Run differential and roulette winning numbers

The Indians are clinging to a +1 win differential (33-32), good for second place in the AL Central and making them one of 8 teams in the AL above .500. Despite their positive record, the Indians have an abysmal -40 run differential, putting them ahead of only the Twins (eek) in the American League.

The obvious interpretation fo these two numbers is that the Indians are not as good as their record suggests and are likely to struggle as the season goes on. This is correct in its judgement of what the Tribe has done so far, but it makes a critical assumption about the Tribe going forward--mainly that they are playing at their true talent level. This view also fails to acknowledge an important reality. The luck the Indians have had (largely driven by 1-run victories) is luck that has already been banked in the form of wins. That luck might regress to normal levels, but there is no reason to think the team will suddenly become extremely unlucky and finish the season with an expected record relative to run differential. This is analogous to the list of previous winning numbers typically displayed above a roulette table. A gambler at a casino might view that board, see that a black number has come up in 14 of the previous 20 spins, and think that black is more likely to come up on the next spin. Another gambler might think that a red number is "due" do to the unexpectedly high number of black wins over the previous 20 spins. Neither assumption is correct. Assuming there is no bias in the wheel or ball, the next spin is equally likely to produce a black or red result. With respect to the Tribe, the "luck" the Indians have had thus far has no impact on their expected luck going forward.

The analogy breaks down in that each spin of a roulette wheel is an independent event, whereas the Indians put a very similar set of players on the field each day, and the result of one game is therefore not an independent result with respect to all of the other games they have played.

Viewed this way, however, the interpretation of the run differential and win differential takes on a different tone. The "luck" with respect to wins is already banked, but there is also unpredictable variation with respect to run differential. In other words, there is an implicit assumption in relating run differential to win differential that a team is performing at its true talent level. In other words, while the team may have gotten lucky, players have neither been lucky or unlucky at this point. This is almost certainly not the case, and the decision to be reasonably optimistic or pessimistic going forward depends on how you evaluate the perform of individual players with respect to their "true ability" so far.

The Indians run differential to date is obviously not a positive indicator going forward, but it does represent already realized luck, which is something the Indians should take advantage of. If the Indians front office thinks the Indians have actually underperformed relative to their talent (and I am sure they internally track these things), that "banked luck" is a realized opportunity that gives the Tribe reason to be more aggressive as the season moves forward into the trade season (much like last year).

So, feel free to be optimistic or pessimistic, but base your optimism or pessimism on the right source.