusting for depreciation / amortization) and changes in working capital. This is not necessary for a high level exercise like this but is academically accurate if we were doing a full valuation.
For a public company, one listed on the stock exchange for instance, annual reports give us all the information we need. However, ball clubs are intensely private companies which are loathe to reveal even a smatter of their financials. One approach is to ballpark (excuse the pun) estimate cash flow. We simply list all the revenues and costs and try to work out the size of each. Let's give this a go for revenue.
Revenues include: tickets, concessions, car parking, advertising, TV / radio rights, mechandising to name a few - I'm sure you can probably list many more. For the time being lets consider the first three. The Braves' attendance in 2005 was 2.6m. Estimating the average ticket price at $20 gives $52m sales from tickets. Adding in concessions - say a beer and a hotdog per person (total $10) - gives an extra $26m. Car parking? The Braves have 10,000 spaces. So lets say that 80% are filled up on average for each game. At $10 per car that is another $8m per game. Just from gamedays we have $88m. We could continue to go through this exercise and work out all other revenue sources - though we'd struggle a little with television revenue given that AOL are the current owners. Luckily Forbes produces an annual estimate of revenue for us. The last available data is 2004 where revenue was estimated at $162m. Given our initial gameday estimate of $88m, $162m doesn't seem too crazy. Actually you could argue that it is a little on the low-side given the intricacies of the TV contract (basically the Braves sell its TV rights at below fair value to inflate AOL's profit and reduce the Braves' - it is a complex subject that almost deserves of an article in its own right if it wasn't such a dull subject). For simplicity lets put a range on revenue of $160m-$180m - that seems about fair.
Ok, now on to costs which primarily consist of player and staff salaries, but also include general operational expenditure and minor league affiliates amongst others. This is easier to do - salaries are reported and fixed costs of running a ball club are easy to estimate. Again, for simplicity we'll take Forbes' figure of $146m. Lets do a quick sense check: payroll is about $90m leaving $50m for other costs - seems about right (I'm happy to trust Forbes as I haven't got the time to work it out).
Going back to our earlier equation we estimate cash flow (revenue minus costs) at approximately $15m-$35m.
This is just for one year, what we need to do is to project this over all future years. Sounds tricky, right? Well here we can cheat a bit. Given that we are only looking for a ballpark estimate we can use a perpetuity valuation technique. This means that we will base future cash flows on current year cash and a constant future growth rate. The formula relies only on three inputs: annual cash flow (calculated above), the rate at which to discount future cash flow and the growth rate in annual cash flow.
The discount rate should reflect two things: general inflation and riskiness of investment - the higher the risk the more we want to discount cash flows far out in the future as there is less certainty over them. Baseball is a stable industry so is reasonably risk free. A discount rate of about 10% is probably about right. Now what about growth? Again, given the many approximations in this analysis we can be reasonably rough and ready here. We'll assume that ticket prices increase in-line with inflation: say 3%.
The formula for perpetuity value is:
cashflow x (1 + growth rate)
discount rate - growth rate
Now we are in a position to work out how much to pay for the Braves. Plugging in the numbers we get a range from $225m to $530m - which is a wide margin (it goes to show you need to make sure your assumptions are as accurate as possible at the outset). How does that number compare to what other people are saying? The Forbes value is $380m, which is pretty much bang in the middle of where we are. Moreover, investment analysts expect a winning bid for the Braves to be in the region of $400m-$450m.
Back to my original question: how much would I pay for the Braves? Well, unlike a normal business, baseball is a uniquee industry with a number of factors which conspire to push up value. Firstly, it is an effective monopoly which is obviously a bonus for any business (witness the fight put up by the Orioles when the Expos relocated). Secondly, baseball inspires passion and loyalty. People are prepared to pay way over the odds for this which skews even the most rigorous analysis. So based on the above, the general price of recent ball club transactions, and the fact that the Braves is a very well run organization, I'd say that a value in the region of $400m is fair. In fact, if I had that sort of money burning a hole in my pocket I'd be sitting with my feet up, smoking a cigar, watching my mighty Braves winning the world series. Unfortunately I can only but dream!
Ultimately a baseball club is a business, just like any other company, and therefore we can value it using similar techniques. The method I'm going to introduce is called Discount Cash Flow (DCF) analysis. Don't be put off by the name, although investment bankers are paid hundreds of thousands of dollars to perfect DCF we will use it in its simplest form.
DCF values a business or investment by calculating the present value of all future cash flows. What does this mean? Suppose that I sell you a product, eg, a financial option, which can be sold this time next year for $100. How much would you pay for it today? $100? Well, no - our trusty friend from the 1970s called inflation means that $100 today is worth less this time next year. If inflation is 5%, $100 next year is worth $95 today. Therefore the maximum that you'd pay in this instance is $95 - less if you wanted to make a profit.
A business is similar except rather than generating a single payment it spits out cash year after year. If we know how much money our business generates in all future years, and also what the inflation rate is for each year, we can work out the maximum that we would pay for it. Ok, so much for the theory, lets see how it works in practice. We need to work out what the present value of all those future cash flows are. A good starting point is to work out what the current year cash flow is. To do this we need to know revenues and costs. Revenue minus cost equals profit and, for this purpose, cash. Technical note: this excludes capital expenditure (adjusting for depreciation / amortization) and changes in working capital. This is not necessary for a high level exercise like this but is academically accurate if we were doing a full valuation.
For a public company, one listed on the stock exchange for instance, annual reports give us all the information we need. However, ball clubs are intensely private companies which are loathe to reveal even a smatter of their financials. One approach is to ballpark (excuse the pun) estimate cash flow. We simply list all the revenues and costs and try to work out the size of each. Let's give this a go for revenue.
Revenues include: tickets, concessions, car parking, advertising, TV / radio rights, mechandising to name a few - I'm sure you can probably list many more. For the time being lets consider the first three. The Braves' attendance in 2005 was 2.6m. Estimating the average ticket price at $20 gives $52m sales from tickets. Adding in concessions - say a beer and a hotdog per person (total $10) - gives an extra $26m. Car parking? The Braves have 10,000 spaces. So lets say that 80% are filled up on average for each game. At $10 per car that is another $8m per game. Just from gamedays we have $88m. We could continue to go through this exercise and work out all other revenue sources - though we'd struggle a little with television revenue given that AOL are the current owners. Luckily Forbes produces an annual estimate of revenue for us. The last available data is 2004 where revenue was estimated at $162m. Given our initial gameday estimate of $88m, $162m doesn't seem too crazy. Actually you could argue that it is a little on the low-side given the intricacies of the TV contract (basically the Braves sell its TV rights at below fair value to inflate AOL's profit and reduce the Braves' - it is a complex subject that almost deserves of an article in its own right if it wasn't such a dull subject). For simplicity lets put a range on revenue of $160m-$180m - that seems about fair.
Ok, now on to costs which primarily consist of player and staff salaries, but also include general operational expenditure and minor league affiliates amongst others. This is easier to do - salaries are reported and fixed costs of running a ball club are easy to estimate. Again, for simplicity we'll take Forbes' figure of $146m. Lets do a quick sense check: payroll is about $90m leaving $50m for other costs - seems about right (I'm happy to trust Forbes as I haven't got the time to work it out).
Going back to our earlier equation we estimate cash flow (revenue minus costs) at approximately $15m-$35m.
This is just for one year, what we need to do is to project this over all future years. Sounds tricky, right? Well here we can cheat a bit. Given that we are only looking for a ballpark estimate we can use a perpetuity valuation technique. This means that we will base future cash flows on current year cash and a constant future growth rate. The formula relies only on three inputs: annual cash flow (calculated above), the rate at which to discount future cash flow and the growth rate in annual cash flow.
The discount rate should reflect two things: general inflation and riskiness of investment - the higher the risk the more we want to discount cash flows far out in the future as there is less certainty over them. Baseball is a stable industry so is reasonably risk free. A discount rate of about 10% is probably about right. Now what about growth? Again, given the many approximations in this analysis we can be reasonably rough and ready here. We'll assume that ticket prices increase in-line with inflation: say 3%.
The formula for perpetuity value is:
cashflow x (1 + growth rate)
discount rate - growth rate
Now we are in a position to work out how much to pay for the Braves. Plugging in the numbers we get a range from $225m to $530m - which is a wide margin (it goes to show you need to make sure your assumptions are as accurate as possible at the outset). How does that number compare to what other people are saying? The Forbes value is $380m, which is pretty much bang in the middle of where we are. Moreover, investment analysts expect a winning bid for the Braves to be in the region of $400m-$450m.
Back to my original question: how much would I pay for the Braves? Well, unlike a normal business, baseball is a uniquee industry with a number of factors which conspire to push up value. Firstly, it is an effective monopoly which is obviously a bonus for any business (witness the fight put up by the Orioles when the Expos relocated). Secondly, baseball inspires passion and loyalty. People are prepared to pay way over the odds for this which skews even the most rigorous analysis. So based on the above, the general price of recent ball club transactions, and the fact that the Braves is a very well run organization, I'd say that a value in the region of $400m is fair. In fact, if I had that sort of money burning a hole in my pocket I'd be sitting with my feet up, smoking a cigar, watching my mighty Braves winning the world series. Unfortunately I can only but dream!
Bonds to sue
So Barry Bonds is suing the authors of the book (Game of Shadows) which, for those of you who have been comatosed for the last couple of weeks, alleges that he took steroids for breakfast, lunch and dinner.
I don't know what form the legal action will take. Speculation is that it will focus on how the authors gathered evidence and not on the content of the book. That is a shame. The allegations, if true, make a sham of Bonds' career. If the action is against the content then I hope he wins; for the sake of baseball Bonds needs to be clean. But the evidence looks damming. Fortunately Barry can probably afford a half-decent lawyer - he'll need it.
I don't know what form the legal action will take. Speculation is that it will focus on how the authors gathered evidence and not on the content of the book. That is a shame. The allegations, if true, make a sham of Bonds' career. If the action is against the content then I hope he wins; for the sake of baseball Bonds needs to be clean. But the evidence looks damming. Fortunately Barry can probably afford a half-decent lawyer - he'll need it.
Coming up ....
Firstly, my apologies for the paucity of posts over the last 2 weeks! I have been on vacation in Southern Africa, where it is practically impossible to get a decent internet connection. Anyway, the good news is that I am back in civilization and will be posting on a number of topics over the coming week or two.
Later today I hope to post an article on how much I'd pay for the Atlanta Braves - yes, this is the same piece I promised when I started this blog some 2 months ago! Shortly after I'll post my review of Tango's, MGL's and Dolphin's book, called The Book. Also not forgetting my season preview which will hopefully be ready before the season starts.
Happy reading and thanks for your support
Later today I hope to post an article on how much I'd pay for the Atlanta Braves - yes, this is the same piece I promised when I started this blog some 2 months ago! Shortly after I'll post my review of Tango's, MGL's and Dolphin's book, called The Book. Also not forgetting my season preview which will hopefully be ready before the season starts.
Happy reading and thanks for your support
Monday, March 06, 2006
Do K pictchers give up more fly balls?
I was struck by something a poster said on the scout message board: " (1) how many extra HR did the pitcher allow because as a strikeout pitcher because he pitches up in the zone and therefore allows more FB, and (2) how many extra walks does this pitcher allow?".
So the question is does a dominant strikeout pitcher give up more flyballs that the average pitcher?
OK this shouldn't be too difficult to answer. Firstly what I did was to analyse pbp data for all pitchers who recorded more than 50 BIP. Here is the plot of K9 against fly ball percentage (includes outfield flies and pop-ups):
Pretty conclusive. Rsq is only 0.03, indicating that there is no relationship between the variables - though you don't need regression to work that out. OK, what about the second assertion: "how many extra walks were allowed [by a high strikout pitcher]?". Again here is the data:
Given the first correlation no surprise again. The conclusion? Just because you are a strikeout pitcher it doesn't mean that you either (a) sacrifice control or (b) give up more fly balls. This makes sense: who accuses Johan Santana of lacking control or Roger Clemens being a fly ball picther. No-one.
So the question is does a dominant strikeout pitcher give up more flyballs that the average pitcher?
OK this shouldn't be too difficult to answer. Firstly what I did was to analyse pbp data for all pitchers who recorded more than 50 BIP. Here is the plot of K9 against fly ball percentage (includes outfield flies and pop-ups):
Pretty conclusive. Rsq is only 0.03, indicating that there is no relationship between the variables - though you don't need regression to work that out. OK, what about the second assertion: "how many extra walks were allowed [by a high strikout pitcher]?". Again here is the data:Given the first correlation no surprise again. The conclusion? Just because you are a strikeout pitcher it doesn't mean that you either (a) sacrifice control or (b) give up more fly balls. This makes sense: who accuses Johan Santana of lacking control or Roger Clemens being a fly ball picther. No-one.