The Cost of Moving from the NL to the AL

“The Astros sale so far has none of the drama that came with the Rangers last year.” That’s from an Associated Press story written in mid-May.

Five months later, we have drama. According to the prospective buyer, Houston-based businessman Jim Crane, Major League Baseball is pressuring him to move the Astros from the National League Central to the American League West. Richard Justice and others have reported that there might be other issues preventing MLB from approving the deal.

I’d rather not speculate about what is or isn’t true, but both sides seem to be doing all they can to intimidate the other into acquiescing. Just this week, a flurry of stories came out suggesting that Crane could walk away from the deal if he isn’t approved by the Nov. 30 deadline stipulated in his agreement with Drayton McLane. Meanwhile, MLB continues to dig into Crane’s past, perhaps sending Crane the message that his options are the American League or no team.

But whatever the reasons for the hold-up, the bottom line is that if the Astros move from the NL Central to the AL West, the team should receive some compensation. In addition to the concerns that Crane has expressed — more 9 p.m. start times and the addition of a designated hitter to the payroll — the real issue is that the American league is the stronger league. And switching leagues will have a direct effect on the Astros’ win total.

A couple weeks ago, Tom Tango was discussing this issue on his blog. In his opinion, the fairest way to determine who moves is to employ what he calls the “You cut the pie, I choose the slice” method. Essentially, one side, the “cutter,” divides the pie, while the other, “the chooser,” picks which division he prefers. In the case of moving divisions, each NL team would put an amount of money in to a pot; if a team thinks the pot is worth switching leagues, that team can take the money and move to the AL. If no team is willing to switch leagues, the pot keeps increasing until a team is willing to move.

That idea got me thinking. How much is membership in the NL worth? To get closer to an answer, we first need to determine the relative strength of the two leagues.

Since 2004, the Junior Circuit has gotten the best of its senior brethren in interleague play.

*Click for a clearer view.

The National League has gotten closer to .500 in the past two years, but a look at the league’s Pythagorean winning percentage (generated by looking at runs scored and runs allowed) suggests that the disparity between leagues was greater this year than in 2010.

In fact, weighting the 2009 Pythag record by 3, the 2010 Pythag record by 4, the 2011 Pythag record by 5 and dividing by 12 (similar to the distribution between present and past performance in Marcel), we can estimate the American League as generating a .543 winning percentage against the National League. To make things a little easier — and to regress toward a mean of .500 — let’s say we expect the AL to have a .540 winning percentage against the NL.

Using Log5, a probability method Bill James originally applied to determine the outcome of a team winning a matchup given each team’s winning percentage, we can estimate how each league would fare against a .500 team.

The Log5 equation is fairly simple: (P-P*Q)/(P+Q-2*P*Q). (P is the winning percentage of the first team and Q is the winning percentage of the second.)

Because we note that the AL has a winning percentage of .540 in games against the NL, our best estimate is that the AL would have a winning percentage of .520 against a .500 team. The NL would have a .480 winning percentage against a .500 team.

Unfortunately, our work isn’t quite done because we know that a disproportionate amount of the AL’s advantage is derived from the American League East. Complicating things further is that the AL East has performed better against other American League teams — rather than National League teams — in recent years.

*Click for a clearer view

The AL East’s issues won’t complicate things as long as the NL has a winning record against the AL West and AL Central. If that were the case, we could conclude that the American League’s advantage is due entirely to the eastern division — and we would estimate the AL West and AL Central as having winning percentages below the .480 we determined the National League had. But that isn’t what we observe. Instead, the AL West and AL Central have played well-above .500 ball against the NL.

*Click for a clearer view.

Using the same weighting scale discussed above, here’s how the groups fared when facing one another:

To get a true estimate of the winning percentage for each AL group against a .500 team, we’ll need to apply some intuition. We already know the NL has a .480 winning percentage against the AL — that’s our baseline. Because the sample size of the American League West and the AL Central is larger, I’m inclined to give more weight to those data. Furthermore, as the AL East graph shows, the performance of the East against the NL in 2010 seems to be a pretty significant outlier given past performance. With all that information, I decided to weight the AL East as a “true” .561 (.561 against a .500 team or in a .500 league), the AL West and AL Central divisions as a true .497 and the NL still as a true .480.

While those numbers might be slightly generous to the teams in the AL East, I think they’re a good estimate given the data we have. The numbers match our already determined .520 value for the AL and .480 for the NL, as under this scenario we observe the NL as having a winning percentage of .460.

With these numbers in hand, we can transform observed Pythagorean records in the NL to expected Pythagorean records in the AL West by using Log5 and some algebra.

Rearranging Log5, we find that a team’s winning percentage against a .500 team = (O*S)/(1-S-O+(2*S*O)).

I’ll refer to this winning percentage as the winning percentage in a neutral league. O is observed winning percentage and S is the strength of schedule against which the winning percentage was achieved. Using this formula, a team that is observed to be .500 playing an NL schedule is determined to have a winning percentage of .484 against a league of .500 teams (the reason that it’s not .480 is that the NL schedule includes 18 interleague games).

We need to make one more addition. If we were to estimate the Phillies’ neutral Pythag, we can’t assume that Philadelphia plays against a league of .480 competition. Without the Phillies, the NL is decidedly worse. I’m hoping someone has a better way of accounting for this, but I tried to overcome the problem by adding what I call a “modifier”. For each team, I looked at the leagues’ total runs scored and run allowed with and without them. Then I compared the Pythagorean winning percentage in both cases. I took the percentage difference and multiplied it by the league the team played in. The Phils’ modifier was 98.2%, so instead of playing against .480 competition, I counted Philadelphia as playing against a league with a .471 winning percentage.

Once we have a league-neutral winning percentage for each team, we can run that winning percentage through an AL West schedule to get an estimate of each team’s Pythagorean win total in the AL West.

*Click to see (I think the discrepancy between the D-backs and Cards is due to some rounding in the Pythagorean totals and possibly the modifier).

From the table above, we see that had the Astros played the 2011 season in the AL West — instead of the NL — we would have expected the ‘Stros to lose an additional 2.8 games. The Astros weren’t likely competing for a playoff spot this year, so losing three wins isn’t necessarily a game changer. But it’s certainly not meaningless, either.

On the other end of the spectrum, the Phillies would have won 4.9 fewer games playing this season in the AL West; the equivalent of staying in the NL but telling Cole Hamels not to show up for the regular season.

But as October reminds us, real value and the goal of every organization revolves around making the playoffs and taking a run at winning the World Series. In the next post, we’ll take a look at how each team’s playoff probability would be impacted by moving from the NL to the AL West. We’ll also try to put a dollar figure on the cost of switching, play around with what a move the the AL East would cost a team and talk a little Game Theory.