Long story short: you should make aging all star for prospect trades at the start of the season, instead of at the trade deadline, if you're at least 70% sure, before the season starts, that the team getting the aging all star will be in playoff contention and that the other team will not.
In Major League Baseball, teams are not allowed (or, in some cases, just significantly hindered) in making trades after the July 31st trade deadline. This left me wondering: in what cases does it make sense to wait until the trade deadline to make trades, and when does it make sense to do it at the start of the year?
Put another way, it's been about ten years since the Seattle Mariners were in playoff contention, and about twenty years since the Yankees weren't--the fact that this is also true this year shouldn't surprise anyone. So why didn't the Mariners trade Ichiro to the Yankees at the beginning of the year?
Most trade deadline trades, like the one involving Ichiro Suzuki, involve a team in playoff contention trading some future prospects and/or money to a team not in contention in return for an (often aging) borderline all-star level player. The advantage of making this trade at the beginning of the year, instead of waiting until halfway through for the trade deadline, is that the team in contention gets the good player for longer and thus the player has more utility for them; the disadvantage is that you might accidentally trade away a good player and then find yourself in playoff contention, or vice versa.
The first thing I investigated was the following: how much does gaining an Ichiro-like player help in the regular season, and how much does it help in the post season? Here were the assumptions I made.
1) All that matters is maximizing chances of winning the world series.
2) The player will add roughly 3 wins to the team (i.e. have a WAR of 3 more than the person they're replacing).
3) The team will be facing teams of equal strength not including the player traded for in the playoffs, and will win with a probability over .500 corresponding to the difference in their inherent winning percentage and their opponents'.
4) The team suspects that they will end up doing something between winning the division by 7 games, and losing by 10 games (roughly the average difference between division leader and second in division in 2011).
The probability of a team winning the world series p_WS = p_PL + p_PLW, the probability of making the playoffs + probability of winning the playoffs.
p_PL will be increased by ~3/20 by making the trade at the beginning of the season, meaning that p_PL will go from 50% to 65%, a proportional increase of .65/.5 = 1.3
To calculate the change in p_PLW, note that they have gained 3/162 ~ .0185 in winning percentage, meaning that they have a 51.85% chance of winning a playoff game (by assumption 3). So, whereas before p_PLW = 12.5%, now p_PLW = 15.6%, a proportional increase of about 1.25.
I had not been expecting this result; I had assumed that the playoffs would be random enough that player quality wouldn't matter as much as it would in the regular season (Because there are more games). But it seams that, in fact, a good player added to a good team might make about as much of an impact in the playoffs as in the regular season. (Note, however, that if you give yourself some partial victory credit for making the playoffs even if you don't win, that that would argue in the other direction.)
So, what's the upshot of this, as far as the trade deadline is concerned? Without trading you have a 50%*12.5% = 6.25% chance of winning the world series. If you trade at the beginning of the year, you have a .65*.156 = 10.14% chance of winning the world series. And if you make a trade at the trade deadline you get about 1.5 extra regular season wins from the player, so (by the same logic) you have roughly a .575*.156 = 8.98% chance of winning the world series.
So, making a before-season trade increases your probability of winning the world series by about 3.89%, whereas making it right before the trade deadline increases it by about 2.74%.
This means that the advantage of making the trade pre-season is that it's about 3.89/2.74 = 1.42 times as effective. Assuming that you'll be pretty sure by mid season whether you're in a playoff race, the question then becomes: before the season, are you at least 1/1.42 ~ 70% sure that your team will be in a competitive playoff race, and the other team won't be? In another post, I'll look at this question.