THE BOOK--Playing The Percentages In Baseball

Very nice.

Even though the team gets a heavy discount, and I do understand the math behind that, I never consider this type of deal a poor decision by a player, especially a pitcher.

That was a fun read.

I agree with JD on the quality of this decision on Moore’s part. I can understand where someone’s marginal utility for dollars would diminish a lot after the first $10m were in the bank. I’m not saying is has to look like that, but I think its pretty sensible to have it look like that.

If my son was offered Moore’s deal, I’d tell him “Your dad was a happy guy and he made less than $100k a year most of his life. So the real question is, will you be happy playing baseball?”

M: One last thing, what happens if I don’t sign?

F: Durham is a beautiful city, you’re gonna love it.

These are not the arbitration years you’re looking for. *waves hand slowly*

I couldn’t believe Tampa would pay that kind of money over that period of time for an unproven pitcher when I first heard of this. Now that I’ve read this, it makes perfect sense, for both sides.

Thanks.

Interesting read. What’s missing from Moore’s point of view is the possibility of additional salary inflation. Sure, today a star first-year arb-eligible pitcher may get $3.5-$4M, but in 3 years he might get $5M. A free agent star may command $30-$35M by the time Moore becomes free agent eligible, maybe more.

By giving a discount to current salary ranges, but being paid in the future, Moore is also giving up the time value of money over that period. Now since current bond yields are quite low (under 1% for 5 year treasuries, and barely over 2% for 10 years) using a risk-free rate to compute the time value won’t change things that much. But if rates rise, or if baseball experiences much larger wage inflation, then Moore could be giving the Rays an even bigger discount than Tango explains.

If you compare arb awards over the last 10 years, I doubt you see much difference, certainly it didn’t keep pace with free agent prices.

That’s because of the way the arb system is setup. There’s a drag aspect to it.  There’s no inflationary aspect to it.

I think there’s a problem with the way the options were valued.  The calculation applies a discount rate which is implicitly based on the probability that Moore with be an ace in the option year and then values the option (relative to a guaranteed contract) based on an exercise probability very different from the one used to discount the option.

Let’s look at those 3 years instead using a single discount rate.  To keep the modeling simple, I’m going to treat Moore as having three true outcomes:  Not on the 25 man roster, barely worth the option price, or an ace worth the example numbers in the original post.  Then we can figure out what probability of being an ace is required to make the option prices fair.  It doesn’t much matter how often he is in each of the other two outcomes (or in between them if we were doing a continuous model) since in either case, he will be paid market price, perhaps plus the option premium.

In year 6, he pockets $1m for an option which will cost him $7m in salary if he’s an ace.  That makes the option a good deal for Moore only if he will be an ace 1/7 of the time or less.

In years 7 and 8, he pockets $2m each year for an option which will cost him $14.5m/year in salary if he’s an ace (averaging the $20m and $25m numbers above).  Again, if he’s an ace more than about 1/7 of the time (ok, ok, 1/7.25), this is a bad deal for him.

I understand why especially in his first contract a player might give a big discount to lock in guaranteed future salary (which he might or might not be playing well enough to earn), but the math on team options is very different, so if I were a player, I would be very reluctant to agree to one at much less than the fair rate.

With $9m guaranteed, the option deal is no longer a question of eliminating the risk of poverty if he blows his arm out in spring training.  It’s a gamble on whether he becomes an ace.  If he thinks the fair odds on that bet are a lot better than 1 in 7 why let the team hold the bet instead of him.

The pricing of the options is the key.  One would think that a player can get the security he needs by signing away all his years without team options, but Longoria and Moore argue otherwise.

In my fake dialogue, I’m suggesting Moore could have gotten an 8 year, 31MM$ guaranteed deal.  Moore is saying he prefers 14MM$ guaranteed, with a chance at 37MM$ instead.

What he is saying is that 9MM$ guaranteed, and then rolling the dice, is not good enough for him.  His minimum level of lifetime security is 14MM$.

I guess that I’m finding the preferences expressed in [9] unlikely.  The discount on expected value that he’s offering on the options is much higher than the discount on expected value that he’s offering on years 4 and 5, in spite of the fact that in years 4 and 5, he’s facing the risk of having very limited savings if he gets injured, while in years 6-8 he’s risking the difference between 9 and 14 million guaranteed.

Rephrasing [10]:  by not taking the $31m guaranteed for 8 years that [9] suggests was his alternative, he’s implicitly saying that he believes that the probability that the options will be exercised is very high, but if he believes that the probability of exercise is that high, he would need to have preferences that I find odd to offer those options at all.

I can understand why someone might be risk averse and take the guaranteed $31m, and I can understand why someone might roll the dice on a free agency payoff, but unless he has something in mind which costs exactly $14m, underpriced team options seem like the worst of both worlds.

I’m not suggesting that Moore has priced his options properly.  I’m just trying to explain how he could have come to the deal he did.

He obviously did not even consider the possibility that he could pull a Lincecum either.  I mean, there must be, what, a 10% chance that he can get a Cy Young before he hits arbitration (about 30:1 each year for 3 years)?

In any case, now that I’ve laid out a process, I’d like to see how much the Straight Arrow readers think he should have gotten.  Let’s see you price each year, and, if you can, back it up with some research.

There is another possibility. The Rays could have played hardball and not given him the opportunity to sign for the guarantee without the option years. The dialogue would have been something like this;

F: We’ll give you $14m guaranteed with the option years or else we play it out and you get to try and stay healthy for three years before you get your first big payday.

M: $14m? Sound great. Where do I sign.

rw: anything is possible, but I doubt it.  It’s ridiculous to think that a GM is going to say: sign for 8 years or for 1: your choice.

There’s a price point for everything.  If the player says “how about 5”, the GM will give him a price for that.